Journal Articles
2025
Silva-Valenzuela, R.; Ortiz-Bernardin, A.; Artioli, E.
A node-based uniform strain virtual element method for elastoplastic solids Journal Article Forthcoming
In: Computational Mechanics, Forthcoming.
Abstract | Links | BibTeX | Tags: elastoplasticity, nodal integration, strain averaging, uniform strain, virtual element method, volumetric locking
@article{svnbuses2024,
title = {A node-based uniform strain virtual element method for elastoplastic solids},
author = {R. Silva-Valenzuela and A. Ortiz-Bernardin and E. Artioli},
url = {https://camlab.cl/wp-content/uploads/2024/12/nvem_elastoplastic_rev1.pdf},
year = {2025},
date = {2025-00-00},
urldate = {2024-00-00},
journal = {Computational Mechanics},
abstract = {A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly-precise virtual elements using a generalization to virtual elements of the node-based uniform strain approach for finite elements. The averaged strain is then used to sample the weak form at the nodes of the mesh leading to a method in which all the field variables, including state and history-dependent variables, are related to the nodes and thus they are tracked only at these locations during the nonlinear computations. Through various elastoplastic benchmark problems, we demonstrate that the NVEM is locking-free while enabling linearly-precise virtual elements to solve elastoplastic solids with accuracy.},
keywords = {elastoplasticity, nodal integration, strain averaging, uniform strain, virtual element method, volumetric locking},
pubstate = {forthcoming},
tppubtype = {article}
}
A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly-precise virtual elements using a generalization to virtual elements of the node-based uniform strain approach for finite elements. The averaged strain is then used to sample the weak form at the nodes of the mesh leading to a method in which all the field variables, including state and history-dependent variables, are related to the nodes and thus they are tracked only at these locations during the nonlinear computations. Through various elastoplastic benchmark problems, we demonstrate that the NVEM is locking-free while enabling linearly-precise virtual elements to solve elastoplastic solids with accuracy.
2024
Yañez, R.; Silvestre, R.; Roby, M.; Neira, A.; Azar, C.; Madera, S.; Ortiz-Bernardin, A.; Carpes, F. P.; la Fuente, C. De
In: Scientific Reports, vol. 14, pp. 11922, 2024.
Abstract | Links | BibTeX | Tags: Anterior cruciate ligament, Biomechanics, Surgery, Transportal, Transtibial
@article{yfe2024,
title = {Finite element graft stress for anteromedial portal, transtibial, and hybrid transtibial femoral drillings under anterior translation and medial rotation: an exploratory study},
author = {R. Yañez and R. Silvestre and M. Roby and A. Neira and C. Azar and S. Madera and A. Ortiz-Bernardin and F. P. Carpes and C. De la Fuente},
url = {https://camlab.cl/wp-content/uploads/2024/06/FE_graft_stress_for_anteromedial_portal.pdf
},
doi = {10.1038/s41598-024-61061-y},
year = {2024},
date = {2024-05-24},
urldate = {2024-05-24},
journal = {Scientific Reports},
volume = {14},
pages = {11922},
abstract = {Stress concentration on the Anterior Cruciate Ligament Reconstruction (ACLr) for femoral drillings is crucial to understanding failures. Therefore, we described the graft stress for transtibial (TT), the anteromedial portal (AM), and hybrid transtibial (HTT) techniques during the anterior tibial translation and medial knee rotation in a finite element model. A healthy participant with a non-medical record of Anterior Cruciate Ligament rupture with regular sports practice underwent finite element analysis. We modeled TT, HTT, AM drillings, and the ACLr as hyperelastic isotropic material. The maximum Von Mises principal stresses and distributions were obtained from anterior tibial translation and medial rotation. During the anterior tibia translation, the HTT, TT, and AM drilling were 31.5 MPa, 34.6 Mpa, and 35.0 MPa, respectively. During the medial knee rotation, the AM, TT, and HTT drilling were 17.3 MPa, 20.3 Mpa, and 21.6 MPa, respectively. The stress was concentrated at the lateral aspect of ACLr,near the femoral tunnel for all techniques independent of the knee movement. Meanwhile, the AM tunnel concentrates the stress at the medial aspect of the ACLr body under medial rotation. The HTT better constrains the anterior tibia translation than AM and TT drillings, while AM does for medial knee rotation.},
keywords = {Anterior cruciate ligament, Biomechanics, Surgery, Transportal, Transtibial},
pubstate = {published},
tppubtype = {article}
}
Stress concentration on the Anterior Cruciate Ligament Reconstruction (ACLr) for femoral drillings is crucial to understanding failures. Therefore, we described the graft stress for transtibial (TT), the anteromedial portal (AM), and hybrid transtibial (HTT) techniques during the anterior tibial translation and medial knee rotation in a finite element model. A healthy participant with a non-medical record of Anterior Cruciate Ligament rupture with regular sports practice underwent finite element analysis. We modeled TT, HTT, AM drillings, and the ACLr as hyperelastic isotropic material. The maximum Von Mises principal stresses and distributions were obtained from anterior tibial translation and medial rotation. During the anterior tibia translation, the HTT, TT, and AM drilling were 31.5 MPa, 34.6 Mpa, and 35.0 MPa, respectively. During the medial knee rotation, the AM, TT, and HTT drilling were 17.3 MPa, 20.3 Mpa, and 21.6 MPa, respectively. The stress was concentrated at the lateral aspect of ACLr,near the femoral tunnel for all techniques independent of the knee movement. Meanwhile, the AM tunnel concentrates the stress at the medial aspect of the ACLr body under medial rotation. The HTT better constrains the anterior tibia translation than AM and TT drillings, while AM does for medial knee rotation.
2023
Ortiz-Bernardin, A.; Silva-Valenzuela, R.; Salinas-Fernández, S.; Hitschfeld-Kahler, N.; Luza, S.; Rebolledo, B.
A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity Journal Article
In: International Journal for Numerical Methods in Engineering, vol. 124, no. 8, pp. 1818-1855, 2023.
Abstract | Links | BibTeX | Tags: linear elasticity, nodal integration, strain averaging, uniform strain, virtual element method, volumetric locking
@article{obnbus2023,
title = {A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity},
author = {A. Ortiz-Bernardin and R. Silva-Valenzuela and S. Salinas-Fernández and N. Hitschfeld-Kahler and S. Luza and B. Rebolledo},
url = {https://camlab.cl/wp-content/uploads/2024/06/node_based_vem_arxiv_r4.pdf},
doi = {10.1002/nme.7189},
year = {2023},
date = {2023-04-30},
urldate = {2023-04-30},
journal = {International Journal for Numerical Methods in Engineering},
volume = {124},
number = {8},
pages = {1818-1855},
abstract = {We propose a combined nodal integration and virtual element method for compressible and nearly incompressible elasticity, wherein the strain is averaged at the nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements. We refer to the proposed technique as the node-based uniform strain virtual element method (NVEM). No additional degrees of freedom are introduced in this approach, thus resulting in a displacement-based formulation. A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations. Through several benchmark problems in compressible and nearly incompressible elasticity as well as in elastodynamics, we demonstrate that the NVEM is accurate, optimally convergent and devoid of volumetric locking.},
keywords = {linear elasticity, nodal integration, strain averaging, uniform strain, virtual element method, volumetric locking},
pubstate = {published},
tppubtype = {article}
}
We propose a combined nodal integration and virtual element method for compressible and nearly incompressible elasticity, wherein the strain is averaged at the nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements. We refer to the proposed technique as the node-based uniform strain virtual element method (NVEM). No additional degrees of freedom are introduced in this approach, thus resulting in a displacement-based formulation. A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations. Through several benchmark problems in compressible and nearly incompressible elasticity as well as in elastodynamics, we demonstrate that the NVEM is accurate, optimally convergent and devoid of volumetric locking.
2022
Salinas-Fernández, S.; Hitschfeld-Kahler, N.; Ortiz-Bernardin, A.; Si, Hang
POLYLLA: polygonal meshing algorithm based on terminal-edge regions Journal Article
In: Engineering with Computers, vol. 38, no. 5, pp. 4545-4567, 2022.
Abstract | Links | BibTeX | Tags: Delaunay triangulations, polygonal mesh, terminal-edge region, virtual element method
@article{sfpol2022,
title = {POLYLLA: polygonal meshing algorithm based on terminal-edge regions},
author = {S. Salinas-Fernández and N. Hitschfeld-Kahler and A. Ortiz-Bernardin and Hang Si},
url = {https://camlab.cl/wp-content/uploads/2024/06/2201.11925v2.pdf},
doi = {10.1007/s00366-022-01643-4},
year = {2022},
date = {2022-05-03},
urldate = {2022-05-03},
journal = {Engineering with Computers},
volume = {38},
number = {5},
pages = {4545-4567},
abstract = {This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that share them. The algorithm is termed Polylla and is divided into three phases. The first phase consists of labeling each edge of the input triangulation according to its size; the second phase builds polygons (simple or not) from terminal-edges regions using the label system; and the third phase transforms each non simple polygon into simple ones. The final mesh contains polygons with convex and non convex shape. Since Voronoi-based meshes are currently the most used polygonal meshes, we compare some geometric properties of our meshes against constrained Voronoi meshes. Several experiments were run to compare the shape and size of polygons, the number of final mesh points and polygons. For the same input, Polylla meshes contain less polygons than Voronoi meshes and the algorithm is simpler and faster than the algorithm to generate constrained Voronoi meshes. Finally, we have validated Polylla meshes by solving the Laplace equation on an L-shaped domain using the virtual element method (VEM). We show that the numerical performance of the VEM using Polylla meshes and Voronoi meshes is similar.},
keywords = {Delaunay triangulations, polygonal mesh, terminal-edge region, virtual element method},
pubstate = {published},
tppubtype = {article}
}
This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that share them. The algorithm is termed Polylla and is divided into three phases. The first phase consists of labeling each edge of the input triangulation according to its size; the second phase builds polygons (simple or not) from terminal-edges regions using the label system; and the third phase transforms each non simple polygon into simple ones. The final mesh contains polygons with convex and non convex shape. Since Voronoi-based meshes are currently the most used polygonal meshes, we compare some geometric properties of our meshes against constrained Voronoi meshes. Several experiments were run to compare the shape and size of polygons, the number of final mesh points and polygons. For the same input, Polylla meshes contain less polygons than Voronoi meshes and the algorithm is simpler and faster than the algorithm to generate constrained Voronoi meshes. Finally, we have validated Polylla meshes by solving the Laplace equation on an L-shaped domain using the virtual element method (VEM). We show that the numerical performance of the VEM using Polylla meshes and Voronoi meshes is similar.
