A Node-Based Uniform Strain Virtual Element Method for Elastic and Inelastic Small Deformation Problems
- Post by: alejandro
- 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 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. The proposed technique is referred to 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 state and history-dependent variables become nodal quantities just like displacements, which facilitates their tracking and postprocessing. Some benchmark problems will be presented to demonstrate that the NVEM is accurate, optimally convergent, and devoid of volumetric locking.
Keywords: virtual element method, nodal integration, strain averaging, uniform strain, linear elasticity, elastoplasticity, volumetric locking.
References
[1] M. A. Puso, J. S. Chen, E. Zywicz, W. Elmer. Meshfree and finite element nodal integration methods. International Journal for Numerical Methods in Engineering. 74(3): 416–446, 2008.
[2] L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini, A. Russo. Basic principles of virtual element methods. Mathematical Models and Methods in Applied Sciences, 23(01):199–214, 2013.
a Department of Mechanical Engineering, Universidad de Chile, Av. Beauchef 851, Santiago 8370456, Chile