TY - JOUR

T1 - A low order 3D virtual element formulation for finite elasto–plastic deformations

AU - Hudobivnik, Blaž

AU - Aldakheel, Fadi

AU - Wriggers, Peter

N1 - Funding information: The corresponding author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable simulation techniques in solid mechanics: development of non-standard discretization methods, mechanical and mathematical analysis” under the project WR 19/50-1. The second author gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the Priority Program SPP 2020 under the project WR 19/58-1.

PY - 2019/2/15

Y1 - 2019/2/15

N2 - This work addresses an efficient low order 3D virtual element method for elastic–plastic solids undergoing large deformations. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The successful application of the method to non-linear problems such as finite strain elasticity and plasticity in 2D leads naturally to the question of its effectiveness and robustness in the third dimension. This work is concerned with the extensions of the virtual element method to problems of 3D finite strain plasticity. Low-order formulations for problems in three dimensions, with elements being arbitrary shaped polyhedra, are considered. The formulation is based on minimization of a pseudo energy expression, with a generalization of a stabilization techniques, introduced for two dimensional polygons, to the three-dimensional domain. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties. For comparison purposes, results of the standard finite element method are also demonstrated.

AB - This work addresses an efficient low order 3D virtual element method for elastic–plastic solids undergoing large deformations. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The successful application of the method to non-linear problems such as finite strain elasticity and plasticity in 2D leads naturally to the question of its effectiveness and robustness in the third dimension. This work is concerned with the extensions of the virtual element method to problems of 3D finite strain plasticity. Low-order formulations for problems in three dimensions, with elements being arbitrary shaped polyhedra, are considered. The formulation is based on minimization of a pseudo energy expression, with a generalization of a stabilization techniques, introduced for two dimensional polygons, to the three-dimensional domain. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties. For comparison purposes, results of the standard finite element method are also demonstrated.

KW - Finite strain plasticity

KW - Stabilization

KW - Three-dimensional

KW - Virtual element method VEM

UR - http://www.scopus.com/inward/record.url?scp=85049079975&partnerID=8YFLogxK

U2 - 10.1007/s00466-018-1593-6

DO - 10.1007/s00466-018-1593-6

M3 - Article

AN - SCOPUS:85049079975

VL - 63

SP - 253

EP - 269

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

IS - 2

ER -