2020
Bustamante, R.; Montero, S.; Ortiz-Bernardin, A.
A novel nonlinear constitutive model for rock: numerical assessment and benchmarking Journal Article
In: Applications in Engineering Science, vol. 3, pp. 100012, 2020.
Abstract | Links | BibTeX | Tags: Isotropic bodies, Nonlinear elasticity, Small strains and rotations, Stress concentration
@article{bmonncm2020,
title = {A novel nonlinear constitutive model for rock: numerical assessment and benchmarking},
author = {R. Bustamante and S. Montero and A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/nonlinear_constitutive_model_for_rock.pdf},
doi = {10.1016/j.apples.2020.100012},
year = {2020},
date = {2020-09-14},
urldate = {2020-09-14},
journal = {Applications in Engineering Science},
volume = {3},
pages = {100012},
abstract = {In this article, we assess and benchmark a novel nonlinear constitutive relation for modeling the behavior of rock, in which the linearized strain tensor is a function of the Cauchy stress tensor. In stark contrast with the linearized theory of elasticity, the main feature of this novel nonlinear constitutive model is that a different behavior is obtained in compression than in tension, which is consisting with the experimental evidence. Four problems are solved using the finite element method: the compression of a cylinder, the biaxial compression of a slab with a circular hole and with an elliptic hole, and the shear of a slab with an elliptic hole. The results are compared with the predictions of the linearized theory of elasticity. In this comparison, it is found that the maximum stresses and their locations are significantly affected by the choice of the constitutive equation.},
keywords = {Isotropic bodies, Nonlinear elasticity, Small strains and rotations, Stress concentration},
pubstate = {published},
tppubtype = {article}
}
In this article, we assess and benchmark a novel nonlinear constitutive relation for modeling the behavior of rock, in which the linearized strain tensor is a function of the Cauchy stress tensor. In stark contrast with the linearized theory of elasticity, the main feature of this novel nonlinear constitutive model is that a different behavior is obtained in compression than in tension, which is consisting with the experimental evidence. Four problems are solved using the finite element method: the compression of a cylinder, the biaxial compression of a slab with a circular hole and with an elliptic hole, and the shear of a slab with an elliptic hole. The results are compared with the predictions of the linearized theory of elasticity. In this comparison, it is found that the maximum stresses and their locations are significantly affected by the choice of the constitutive equation.
Silva-Valenzuela, R.; Ortiz-Bernardin, A.; Sukumar, N.; Artioli, E.; Hitschfeld-Kahler, N.
A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition Journal Article
In: International Journal for Numerical Methods in Engineering, vol. 121, no. 10, pp. 2174-2205, 2020.
Abstract | Links | BibTeX | Tags: maximum-entropy, meshfree methods, nodal integration, patch test, stability, virtual element method
@article{sobnis2020,
title = {A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition},
author = {R. Silva-Valenzuela and A. Ortiz-Bernardin and N. Sukumar and E. Artioli and N. Hitschfeld-Kahler},
url = {https://camlab.cl/wp-content/uploads/2024/06/nived_revised_rgate.pdf},
doi = {10.1002/nme.6304},
year = {2020},
date = {2020-05-30},
urldate = {2020-05-30},
journal = {International Journal for Numerical Methods in Engineering},
volume = {121},
number = {10},
pages = {2174-2205},
abstract = {In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field variables, although the proposed scheme is applicable to any linear meshfree approximant. In our approach, the weak form integrals are nodally integrated using nodal representative cells that carry the nodal displacements and state variables such as strains and stresses. The nodal integration is performed using the virtual element decomposition, wherein the bilinear form is decomposed into a consistency part and a stability part that ensure consistency and stability of the method. The performance of the proposed nodal integration scheme is assessed through benchmark problems in linear and nonlinear analysis of solids for small displacements and small-strain kinematics. Numerical results are presented for linear elastostatics and linear elastodynamics, and viscoelasticity. We demonstrate that the proposed nodally integrated meshfree method is accurate, converges optimally, and is more reliable and robust than a standard cell-based Gauss integrated meshfree method.},
keywords = {maximum-entropy, meshfree methods, nodal integration, patch test, stability, virtual element method},
pubstate = {published},
tppubtype = {article}
}
In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field variables, although the proposed scheme is applicable to any linear meshfree approximant. In our approach, the weak form integrals are nodally integrated using nodal representative cells that carry the nodal displacements and state variables such as strains and stresses. The nodal integration is performed using the virtual element decomposition, wherein the bilinear form is decomposed into a consistency part and a stability part that ensure consistency and stability of the method. The performance of the proposed nodal integration scheme is assessed through benchmark problems in linear and nonlinear analysis of solids for small displacements and small-strain kinematics. Numerical results are presented for linear elastostatics and linear elastodynamics, and viscoelasticity. We demonstrate that the proposed nodally integrated meshfree method is accurate, converges optimally, and is more reliable and robust than a standard cell-based Gauss integrated meshfree method.
Francis, A.; Ortiz-Bernardin, A.; Bordas, S. P. A.; Natarajan, S.
A MINI element over star convex polytopes Journal Article
In: Finite Elements in Analysis and Design, vol. 172, pp. 103368, 2020.
Abstract | Links | BibTeX | Tags: arbitrary polytopes, bubble basis functions, nearly-incompressible elasticity, SFEM, strain smoothing, VANP operator, volumetric locking
@article{fobmini2020,
title = {A MINI element over star convex polytopes},
author = {A. Francis and A. Ortiz-Bernardin and S. P. A. Bordas and S. Natarajan},
url = {https://camlab.cl/wp-content/uploads/2024/06/mini_element_star_convex_polytopes.pdf},
doi = {10.1016/j.finel.2019.103368},
year = {2020},
date = {2020-01-29},
urldate = {2020-01-29},
journal = {Finite Elements in Analysis and Design},
volume = {172},
pages = {103368},
abstract = {In this paper, we extend the concept of MINI element over triangles to star convex arbitrary polytopes. This is achieved by employing the volume averaged nodal projection (VANP) method over polytopes in combination with the strain smoothing technique. Within this framework, the dilatation strain is projected onto the linear approximation space, thus resulting in a purely displacement based formulation. The stability is ensured by enhancing the displacement field with bubble basis functions. The salient features of the proposed method are two fold: the VANP alleviates the locking phenomenon and the strain smoothing suppresses the need to compute the derivative of the basis functions, thus reducing the computational burden. Various benchmark problems in two and three dimensions are numerically solved to demonstrate the robustness, accuracy and the convergence properties of the proposed framework.},
keywords = {arbitrary polytopes, bubble basis functions, nearly-incompressible elasticity, SFEM, strain smoothing, VANP operator, volumetric locking},
pubstate = {published},
tppubtype = {article}
}
In this paper, we extend the concept of MINI element over triangles to star convex arbitrary polytopes. This is achieved by employing the volume averaged nodal projection (VANP) method over polytopes in combination with the strain smoothing technique. Within this framework, the dilatation strain is projected onto the linear approximation space, thus resulting in a purely displacement based formulation. The stability is ensured by enhancing the displacement field with bubble basis functions. The salient features of the proposed method are two fold: the VANP alleviates the locking phenomenon and the strain smoothing suppresses the need to compute the derivative of the basis functions, thus reducing the computational burden. Various benchmark problems in two and three dimensions are numerically solved to demonstrate the robustness, accuracy and the convergence properties of the proposed framework.
2019
Meruane, V.; Espinoza, C.; Droguett, E. Lopez; Ortiz-Bernardin, A.
Impact identification using nonlinear dimensionality reduction and supervised learning Journal Article
In: Smart Materials and Structures, vol. 28, no. 11, pp. 115005, 2019.
Abstract | Links | BibTeX | Tags: autoencoders, impact identification, linear approximation, maximum-entropy, nonlinear dimensionality reduction techniques
@article{melii2019,
title = {Impact identification using nonlinear dimensionality reduction and supervised learning},
author = {V. Meruane and C. Espinoza and E. Lopez Droguett and A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/impact2018v3_final_preprint.pdf},
doi = {10.1088/1361-665X/ab419e},
year = {2019},
date = {2019-10-01},
urldate = {2019-10-01},
journal = {Smart Materials and Structures},
volume = {28},
number = {11},
pages = {115005},
abstract = {Real-time monitoring systems that can automatically locate and identify impacts as they occur have become increasingly attractive for ensuring safety and preventing catastrophic accidents in aerospace structures. In most cases, a set of piezoelectric transducers distributed over the structure captures strain–time data, which are preprocessed to extract relevant features that are fed to a supervised learning algorithm to detect, locate, and quantify impacts. The best results achieved to date in feature extraction for impact identification have been obtained with the use of principal component analysis (PCA). However, this technique cannot handle complex nonlinear data. The primary contribution of this study is the implementation of a novel impact identification algorithm that uses a supervised learning algorithm called linear approximation with maximum entropy (LME) in conjunction with different linear and nonlinear dimensionality reduction techniques, including PCA, kernel PCA, Isomap, local linear embedding (LLE), and multilayer autoencoders. The performance of LME with the different reduction techniques is tested with two experimental applications. The results show that the techniques that do not employ graphs, such as PCA, kernel PCA, and autoencoders, perform better, and the method that provides the best results is LME in conjunction with autoencoders. It is further demonstrated that LME with autoencoders works better than the algorithms available in the literature for similar problems.},
keywords = {autoencoders, impact identification, linear approximation, maximum-entropy, nonlinear dimensionality reduction techniques},
pubstate = {published},
tppubtype = {article}
}
Real-time monitoring systems that can automatically locate and identify impacts as they occur have become increasingly attractive for ensuring safety and preventing catastrophic accidents in aerospace structures. In most cases, a set of piezoelectric transducers distributed over the structure captures strain–time data, which are preprocessed to extract relevant features that are fed to a supervised learning algorithm to detect, locate, and quantify impacts. The best results achieved to date in feature extraction for impact identification have been obtained with the use of principal component analysis (PCA). However, this technique cannot handle complex nonlinear data. The primary contribution of this study is the implementation of a novel impact identification algorithm that uses a supervised learning algorithm called linear approximation with maximum entropy (LME) in conjunction with different linear and nonlinear dimensionality reduction techniques, including PCA, kernel PCA, Isomap, local linear embedding (LLE), and multilayer autoencoders. The performance of LME with the different reduction techniques is tested with two experimental applications. The results show that the techniques that do not employ graphs, such as PCA, kernel PCA, and autoencoders, perform better, and the method that provides the best results is LME in conjunction with autoencoders. It is further demonstrated that LME with autoencoders works better than the algorithms available in the literature for similar problems.
