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A Node-Based Uniform Strain Virtual Element Method for Elastoplastic Solids

  • January 9, 2024
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A talk given by A. Ortiz-Bernardin at COMPLAS 2023, September 6, 2023, Barcelona, Spain. A NODE-BASED UNIFORM STRAIN VIRTUAL ELEMENT METHOD FOR ELASTOPLASTIC SOLIDS A. ORTIZ-BERNARDIN a and Edoardo Artioli b Abstract. This work presents our recent advances on developing the extension of the node-based uniform strain virtual element method (NVEM) [1] to elastoplastic applications.

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A Node-Based Uniform Strain Virtual Element Method for Elastic and Inelastic Small Deformation Problems

  • December 16, 2022
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A talk given by A. Ortiz-Bernardin at CSFWGBC 2022, June 2, 2022, Ascona, Switzerland. A NODE-BASED UNIFORM STRAIN VIRTUAL ELEMENT METHOD FOR ELASTIC AND INELASTIC SMALL DEFORMATION PROBLEMS A. ORTIZ-BERNARDIN a Abstract. A combined nodal integration and virtual element method is presented for elastic and inelastic small deformation problems, wherein the strain is averaged at

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Accepted Paper: A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity

  • December 16, 2022
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Paper Accepted for Publication in International Journal for Numerical Methods in Engineering A. Ortiz-Bernardin, R. Silva-Valenzuela, S. Salinas-Fernández, N. Hitschfeld-Kahler, S. Luza, B. Rebolledo, “A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity” ABSTRACT We propose a combined nodal integration and virtual element method for compressible and nearly incompressible elasticity, wherein the strain is averaged at the

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A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity

  • December 16, 2022
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International Journal for Numerical Methods in EngineeringVol. 124, No. 8, pp. 1818-1855, 2023 A. Ortiz-Bernardin, R. Silva-Valenzuela, S. Salinas-Fernández, N. Hitschfeld-Kahler, S. Luza, B. Rebolledo 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

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Development and assessment of a combined nodal integration and virtual element method for small and large deformation solid mechanics simulations

  • June 20, 2022
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2022 – 2025 Principal Investigator: Alejandro Ortiz-Bernardin. Project funded by ANID-FONDECYT (Grant Nº 1221325) Nodal integration is a numerical integration scheme for Galerkin weak forms, where the weak form integrals are sampled at the nodes. In this type of scheme, state and history-dependent variables become nodal quantities and thus in nonlinear computations they are tracked only

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A Meshfree Nodal Integration Method for Elastic and Elastoplastic Applications Using The Virtual Element Decomposition

  • December 23, 2019
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A talk given by A. Ortiz-Bernardin at COMPLAS 2019, September 3, 2019, Barcelona, Spain. A MESHFREE NODAL INTEGRATION METHOD FOR ELASTIC AND ELASTOPLASTIC APPLICATIONS USING THE VIRTUAL ELEMENT DECOMPOSITION A. ORTIZ-BERNARDIN a, E. ARTIOLI b, AND R. SILVA-VALENZUELA a Abstract. In meshfree Galerkin methods to solve partial differential equations, a cloud of nodes is used

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Sample of two-dimensional nodal cells used in nodal integration

Accepted Paper: A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition

  • December 18, 2019
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Paper Accepted for Publication in International Journal for Numerical Methods in Engineering R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli,  N. Hitschfeld-Kahler, “A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition” ABSTRACT In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical

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Sample of two-dimensional nodal cells used in nodal integration

A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition

  • December 18, 2019
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International Journal for Numerical Methods in Engineering Vol. 121, No. 10, pp. 2174-2205, 2020 R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli,  N. Hitschfeld-Kahler 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

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The Virtual Element Decomposition: A New Paradigm for Developing Nodal Integration Schemes for Meshfree Galerkin Methods

  • January 24, 2019
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A talk given by A. Ortiz-Bernardin at WONAPDE 2019, January 22, 2019, Concepción, Chile. THE VIRTUAL ELEMENT DECOMPOSITION: A NEW PARADIGM FOR DEVELOPING NODAL INTEGRATION SCHEMES FOR MESHFREE GALERKIN METHODS R. SILVA-VALENZUELA a, A. ORTIZ-BERNARDIN a, N. SUKUMAR b AND E. ARTIOLI c Abstract. In meshfree Galerkin methods to solve partial differential equations, a cloud of nodes

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Enhancing the robustness of meshfree Galerkin methods for solid mechanics simulations using the virtual element decomposition

  • October 11, 2018
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2018 – 2021 Principal Investigator: Alejandro Ortiz-Bernardin. Project funded by CONICYT-FONDECYT (Grant Nº 1181192) Meshfree methods have several attributes that make them attractive for simulation in mechanics. Two important ones are summarized as follows. The meshfree approximation is independent of the definition of a finite element mesh — the approximation is constructed based solely on nodal locations.

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