Stabilization‐free virtual element method for 2D elastoplastic problems

In this paper, a novel first‐ and second‐order stabilization‐free virtual element method is proposed for two‐dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2024-08, Vol.125 (15), p.n/a
Main Authors: Xu, Bing‐Bing, Wang, Yi‐Fan, Wriggers, Peter
Format: Article
Language:English
Subjects:
Elastoplasticity
nonlinear
Nonlinear response
plasticity
Stabilization
stabilization‐free
Strain
virtual element method
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Summary:In this paper, a novel first‐ and second‐order stabilization‐free virtual element method is proposed for two‐dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher‐order L2$$ {L}_2 $$ projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization‐free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. J2$$ {J}_2 $$ plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization‐free virtual element method.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.7490