Ortiz-Bernardin, A.; Alvarez, C.; Hitschfeld-Kahler, N.; Russo, A.; Silva-Valenzuela, R.; Olate-Sanzana, E.
Veamy: an extensible object-oriented C++ library for the virtual element method Journal Article
In: Numerical Algorithms, vol. 82, pp. 1189-1220, 2019.
Abstract | Links | BibTeX | Tags: C++, object-oriented programming, polygonal meshes, virtual element method
@article{obaveamy2019,
title = {Veamy: an extensible object-oriented C++ library for the virtual element method},
author = {A. Ortiz-Bernardin and C. Alvarez and N. Hitschfeld-Kahler and A. Russo and R. Silva-Valenzuela and E. Olate-Sanzana},
url = {https://camlab.cl/wp-content/uploads/2024/06/veamy_revised_v2.pdf},
doi = {10.1007/s11075-018-00651-0},
year = {2019},
date = {2019-01-15},
urldate = {2019-01-15},
journal = {Numerical Algorithms},
volume = {82},
pages = {1189-1220},
abstract = {This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in two dimensions have been chosen as the starting stage for the development of this library. The theory of the VEM, upon which Veamy is built, is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis. Several examples are provided to demonstrate the usage of Veamy, and in particular, one of them features the interaction between Veamy and the polygonal mesh generator PolyMesher. A computational performance comparison between VEM and FEM is also conducted. Veamy is free and open source software.},
keywords = {C++, object-oriented programming, polygonal meshes, virtual element method},
pubstate = {published},
tppubtype = {article}
}
This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in two dimensions have been chosen as the starting stage for the development of this library. The theory of the VEM, upon which Veamy is built, is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis. Several examples are provided to demonstrate the usage of Veamy, and in particular, one of them features the interaction between Veamy and the polygonal mesh generator PolyMesher. A computational performance comparison between VEM and FEM is also conducted. Veamy is free and open source software.
2018
Ortiz-Bernardin, A.; Köbrich, P.; Hale, J. S.; Olate-Sanzana, E.; Bordas, S. P. A.; Natarajan, S.
A volume-averaged nodal projection method for the Reissner-Mindlin plate model Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 341, pp. 827-850, 2018.
Abstract | Links | BibTeX | Tags: maximum-entropy, meshfree methods, Reissner-Mindlin plate, shear-locking, VANP method
@article{obkvanp2018,
title = {A volume-averaged nodal projection method for the Reissner-Mindlin plate model},
author = {A. Ortiz-Bernardin and P. Köbrich and J. S. Hale and E. Olate-Sanzana and S. P. A. Bordas and S. Natarajan},
url = {https://camlab.cl/wp-content/uploads/2024/06/vanp-RM-plates-final-preprint.pdf},
doi = {10.1016/j.cma.2018.07.023},
year = {2018},
date = {2018-11-01},
urldate = {2018-11-01},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {341},
pages = {827-850},
abstract = {We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses.},
keywords = {maximum-entropy, meshfree methods, Reissner-Mindlin plate, shear-locking, VANP method},
pubstate = {published},
tppubtype = {article}
}
We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses.
Montero, S.; Bustamante, R.; Ortiz-Bernardin, A.
On the behaviour of spherical inclusions in a cylinder under tension loads Journal Article
In: Ingenius, vol. 19, pp. 69-78, 2018.
Abstract | Links | BibTeX | Tags: constitutive equations, elastic bodies, finite element method, Isotropic bodies, Nonlinear elasticity, strain limiting behavior
@article{mbbsi2018,
title = {On the behaviour of spherical inclusions in a cylinder under tension loads},
author = {S. Montero and R. Bustamante and A. Ortiz-Bernardin},
url = {https://revistas.ups.edu.ec/index.php/ingenius/article/view/19.2018.07},
doi = {10.17163/ings.n19.2018.07},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Ingenius},
volume = {19},
pages = {69-78},
abstract = {In the present paper the behaviour of a hyperelastic body is studied, considering the presence of one, two and more spherical inclusions, under the effect of an external tension load. The inclusions are modelled as nonlinear elastic bodies that undergo small strains. For the material constitutive relation, a relatively new type of model is used, wherein the strains (linearized strain) are assumed to be nonlinear functions of the stresses. In particular, a function is used that keeps the strains small, independently of the magnitude of the external loads. In order to simplify the problem, the hyperelastic medium and the inclusions are modelled as axial-symmetric bodies. The finite element method is used to obtain results for these boundary value problems. The objective of using these new models for elastic bodies in the case of the inclusions is to study the behaviour of such bodies in the case of concentration of stresses, which happens near the interface with the surrounding matrix. From the results presented in this paper, it is possible to observe that despite the relatively large magnitude for the stresses, the strains for the inclusions remain small, which would be closer to the actual behaviour of real inclusions made of brittle materials, which cannot show large strains.},
keywords = {constitutive equations, elastic bodies, finite element method, Isotropic bodies, Nonlinear elasticity, strain limiting behavior},
pubstate = {published},
tppubtype = {article}
}
In the present paper the behaviour of a hyperelastic body is studied, considering the presence of one, two and more spherical inclusions, under the effect of an external tension load. The inclusions are modelled as nonlinear elastic bodies that undergo small strains. For the material constitutive relation, a relatively new type of model is used, wherein the strains (linearized strain) are assumed to be nonlinear functions of the stresses. In particular, a function is used that keeps the strains small, independently of the magnitude of the external loads. In order to simplify the problem, the hyperelastic medium and the inclusions are modelled as axial-symmetric bodies. The finite element method is used to obtain results for these boundary value problems. The objective of using these new models for elastic bodies in the case of the inclusions is to study the behaviour of such bodies in the case of concentration of stresses, which happens near the interface with the surrounding matrix. From the results presented in this paper, it is possible to observe that despite the relatively large magnitude for the stresses, the strains for the inclusions remain small, which would be closer to the actual behaviour of real inclusions made of brittle materials, which cannot show large strains.
2017
Meruane, V.; Lasen, M.; Droguett, E. López; Ortiz-Bernardin, A.
Modal strain energy-based debonding assessment of sandwich panels using a linear approximation with maximum entropy Journal Article
In: Entropy, vol. 19, no. 11, pp. 619, 2017.
Abstract | Links | BibTeX | Tags: damage assessment, debonding, linear approximation, maximum-entropy, modal strain energy, sandwich panel
@article{mlmsed2017,
title = {Modal strain energy-based debonding assessment of sandwich panels using a linear approximation with maximum entropy},
author = {V. Meruane and M. Lasen and E. López Droguett and A. Ortiz-Bernardin},
doi = {10.3390/e19110619},
year = {2017},
date = {2017-11-17},
urldate = {2017-11-17},
journal = {Entropy},
volume = {19},
number = {11},
pages = {619},
abstract = {Sandwich structures are very attractive due to their high strength at a minimum weight, and, therefore, there has been a rapid increase in their applications. Nevertheless, these structures may present imperfect bonding or debonding between the skins and core as a result of manufacturing defects or impact loads, degrading their mechanical properties. To improve both the safety and functionality of these systems, structural damage assessment methodologies can be implemented. This article presents a damage assessment algorithm to localize and quantify debonds in sandwich panels. The proposed algorithm uses damage indices derived from the modal strain energy method and a linear approximation with a maximum entropy algorithm. Full-field vibration measurements of the panels were acquired using a high-speed 3D digital image correlation (DIC) system. Since the number of damage indices per panel is too large to be used directly in a regression algorithm, reprocessing of the data using principal component analysis (PCA) and kernel PCA has been performed. The results demonstrate that the proposed methodology accurately identifies debonding in composite panels.},
keywords = {damage assessment, debonding, linear approximation, maximum-entropy, modal strain energy, sandwich panel},
pubstate = {published},
tppubtype = {article}
}
Sandwich structures are very attractive due to their high strength at a minimum weight, and, therefore, there has been a rapid increase in their applications. Nevertheless, these structures may present imperfect bonding or debonding between the skins and core as a result of manufacturing defects or impact loads, degrading their mechanical properties. To improve both the safety and functionality of these systems, structural damage assessment methodologies can be implemented. This article presents a damage assessment algorithm to localize and quantify debonds in sandwich panels. The proposed algorithm uses damage indices derived from the modal strain energy method and a linear approximation with a maximum entropy algorithm. Full-field vibration measurements of the panels were acquired using a high-speed 3D digital image correlation (DIC) system. Since the number of damage indices per panel is too large to be used directly in a regression algorithm, reprocessing of the data using principal component analysis (PCA) and kernel PCA has been performed. The results demonstrate that the proposed methodology accurately identifies debonding in composite panels.
Ortiz-Bernardin, A.; Russo, A.; Sukumar, N.
Consistent and stable meshfree Galerkin methods using the virtual element decomposition Journal Article
In: International Journal for Numerical Methods in Engineering, vol. 112, no. 7, pp. 655-684, 2017.
Abstract | Links | BibTeX | Tags: maximum-entropy, meshfree methods, numerical integration, patch test, stability, virtual element method
@article{obrscsmg2017,
title = {Consistent and stable meshfree Galerkin methods using the virtual element decomposition},
author = {A. Ortiz-Bernardin and A. Russo and N. Sukumar},
url = {https://camlab.cl/wp-content/uploads/2024/06/maxent_vem_personal_preprint.pdf},
doi = {10.1002/nme.5519},
year = {2017},
date = {2017-11-16},
urldate = {2017-11-16},
journal = {International Journal for Numerical Methods in Engineering},
volume = {112},
number = {7},
pages = {655-684},
abstract = {Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth (nonpolynomial functions), and they do not rely on an underlying mesh structure for their construction. These features render meshfree methods to be particularly appealing for higher-order PDEs and for large deformation simulations of solid continua. However, a deficiency that still persists in meshfree Galerkin methods is the inaccuracies in numerical integration, which affects the consistency and stability of the method. Several previous contributions have tackled the issue of integration errors with an eye on consistency, but without explicitly ensuring stability. In this paper, we draw on the recently proposed virtual element method, to present a formulation that guarantees both the consistency and stability of the approximate bilinear form. We adopt maximum-entropy meshfree basis functions, but other meshfree basis functions can also be used within this framework. Numerical results for several two- and three-dimensional elliptic (Poisson and linear elastostatic) boundary-value problems that demonstrate the effectiveness of the proposed formulation are presented.},
keywords = {maximum-entropy, meshfree methods, numerical integration, patch test, stability, virtual element method},
pubstate = {published},
tppubtype = {article}
}
Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth (nonpolynomial functions), and they do not rely on an underlying mesh structure for their construction. These features render meshfree methods to be particularly appealing for higher-order PDEs and for large deformation simulations of solid continua. However, a deficiency that still persists in meshfree Galerkin methods is the inaccuracies in numerical integration, which affects the consistency and stability of the method. Several previous contributions have tackled the issue of integration errors with an eye on consistency, but without explicitly ensuring stability. In this paper, we draw on the recently proposed virtual element method, to present a formulation that guarantees both the consistency and stability of the approximate bilinear form. We adopt maximum-entropy meshfree basis functions, but other meshfree basis functions can also be used within this framework. Numerical results for several two- and three-dimensional elliptic (Poisson and linear elastostatic) boundary-value problems that demonstrate the effectiveness of the proposed formulation are presented.
Meruane, V.; Véliz, P.; Droguett, E. López; Ortiz-Bernardin, A.
In: Entropy, vol. 19, no. 4, pp. 137, 2017.
Abstract | Links | BibTeX | Tags: barely visible impact damage, impact identification, linear approximation, maximum-entropy, principal component analysis, sandwich panel
@article{mvlilq2017,
title = {Impact location and quantification on an aluminum sandwich panel using principal component analysis and linear approximation with maximum entropy},
author = {V. Meruane and P. Véliz and E. López Droguett and A. Ortiz-Bernardin},
doi = {10.3390/e19040137},
year = {2017},
date = {2017-03-25},
urldate = {2017-03-25},
journal = {Entropy},
volume = {19},
number = {4},
pages = {137},
abstract = {To avoid structural failures it is of critical importance to detect, locate and quantify impact damage as soon as it occurs. This can be achieved by impact identification methodologies, which continuously monitor the structure, detecting, locating, and quantifying impacts as they occur. This article presents an improved impact identification algorithm that uses principal component analysis (PCA) to extract features from the monitored signals and an algorithm based on linear approximation with maximum entropy to estimate the impacts. The proposed methodology is validated with two experimental applications, which include an aluminum plate and an aluminum sandwich panel. The results are compared with those of other impact identification algorithms available in literature, demonstrating that the proposed method outperforms these algorithms.},
keywords = {barely visible impact damage, impact identification, linear approximation, maximum-entropy, principal component analysis, sandwich panel},
pubstate = {published},
tppubtype = {article}
}
To avoid structural failures it is of critical importance to detect, locate and quantify impact damage as soon as it occurs. This can be achieved by impact identification methodologies, which continuously monitor the structure, detecting, locating, and quantifying impacts as they occur. This article presents an improved impact identification algorithm that uses principal component analysis (PCA) to extract features from the monitored signals and an algorithm based on linear approximation with maximum entropy to estimate the impacts. The proposed methodology is validated with two experimental applications, which include an aluminum plate and an aluminum sandwich panel. The results are compared with those of other impact identification algorithms available in literature, demonstrating that the proposed method outperforms these algorithms.
Francis, A.; Ortiz-Bernardin, A.; Bordas, S. P. A.; Natarajan, S.
Linear smoothed polygonal and polyhedral finite elements Journal Article
In: International Journal for Numerical Methods in Engineering, vol. 109, no. 9, pp. 1263–1288, 2017.
Abstract | Links | BibTeX | Tags: linear smoothing, numerical integration, patch test, polytope elements, quadratic serendipity, Smoothed finite element method
@article{fobblsp2017,
title = {Linear smoothed polygonal and polyhedral finite elements},
author = {A. Francis and A. Ortiz-Bernardin and S. P. A. Bordas and S. Natarajan},
url = {https://camlab.cl/wp-content/uploads/2024/06/2015_LinearSmoothing_R1.pdf},
doi = {10.1002/nme.5324},
year = {2017},
date = {2017-03-02},
urldate = {2017-03-02},
journal = {International Journal for Numerical Methods in Engineering},
volume = {109},
number = {9},
pages = {1263–1288},
abstract = {It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations. The accuracy is also improved, and all the methods tested pass the patch test to machine precision.},
keywords = {linear smoothing, numerical integration, patch test, polytope elements, quadratic serendipity, Smoothed finite element method},
pubstate = {published},
tppubtype = {article}
}
It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations. The accuracy is also improved, and all the methods tested pass the patch test to machine precision.
2016
Sanchez, N.; Meruane, V.; Ortiz-Bernardin, A.
A novel impact identification algorithm based on a linear approximation with maximum entropy Journal Article
In: Smart Materials and Structures, vol. 25, no. 9, pp. 095050, 2016.
Abstract | Links | BibTeX | Tags: damage assessment, impact identification, linear approximation, maximum-entropy, structural health monitoring
@article{smobnii2016,
title = {A novel impact identification algorithm based on a linear approximation with maximum entropy},
author = {N. Sanchez and V. Meruane and A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/impact_LMEv3.pdf},
doi = {10.1088/0964-1726/25/9/095050},
year = {2016},
date = {2016-08-24},
urldate = {2016-08-24},
journal = {Smart Materials and Structures},
volume = {25},
number = {9},
pages = {095050},
abstract = {This article presents a novel impact identification algorithm that uses a linear approximation handled by a statistical inference model based on the maximum-entropy principle, termed linear approximation with maximum entropy (LME). Unlike other regression algorithms as Artificial Neural Networks (ANN) and Support Vector Machines (SVM), the proposed algorithm requires only one parameter to be selected and the impact is identified after solving a convex optimization problem that has a unique solution. In addition, with LME data is processed in a period of time that is comparable to the one of other algorithms. The performance of the proposed methodology is validated by considering an experimental aluminum plate. Time varying strain data is measured using four piezoceramic sensors bonded to the plate. To demonstrate the potential of the proposed approach over existing ones, results obtained via LME are compared with those of ANN and Least Square Support Vector Machines (LSSVM). The results demonstrate that with a low number of sensors it is possible to accurately locate and quantify impacts on a structure and that LME outperforms other impact identification algorithms.},
keywords = {damage assessment, impact identification, linear approximation, maximum-entropy, structural health monitoring},
pubstate = {published},
tppubtype = {article}
}
This article presents a novel impact identification algorithm that uses a linear approximation handled by a statistical inference model based on the maximum-entropy principle, termed linear approximation with maximum entropy (LME). Unlike other regression algorithms as Artificial Neural Networks (ANN) and Support Vector Machines (SVM), the proposed algorithm requires only one parameter to be selected and the impact is identified after solving a convex optimization problem that has a unique solution. In addition, with LME data is processed in a period of time that is comparable to the one of other algorithms. The performance of the proposed methodology is validated by considering an experimental aluminum plate. Time varying strain data is measured using four piezoceramic sensors bonded to the plate. To demonstrate the potential of the proposed approach over existing ones, results obtained via LME are compared with those of ANN and Least Square Support Vector Machines (LSSVM). The results demonstrate that with a low number of sensors it is possible to accurately locate and quantify impacts on a structure and that LME outperforms other impact identification algorithms.
Montero, S.; Bustamante, R.; Ortiz-Bernardin, A.
A finite element analysis of some boundary value problems for a new type of constitutive relation for elastic bodies Journal Article
In: Acta Mechanica, vol. 227, no. 2, pp. 601-615, 2016.
Abstract | Links | BibTeX | Tags: elastic bodies, finite element analysis, finite element method, implicit elasticity, Nonlinear elasticity
@article{mbobfeabvp2016,
title = {A finite element analysis of some boundary value problems for a new type of constitutive relation for elastic bodies},
author = {S. Montero and R. Bustamante and A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/implicit_elasticity_montero_bustamante_ortizbernardin_2015.pdf},
doi = {10.1007/s00707-015-1480-6},
year = {2016},
date = {2016-02-01},
urldate = {2016-02-01},
journal = {Acta Mechanica},
volume = {227},
number = {2},
pages = {601-615},
abstract = {Recently, there has been interest in the study of a new class of constitutive relation, wherein the linearized strain tensor is assumed to be a function of the stresses. In this communication, some boundary value problems are solved using the finite element method, and the solid material being described by such a constitutive relation, where the stresses can be arbitrarily ‘large’, but strains remain small. Three problems are analyzed, namely the traction of a plate with hyperbolic boundaries, a plate with a point load and the traction of a plate with an elliptic hole. The results for the stresses and strains are compared with the predictions that are obtained by using the constitutive equation of the classical linearized theory of elasticity.},
keywords = {elastic bodies, finite element analysis, finite element method, implicit elasticity, Nonlinear elasticity},
pubstate = {published},
tppubtype = {article}
}
Recently, there has been interest in the study of a new class of constitutive relation, wherein the linearized strain tensor is assumed to be a function of the stresses. In this communication, some boundary value problems are solved using the finite element method, and the solid material being described by such a constitutive relation, where the stresses can be arbitrarily ‘large’, but strains remain small. Three problems are analyzed, namely the traction of a plate with hyperbolic boundaries, a plate with a point load and the traction of a plate with an elliptic hole. The results for the stresses and strains are compared with the predictions that are obtained by using the constitutive equation of the classical linearized theory of elasticity.
2015
Ortiz-Bernardin, A.; Puso, M. A.; Sukumar, N.
Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 293, pp. 348–374, 2015.
Abstract | Links | BibTeX | Tags: Delaunay meshes, F-bar method, hyperelasticity, large deformations, maximum-entropy, meshfree methods
@article{obpsirn2015,
title = {Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations},
author = {A. Ortiz-Bernardin and M.A. Puso and N. Sukumar},
url = {https://camlab.cl/wp-content/uploads/2024/06/vanp_hyperelastic_final_preprint.pdf},
doi = {10.1016/j.cma.2015.05.009},
year = {2015},
date = {2015-08-15},
urldate = {2015-08-15},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {293},
pages = {348–374},
abstract = {A displacement-based Galerkin meshfree method for large deformation analysis of nearly-incompressible elastic solids is presented. Nodal discretization of the domain is defined by a Delaunay tessellation (three-node triangles and four-node tetrahedra), which is used to form the meshfree basis functions and to numerically integrate the weak form integrals. In the proposed approach for nearly-incompressible solids, a volume-averaged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes. The nodal dilatational constraint is then projected onto the linear approximation space. The displacement field is constructed on the linear space and enriched with bubble-like meshfree basis functions for stability. The new procedure leads to a displacement-based formulation that is similar to F-bar methodologies in finite elements and isogeometric analysis. We adopt maximum-entropy meshfree basis functions, and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions. The nonlinear simulations reveal that the proposed methodology provides improved robustness for nearly-incompressible large deformation analysis on Delaunay meshes.},
keywords = {Delaunay meshes, F-bar method, hyperelasticity, large deformations, maximum-entropy, meshfree methods},
pubstate = {published},
tppubtype = {article}
}
A displacement-based Galerkin meshfree method for large deformation analysis of nearly-incompressible elastic solids is presented. Nodal discretization of the domain is defined by a Delaunay tessellation (three-node triangles and four-node tetrahedra), which is used to form the meshfree basis functions and to numerically integrate the weak form integrals. In the proposed approach for nearly-incompressible solids, a volume-averaged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes. The nodal dilatational constraint is then projected onto the linear approximation space. The displacement field is constructed on the linear space and enriched with bubble-like meshfree basis functions for stability. The new procedure leads to a displacement-based formulation that is similar to F-bar methodologies in finite elements and isogeometric analysis. We adopt maximum-entropy meshfree basis functions, and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions. The nonlinear simulations reveal that the proposed methodology provides improved robustness for nearly-incompressible large deformation analysis on Delaunay meshes.
Ortiz-Bernardin, A.; Sfyris, D.
A finite element formulation for stressed bodies with continuous distribution of edge dislocations Journal Article
In: Acta Mechanica, vol. 226, no. 5, pp. 1621-1640, 2015.
Abstract | Links | BibTeX | Tags: inhomogeneous body, Materially uniform, multiplicative decomposition, nonlinear finite elements
@article{obsfefsb2015,
title = {A finite element formulation for stressed bodies with continuous distribution of edge dislocations},
author = {A. Ortiz-Bernardin and D. Sfyris},
url = {https://camlab.cl/wp-content/uploads/2024/06/aob_ds_continuous_dislocations_accepted_preprint.pdf},
doi = {10.1007/s00707-014-1273-3},
year = {2015},
date = {2015-05-01},
urldate = {2015-05-01},
journal = {Acta Mechanica},
volume = {226},
number = {5},
pages = {1621-1640},
abstract = {On using Noll’s theory of materially uniform but inhomogeneous bodies, a nonlinear finite element method for treating a body with a continuous distribution of edge dislocations is presented. To this end, we use the multiplicative decomposition of the deformation gradient, which is herein referred to as the F* decomposition. The nonlinear finite element method is devised starting from a hyperelastic-like strain energy as a function of F*. By making a specific assumption for the uniform reference, we model a bar with a continuous distribution of edge dislocations parallel to the plane that defines a cross section of the bar and with the Burgers vector along the axial direction of the bar. This body is subjected to pure tension along its axial direction and we examine how the presence of the defects affects the elastic solution. The numerical results are juxtaposed with the analogous ones that are obtained from the corresponding elastic material. It appears that the field of the defects affects the nonlinearity in the stress-strain response in the sense that stresses grow “faster” pointwise in the dislocated body. Thus, if a definite yield limit exists it is approached faster by the dislocated model at hand due to the presence of defects in the as-received body.
We also focus our attention in the case of only one dislocation and conclude that near the core region our model predicts finite stresses. Finally, a close loop consisting of a screw and an edge segment is treated within this theory. As expected, it appears that near the loop stresses are concentrated. Our framework is valid for a body with a frozen distribution of dislocations, namely, the defects exist but are not allowed to move. So, essentially, it models an elastic body with internal stresses resulting from dislocations. Thus, our approach is assumed to be one step before the initiation of plasticity and we are interested in how the field of the inhomogeneity that arises from a fixed distribution of defects affects the elastic solution. This is the first attempt to apply the multiplicative decomposition to problems with dislocations in the literature, thereby highlighting that Noll’s abstract approach can be put into the perspective of standard engineering computations.},
keywords = {inhomogeneous body, Materially uniform, multiplicative decomposition, nonlinear finite elements},
pubstate = {published},
tppubtype = {article}
}
On using Noll’s theory of materially uniform but inhomogeneous bodies, a nonlinear finite element method for treating a body with a continuous distribution of edge dislocations is presented. To this end, we use the multiplicative decomposition of the deformation gradient, which is herein referred to as the F* decomposition. The nonlinear finite element method is devised starting from a hyperelastic-like strain energy as a function of F*. By making a specific assumption for the uniform reference, we model a bar with a continuous distribution of edge dislocations parallel to the plane that defines a cross section of the bar and with the Burgers vector along the axial direction of the bar. This body is subjected to pure tension along its axial direction and we examine how the presence of the defects affects the elastic solution. The numerical results are juxtaposed with the analogous ones that are obtained from the corresponding elastic material. It appears that the field of the defects affects the nonlinearity in the stress-strain response in the sense that stresses grow “faster” pointwise in the dislocated body. Thus, if a definite yield limit exists it is approached faster by the dislocated model at hand due to the presence of defects in the as-received body.
We also focus our attention in the case of only one dislocation and conclude that near the core region our model predicts finite stresses. Finally, a close loop consisting of a screw and an edge segment is treated within this theory. As expected, it appears that near the loop stresses are concentrated. Our framework is valid for a body with a frozen distribution of dislocations, namely, the defects exist but are not allowed to move. So, essentially, it models an elastic body with internal stresses resulting from dislocations. Thus, our approach is assumed to be one step before the initiation of plasticity and we are interested in how the field of the inhomogeneity that arises from a fixed distribution of defects affects the elastic solution. This is the first attempt to apply the multiplicative decomposition to problems with dislocations in the literature, thereby highlighting that Noll’s abstract approach can be put into the perspective of standard engineering computations.
We also focus our attention in the case of only one dislocation and conclude that near the core region our model predicts finite stresses. Finally, a close loop consisting of a screw and an edge segment is treated within this theory. As expected, it appears that near the loop stresses are concentrated. Our framework is valid for a body with a frozen distribution of dislocations, namely, the defects exist but are not allowed to move. So, essentially, it models an elastic body with internal stresses resulting from dislocations. Thus, our approach is assumed to be one step before the initiation of plasticity and we are interested in how the field of the inhomogeneity that arises from a fixed distribution of defects affects the elastic solution. This is the first attempt to apply the multiplicative decomposition to problems with dislocations in the literature, thereby highlighting that Noll’s abstract approach can be put into the perspective of standard engineering computations.
Meruane, V.; Ortiz-Bernardin, A.
Structural damage assessment using linear approximation with maximum entropy and transmissibility data Journal Article
In: Mechanical Systems and Signal Processing, vol. 54-55, pp. 210-223, 2015.
Abstract | Links | BibTeX | Tags: linear approximation, maximum-entropy, Structural damage assessment, supervised learning algorithms
@article{mobsda2015,
title = {Structural damage assessment using linear approximation with maximum entropy and transmissibility data},
author = {V. Meruane and A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/structural_damage_assessment_maxent.pdf},
doi = {10.1016/j.ymssp.2014.08.018},
year = {2015},
date = {2015-03-01},
urldate = {2015-03-01},
journal = {Mechanical Systems and Signal Processing},
volume = {54-55},
pages = {210-223},
abstract = {Supervised learning algorithms have been proposed as a suitable alternative to model updating methods in structural damage assessment, being Artificial Neural Networks the most frequently used. Notwithstanding, the slow learning speed and the large number of parameters that need to be tuned within the training stage have been a major bottleneck in their application. This article presents a new algorithm for real-time damage assessment that uses a linear approximation method in conjunction with antiresonant frequencies that are identified from transmissibility functions. The linear approximation is handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of Neural Networks. The performance of the proposed methodology is validated by considering three experimental structures: an eight-degree-of-freedom (DOF) mass-spring system, a beam, and an exhaust system of a car. To demonstrate the potential of the proposed algorithm over existing ones, the obtained results are compared with those of a model updating method based on parallel genetic algorithms and a multilayer feedforward neural network approach.},
keywords = {linear approximation, maximum-entropy, Structural damage assessment, supervised learning algorithms},
pubstate = {published},
tppubtype = {article}
}
Supervised learning algorithms have been proposed as a suitable alternative to model updating methods in structural damage assessment, being Artificial Neural Networks the most frequently used. Notwithstanding, the slow learning speed and the large number of parameters that need to be tuned within the training stage have been a major bottleneck in their application. This article presents a new algorithm for real-time damage assessment that uses a linear approximation method in conjunction with antiresonant frequencies that are identified from transmissibility functions. The linear approximation is handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of Neural Networks. The performance of the proposed methodology is validated by considering three experimental structures: an eight-degree-of-freedom (DOF) mass-spring system, a beam, and an exhaust system of a car. To demonstrate the potential of the proposed algorithm over existing ones, the obtained results are compared with those of a model updating method based on parallel genetic algorithms and a multilayer feedforward neural network approach.
Ortiz-Bernardin, A.; Hale, J. S.; Cyron, C. J.
Volume-averaged nodal projection method for nearly-incompressible elasticity using meshfree and bubble basis functions Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 285, pp. 427-451, 2015.
Abstract | Links | BibTeX | Tags: bubble functions, meshfree methods, nearly-incompressible elasticity, projection methods, volume-averaged pressure, volume-averaged strains, volumetric locking
@article{obhcvanp2015,
title = {Volume-averaged nodal projection method for nearly-incompressible elasticity using meshfree and bubble basis functions},
author = {A. Ortiz-Bernardin and J.S. Hale and C. J. Cyron},
url = {https://camlab.cl/wp-content/uploads/2024/06/meshfree-vol-nodal-avg-proj-meth-2013-final-lowres.pdf},
doi = {10.1016/j.cma.2014.11.018},
year = {2015},
date = {2015-03-01},
urldate = {2015-03-01},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {285},
pages = {427-451},
abstract = {We present a displacement-based Galerkin meshfree method for the analysis of nearly-incompressible linear elastic solids, where low-order simplicial tessellations (i.e., 3-node triangular or 4-node tetrahedral meshes) are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions. In this approach, a volume-averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal- or lower-order than the approximation space for the displacement field resulting in a locking-free method. The stability of the method is provided via bubble-like basis functions. Because the notion of an ‘element’ or ‘cell’ is not present in the computation of the meshfree basis functions such low-order tessellations can be used regardless of the order of the approximation spaces desired. First- and second-order meshfree basis functions are chosen as a particular case in the proposed method. Numerical examples are provided in two and three dimensions to demonstrate the robustness of the method, its ability to avoid volumetric locking in the nearly-incompressible regime, and its improved performance when compared to the MINI finite element scheme on the simplicial mesh.},
keywords = {bubble functions, meshfree methods, nearly-incompressible elasticity, projection methods, volume-averaged pressure, volume-averaged strains, volumetric locking},
pubstate = {published},
tppubtype = {article}
}
We present a displacement-based Galerkin meshfree method for the analysis of nearly-incompressible linear elastic solids, where low-order simplicial tessellations (i.e., 3-node triangular or 4-node tetrahedral meshes) are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions. In this approach, a volume-averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal- or lower-order than the approximation space for the displacement field resulting in a locking-free method. The stability of the method is provided via bubble-like basis functions. Because the notion of an ‘element’ or ‘cell’ is not present in the computation of the meshfree basis functions such low-order tessellations can be used regardless of the order of the approximation spaces desired. First- and second-order meshfree basis functions are chosen as a particular case in the proposed method. Numerical examples are provided in two and three dimensions to demonstrate the robustness of the method, its ability to avoid volumetric locking in the nearly-incompressible regime, and its improved performance when compared to the MINI finite element scheme on the simplicial mesh.
2014
Meruane, V.; del Fierro, V.; Ortiz-Bernardin, A.
A maximum entropy approach to assess debonding in honeycomb aluminum plates Journal Article
In: Entropy, vol. 16, no. 5, pp. 2869-2889, 2014.
Abstract | Links | BibTeX | Tags: damage assessment, debonding, honeycomb, linear approximation, maximum-entropy, Sandwich structures
@article{mdobmea2014,
title = {A maximum entropy approach to assess debonding in honeycomb aluminum plates},
author = {V. Meruane and V. del Fierro and A. Ortiz-Bernardin},
doi = {10.3390/e16052869},
year = {2014},
date = {2014-05-23},
urldate = {2014-05-23},
journal = {Entropy},
volume = {16},
number = {5},
pages = {2869-2889},
abstract = {Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, due to manufacturing defects or impact loads, these structures can be subject to imperfect bonding or debonding between the skin and the honeycomb core. The presence of debonding reduces the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This article presents a new supervised learning algorithm to identify debonded regions in aluminum honeycomb panels. The algorithm uses a linear approximation method handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of neural networks. The honeycomb panels are modeled with finite elements using a simplified three-layer shell model. The adhesive layer between the skin and core is modeled using linear springs, the rigidities of which are reduced in debonded sectors. The algorithm is validated using experimental data of an aluminum honeycomb panel under different damage scenarios.},
keywords = {damage assessment, debonding, honeycomb, linear approximation, maximum-entropy, Sandwich structures},
pubstate = {published},
tppubtype = {article}
}
Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, due to manufacturing defects or impact loads, these structures can be subject to imperfect bonding or debonding between the skin and the honeycomb core. The presence of debonding reduces the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This article presents a new supervised learning algorithm to identify debonded regions in aluminum honeycomb panels. The algorithm uses a linear approximation method handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of neural networks. The honeycomb panels are modeled with finite elements using a simplified three-layer shell model. The adhesive layer between the skin and core is modeled using linear springs, the rigidities of which are reduced in debonded sectors. The algorithm is validated using experimental data of an aluminum honeycomb panel under different damage scenarios.
Ortiz-Bernardin, A.; Bustamante, R.; Rajagopal, K. R.
A numerical study of elastic bodies that are described by constitutive equations that exhibit limited strains Journal Article
In: International Journal of Solids and Structures, vol. 51, no. 3-4, pp. 875-885, 2014.
Abstract | Links | BibTeX | Tags: implicit elasticity, nonlinear finite elements, small strain, unbounded stress
@article{obbrnseb2014,
title = {A numerical study of elastic bodies that are described by constitutive equations that exhibit limited strains},
author = {A. Ortiz-Bernardin and R. Bustamante and K.R. Rajagopal},
url = {https://camlab.cl/wp-content/uploads/2024/06/num_study_const_equations_limited_strain_revised.pdf},
doi = {10.1016/j.ijsolstr.2013.11.014},
year = {2014},
date = {2014-02-01},
urldate = {2014-02-01},
journal = {International Journal of Solids and Structures},
volume = {51},
number = {3-4},
pages = {875-885},
abstract = {Recently, a very general and novel class of implicit bodies has been developed to describe the elastic response of solids. It contains as a special subclass the classical Cauchy and Green elastic bodies. Within the class of such bodies, one can obtain through a rigorous approximation, constitutive relations for the linearized strain as a nonlinear function of the stress. Such an approximation is not possible within classical theories of Cauchy and Green elasticity, where the process of linearization will only lead to the classical linearized elastic body.
In this paper, we study numerically the states of stress and strain in a finite rectangular plate with an elliptic hole and a stepped flat tension bar with shoulder fillets, within the context of the new class of models for elastic bodies that guarantees that the linearized strain would stay bounded and limited below a value that can be fixed a priori, thereby guaranteeing the validity of the use of the model. This is in contrast to the classical linearized elastic model, wherein the strains can become large enough in the body leading to an obvious inconsistency.},
keywords = {implicit elasticity, nonlinear finite elements, small strain, unbounded stress},
pubstate = {published},
tppubtype = {article}
}
Recently, a very general and novel class of implicit bodies has been developed to describe the elastic response of solids. It contains as a special subclass the classical Cauchy and Green elastic bodies. Within the class of such bodies, one can obtain through a rigorous approximation, constitutive relations for the linearized strain as a nonlinear function of the stress. Such an approximation is not possible within classical theories of Cauchy and Green elasticity, where the process of linearization will only lead to the classical linearized elastic body.
In this paper, we study numerically the states of stress and strain in a finite rectangular plate with an elliptic hole and a stepped flat tension bar with shoulder fillets, within the context of the new class of models for elastic bodies that guarantees that the linearized strain would stay bounded and limited below a value that can be fixed a priori, thereby guaranteeing the validity of the use of the model. This is in contrast to the classical linearized elastic model, wherein the strains can become large enough in the body leading to an obvious inconsistency.
In this paper, we study numerically the states of stress and strain in a finite rectangular plate with an elliptic hole and a stepped flat tension bar with shoulder fillets, within the context of the new class of models for elastic bodies that guarantees that the linearized strain would stay bounded and limited below a value that can be fixed a priori, thereby guaranteeing the validity of the use of the model. This is in contrast to the classical linearized elastic model, wherein the strains can become large enough in the body leading to an obvious inconsistency.
2012
Ortiz, A.; Bustamante, R.; Rajagopal, K. R.
A numerical study of a plate with a hole for a new class of elastic bodies Journal Article
In: Acta Mechanica, vol. 223, no. 9, pp. 1971-1981, 2012.
Abstract | Links | BibTeX | Tags: elastic body, finite element analysis, finite element method, implicit elasticity, Nonlinear elasticity
@article{obrnsp2012,
title = {A numerical study of a plate with a hole for a new class of elastic bodies},
author = {A. Ortiz and R. Bustamante and K.R. Rajagopal},
url = {https://camlab.cl/wp-content/uploads/2024/06/new_elast_mat_2D_finite_element_6.pdf},
doi = {10.1007/s00707-012-0690-4},
year = {2012},
date = {2012-06-21},
urldate = {2012-06-21},
journal = {Acta Mechanica},
volume = {223},
number = {9},
pages = {1971-1981},
abstract = {It has been shown recently that the class of elastic bodies is much larger than the classical Cauchy and Green elastic bodies, if by an elastic body one means a body incapable of dissipation (converting working into heat). In this paper, we study the boundary value problem of a hole in a finite nonlinear elastic plate that belongs to a subset of this class of the generalization of elastic bodies, subject to a uniaxial state of traction at the boundary (see Fig. 1.) We consider several different specific models, including one that exhibits limiting strain. As the plate is finite, we have to solve the problem numerically, and we use the finite element method to solve the problem. In marked contrast to the results for the classical linearized elastic body, we find that the strains grow far slower than the stress.},
keywords = {elastic body, finite element analysis, finite element method, implicit elasticity, Nonlinear elasticity},
pubstate = {published},
tppubtype = {article}
}
It has been shown recently that the class of elastic bodies is much larger than the classical Cauchy and Green elastic bodies, if by an elastic body one means a body incapable of dissipation (converting working into heat). In this paper, we study the boundary value problem of a hole in a finite nonlinear elastic plate that belongs to a subset of this class of the generalization of elastic bodies, subject to a uniaxial state of traction at the boundary (see Fig. 1.) We consider several different specific models, including one that exhibits limiting strain. As the plate is finite, we have to solve the problem numerically, and we use the finite element method to solve the problem. In marked contrast to the results for the classical linearized elastic body, we find that the strains grow far slower than the stress.
2011
Ortiz, A.; Puso, M. A.; Sukumar, N.
Maximum-entropy meshfree method for incompressible media problems Journal Article
In: Finite Elements in Analysis and Design, vol. 47, no. 6, pp. 572-585, 2011.
Links | BibTeX | Tags: elasticity, maximum-entropy, meshfree methods, numerical integration, Stokes problem, volumetric locking
@article{opsmem2011,
title = {Maximum-entropy meshfree method for incompressible media problems},
author = {A. Ortiz and M.A. Puso and N. Sukumar},
url = {https://camlab.cl/wp-content/uploads/2024/06/mem-melosh-v1.pdf},
doi = {10.1016/j.finel.2010.12.009},
year = {2011},
date = {2011-06-01},
urldate = {2011-06-01},
journal = {Finite Elements in Analysis and Design},
volume = {47},
number = {6},
pages = {572-585},
keywords = {elasticity, maximum-entropy, meshfree methods, numerical integration, Stokes problem, volumetric locking},
pubstate = {published},
tppubtype = {article}
}
2010
Ortiz, A.; Puso, M. A.; Sukumar, N.
Maximum-entropy meshfree method for compressible and near-incompressible elasticity Journal Article
In: Computer Methods in Applied Mechanics and Engineering, vol. 119, no. 25-28, pp. 1859-1871, 2010.
Abstract | Links | BibTeX | Tags: assumed strain, convex approximation, linear elasticity, maximum-entropy, meshfree methods, numerical integration, volumetric locking
@article{opsmem2010,
title = {Maximum-entropy meshfree method for compressible and near-incompressible elasticity},
author = {A. Ortiz and M.A. Puso and N. Sukumar},
url = {https://camlab.cl/wp-content/uploads/2024/06/mem.pdf},
doi = {10.1016/j.cma.2010.02.013},
year = {2010},
date = {2010-05-15},
urldate = {2010-05-15},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {119},
number = {25-28},
pages = {1859-1871},
abstract = {Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a locking-free small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum-entropy meshfree formulation.},
keywords = {assumed strain, convex approximation, linear elasticity, maximum-entropy, meshfree methods, numerical integration, volumetric locking},
pubstate = {published},
tppubtype = {article}
}
Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a locking-free small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum-entropy meshfree formulation.
2003
Donoso, J. R.; Ortiz, A.; Labbe, F.
Numerical evaluation of the effect of the weld metal on the constraint factor in bi-metal C(T) specimens Journal Article
In: Revista de Metalurgia, vol. 39, no. 5, pp. 357-366, 2003.
Abstract | Links | BibTeX | Tags: common format, constraint factor, elastic-plastic fracture, fracture toughness
@article{dolnee2003,
title = {Numerical evaluation of the effect of the weld metal on the constraint factor in bi-metal C(T) specimens},
author = {J.R. Donoso and A. Ortiz and F. Labbe},
url = {https://revistademetalurgia.revistas.csic.es/index.php/revistademetalurgia/article/view/348},
doi = {10.3989/revmetalm.2003.v39.i5.348},
year = {2003},
date = {2003-10-30},
urldate = {2003-10-30},
journal = {Revista de Metalurgia},
volume = {39},
number = {5},
pages = {357-366},
abstract = {The effect of the weld metal on the out-of-plane constraint in C(T) bi-material specimens was studied using the Common Format Equation (CEE) and its associated constraint factor, Ω*, as a function of the thickness-to-ligament ratio, B/b. The values of Ω* for one-material specimens (base metal) and bi-material specimens (base metal plus weld metal) were compared. The presence of weld metal lowers the degree of constraint in the bi-material specimens in relation to the base metal specimens, for a given B/b value. This effect is attenuated for deeply cracked specimens, the Ω* values being similar for the one-material and the bi-material specimens.},
keywords = {common format, constraint factor, elastic-plastic fracture, fracture toughness},
pubstate = {published},
tppubtype = {article}
}
The effect of the weld metal on the out-of-plane constraint in C(T) bi-material specimens was studied using the Common Format Equation (CEE) and its associated constraint factor, Ω*, as a function of the thickness-to-ligament ratio, B/b. The values of Ω* for one-material specimens (base metal) and bi-material specimens (base metal plus weld metal) were compared. The presence of weld metal lowers the degree of constraint in the bi-material specimens in relation to the base metal specimens, for a given B/b value. This effect is attenuated for deeply cracked specimens, the Ω* values being similar for the one-material and the bi-material specimens.
Papers in Conference Proceedings
2020
Torres, J.; Hitschfeld, N.; Ruiz, R. O.; Ortiz-Bernardin, A.
Convex Polygon Packing Based Meshing Algorithm for Modeling of Rock and Porous Media Proceedings
Computational Science – ICCS 2020. ICCS 2020. Lecture Notes in Computer Science, vol 12141. Springer, Cham, 2020.
Abstract | Links | BibTeX | Tags: computational geometry, geometric packing, polygonal meshes, virtual element method
@proceedings{throbcpp2020,
title = {Convex Polygon Packing Based Meshing Algorithm for Modeling of Rock and Porous Media},
author = {J. Torres and N. Hitschfeld and R. O. Ruiz and A. Ortiz-Bernardin},
editor = {Krzhizhanovskaya V. et al.},
doi = {10.1007/978-3-030-50426-7_20},
year = {2020},
date = {2020-06-15},
urldate = {2020-06-15},
publisher = {Computational Science – ICCS 2020. ICCS 2020. Lecture Notes in Computer Science, vol 12141. Springer},
address = {Cham},
abstract = {In this work, we propose new packing algorithm designed for the generation of polygon meshes to be used for modeling of rock and porous media based on the virtual element method. The packing problem to be solved corresponds to a two-dimensional packing of convex-shape polygons and is based on the locus operation used for the advancing front approach. Additionally, for the sake of simplicity, we decided to restrain the polygon rotation in the packing process. Three heuristics are presented to simplify the packing problem: density heuristic, gravity heuristic and the multi-layer packing. The decision made by those three heuristic are prioritizing on minimizing the area, inserting polygons on the minimum Y coordinate and pack polygons in multiple layers dividing the input in multiple lists, respectively. Finally, we illustrate the potential of the generated meshes by solving a diffusion problem, where the discretized domain consisted in polygons and spaces with different conductivities. Due to the arbitrary shape of polygons and spaces that are generated by the packing algorithm, the virtual element method was used to solve the diffusion problem numerically.},
keywords = {computational geometry, geometric packing, polygonal meshes, virtual element method},
pubstate = {published},
tppubtype = {proceedings}
}
In this work, we propose new packing algorithm designed for the generation of polygon meshes to be used for modeling of rock and porous media based on the virtual element method. The packing problem to be solved corresponds to a two-dimensional packing of convex-shape polygons and is based on the locus operation used for the advancing front approach. Additionally, for the sake of simplicity, we decided to restrain the polygon rotation in the packing process. Three heuristics are presented to simplify the packing problem: density heuristic, gravity heuristic and the multi-layer packing. The decision made by those three heuristic are prioritizing on minimizing the area, inserting polygons on the minimum Y coordinate and pack polygons in multiple layers dividing the input in multiple lists, respectively. Finally, we illustrate the potential of the generated meshes by solving a diffusion problem, where the discretized domain consisted in polygons and spaces with different conductivities. Due to the arbitrary shape of polygons and spaces that are generated by the packing algorithm, the virtual element method was used to solve the diffusion problem numerically.
2014
Meruane, V.; del Fierro, V.; Ortiz-Bernardin, A.
Proceedings of the Twelfth International Conference on Computational Structures Technology, Civil-Comp Press, Stirlingshire, UK, no. 120, 2014, ISSN: 1759-3433.
Abstract | Links | BibTeX | Tags: damage assessment, debonding, honeycomb, maximum-entropy, Sandwich structures
@proceedings{mdobmesl2014,
title = {A maximum entropy supervised learning algorithm for the identification of skin/core debonding in honeycomb aluminium panels},
author = {V. Meruane and V. del Fierro and A. Ortiz-Bernardin},
editor = {B.H.V. Topping and P. Iványi},
url = {https://camlab.cl/wp-content/uploads/2024/06/maxent_honeycomb_CST2014.pdf},
doi = {10.4203/ccp.106.120},
issn = {1759-3433},
year = {2014},
date = {2014-09-05},
urldate = {2014-09-05},
issuetitle = {Proceedings of the Twelfth International Conference on Computational Structures Technology},
number = {120},
publisher = {Proceedings of the Twelfth International Conference on Computational Structures Technology, Civil-Comp Press},
address = {Stirlingshire, UK},
abstract = {Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, due to manufacturing defects or impact loads, these structures can be subject to imperfect bonding or debonding between the skin and the honeycomb core. The presence of debonding reduces the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This paper presents a new supervised learning algorithm to identify debonded regions in aluminium honeycomb panels. The algorithm uses a linear approximation method handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of neural networks. The honeycomb panels are modelled with finite elements using a simplified three-panel shell model. The adhesive layer between the skin and core is modelled using linear springs, the rigidities of which are reduced in debonded sectors. The algorithm is validated using experimental data of an aluminium honeycomb panel under different damage scenarios.},
keywords = {damage assessment, debonding, honeycomb, maximum-entropy, Sandwich structures},
pubstate = {published},
tppubtype = {proceedings}
}
Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, due to manufacturing defects or impact loads, these structures can be subject to imperfect bonding or debonding between the skin and the honeycomb core. The presence of debonding reduces the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This paper presents a new supervised learning algorithm to identify debonded regions in aluminium honeycomb panels. The algorithm uses a linear approximation method handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of neural networks. The honeycomb panels are modelled with finite elements using a simplified three-panel shell model. The adhesive layer between the skin and core is modelled using linear springs, the rigidities of which are reduced in debonded sectors. The algorithm is validated using experimental data of an aluminium honeycomb panel under different damage scenarios.
Meruane, V.; Ortiz-Bernardin, A.
Vibration-based damage assessment using linear approximation with maximum entropy Proceedings
Proceedings of Pan-American Congress of Applied Mechanics - PACAM XIV, 2014.
Abstract | Links | BibTeX | Tags: linear approximation, maximum-entropy, Structural damage assessment, supervised learning algorithms
@proceedings{mobvbda2014,
title = {Vibration-based damage assessment using linear approximation with maximum entropy},
author = {V. Meruane and A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/vmeruane_aortiz_PACAMXIV.pdf},
year = {2014},
date = {2014-03-28},
urldate = {2014-03-28},
issuetitle = {Proceedings of Pan-American Congress of Applied Mechanics - PACAM XIV},
publisher = {Proceedings of Pan-American Congress of Applied Mechanics - PACAM XIV},
abstract = {Supervised learning algorithms have been proposed as a suitable alternative to model updating methods in vibration-based damage assessment, being Artificial Neural Networks the most frequently used. Notwithstanding, the slow learning speed and the large number of parameters that need to be tuned within the training stage have been a major bottleneck in their application. This article presents a new supervised learning algorithm for real-time damage assessment that uses a linear approximation method in conjunction with vibration characteristics measured from the damaged structure. The linear approximation is handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of Neural Networks. The performance of the proposed methodology is validated by considering two experimental structures: an eight-degree-of-freedom (DOF) mass-spring system and an exhaust system of a car},
keywords = {linear approximation, maximum-entropy, Structural damage assessment, supervised learning algorithms},
pubstate = {published},
tppubtype = {proceedings}
}
Supervised learning algorithms have been proposed as a suitable alternative to model updating methods in vibration-based damage assessment, being Artificial Neural Networks the most frequently used. Notwithstanding, the slow learning speed and the large number of parameters that need to be tuned within the training stage have been a major bottleneck in their application. This article presents a new supervised learning algorithm for real-time damage assessment that uses a linear approximation method in conjunction with vibration characteristics measured from the damaged structure. The linear approximation is handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of Neural Networks. The performance of the proposed methodology is validated by considering two experimental structures: an eight-degree-of-freedom (DOF) mass-spring system and an exhaust system of a car
Unpublished Documents
2020
Ortiz-Bernardin, A.
Primeros Pasos en el Método del Elemento Finito: Teoría e Implementación en Una Dimensión Unpublished
2020.
Links | BibTeX | Tags: finite element method
@unpublished{obppmef2020,
title = {Primeros Pasos en el Método del Elemento Finito: Teoría e Implementación en Una Dimensión},
author = {A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/primeros_pasos_mef1d_rev4.pdf},
year = {2020},
date = {2020-05-03},
urldate = {2020-05-03},
keywords = {finite element method},
pubstate = {published},
tppubtype = {unpublished}
}
2017
Ortiz-Bernardin, A.
Precauciones acerca del uso del elemento beam en simulaciones por el método del elemento finito Unpublished
2017.
Links | BibTeX | Tags: finite element method
@unpublished{obbeam2017,
title = {Precauciones acerca del uso del elemento beam en simulaciones por el método del elemento finito},
author = {A. Ortiz-Bernardin},
url = {https://camlab.cl/wp-content/uploads/2024/06/precauciones_elemento_beam.pdf},
year = {2017},
date = {2017-01-06},
urldate = {2017-01-06},
keywords = {finite element method},
pubstate = {published},
tppubtype = {unpublished}
}
Doctoral Dissertation
2011
Ortiz, AA.
Maximum-Entropy Meshfree Method for Linear and Nonlinear Elasticity PhD Thesis
Office of Graduate Studies, University of California, Davis, California, 2011.
Abstract | Links | BibTeX | Tags: linear elasticity, maximum-entropy, meshfree methods, Nonlinear elasticity, nonlinear finite elements
@phdthesis{omem2011,
title = {Maximum-Entropy Meshfree Method for Linear and Nonlinear Elasticity},
author = {AA. Ortiz},
url = {https://camlab.cl/wp-content/uploads/2024/06/aortiz_phd_dissertation.pdf},
year = {2011},
date = {2011-01-05},
urldate = {2011-01-05},
school = {Office of Graduate Studies, University of California, Davis, California},
abstract = {A Galerkin-based maximum-entropy meshfree method for linear and nonlinear elastic media is developed. The standard displacement-based Galerkin formulation is used to model compressible linear elastic solids, whereas the classical u-p mixed formulation for near-incompressible linear elastic media is adopted to formulate a volume-averaged nodal technique in which the pressure variable is eliminated from the analysis. This results in a single-field formulation that is devoid of volumetric locking. A modified Gauss integration technique that alleviates integration errors in meshfree methods with guaranteed patch test satisfaction to machine precision is devised. The performance of the maximum-entropy meshfree method is assessed for problems in compressible and near-incompressible linear elastic media using three-node triangular and four-node tetrahedral background meshes. Both structured and unstructured meshes are considered to assess the accuracy, performance and stability of the maximum-entropy meshfree method by means of various numerical experiments, which include patch tests, bending dominated problem, combined bending-shear problem, rigid indentation, Stokes flow and numerical stability tests.
An extension of the volume-averaged nodal technique is proposed for the analysis of near-incompressible nonlinear elastic solids in two dimensions. In the nonlinear version, the volume change ratio of the dilatational constraint, namely J, is volume-averaged around nodes leading to a locking-free displacement-based formulation. The excellent performance of the maximum-entropy meshfree method for problems in near-incompressible nonlinear elastic solids is demonstrated via three standard two-dimensional numerical experiments—a combined bending-shear problem, a plane strain compression of a rubber block and a frictionless indentation problem. Three-node structured and unstructured triangular background meshes are employed and the results are compared to two finite element methods that use such meshes, namely, the linear displacement/constant pressure triangle and the linear displacement/linear pressure triangle enriched with a displacement bubble node (MINI element). The two-dimensional nonlinear simulations reveal that the maximum-entropy meshfree method effectively improves the poor performance of linear triangular meshes in the analysis of near-incompressible solids at finite strains.},
keywords = {linear elasticity, maximum-entropy, meshfree methods, Nonlinear elasticity, nonlinear finite elements},
pubstate = {published},
tppubtype = {phdthesis}
}
A Galerkin-based maximum-entropy meshfree method for linear and nonlinear elastic media is developed. The standard displacement-based Galerkin formulation is used to model compressible linear elastic solids, whereas the classical u-p mixed formulation for near-incompressible linear elastic media is adopted to formulate a volume-averaged nodal technique in which the pressure variable is eliminated from the analysis. This results in a single-field formulation that is devoid of volumetric locking. A modified Gauss integration technique that alleviates integration errors in meshfree methods with guaranteed patch test satisfaction to machine precision is devised. The performance of the maximum-entropy meshfree method is assessed for problems in compressible and near-incompressible linear elastic media using three-node triangular and four-node tetrahedral background meshes. Both structured and unstructured meshes are considered to assess the accuracy, performance and stability of the maximum-entropy meshfree method by means of various numerical experiments, which include patch tests, bending dominated problem, combined bending-shear problem, rigid indentation, Stokes flow and numerical stability tests.
An extension of the volume-averaged nodal technique is proposed for the analysis of near-incompressible nonlinear elastic solids in two dimensions. In the nonlinear version, the volume change ratio of the dilatational constraint, namely J, is volume-averaged around nodes leading to a locking-free displacement-based formulation. The excellent performance of the maximum-entropy meshfree method for problems in near-incompressible nonlinear elastic solids is demonstrated via three standard two-dimensional numerical experiments—a combined bending-shear problem, a plane strain compression of a rubber block and a frictionless indentation problem. Three-node structured and unstructured triangular background meshes are employed and the results are compared to two finite element methods that use such meshes, namely, the linear displacement/constant pressure triangle and the linear displacement/linear pressure triangle enriched with a displacement bubble node (MINI element). The two-dimensional nonlinear simulations reveal that the maximum-entropy meshfree method effectively improves the poor performance of linear triangular meshes in the analysis of near-incompressible solids at finite strains.
An extension of the volume-averaged nodal technique is proposed for the analysis of near-incompressible nonlinear elastic solids in two dimensions. In the nonlinear version, the volume change ratio of the dilatational constraint, namely J, is volume-averaged around nodes leading to a locking-free displacement-based formulation. The excellent performance of the maximum-entropy meshfree method for problems in near-incompressible nonlinear elastic solids is demonstrated via three standard two-dimensional numerical experiments—a combined bending-shear problem, a plane strain compression of a rubber block and a frictionless indentation problem. Three-node structured and unstructured triangular background meshes are employed and the results are compared to two finite element methods that use such meshes, namely, the linear displacement/constant pressure triangle and the linear displacement/linear pressure triangle enriched with a displacement bubble node (MINI element). The two-dimensional nonlinear simulations reveal that the maximum-entropy meshfree method effectively improves the poor performance of linear triangular meshes in the analysis of near-incompressible solids at finite strains.