TY - JOUR
T1 - Some basic formulations of the virtual element method (VEM) for finite deformations
AU - Chi, H.
AU - da Veiga, L. Beirão
AU - Paulino, G. H.
N1 - Funding Information:
HC and GHP acknowledge support from the US National Science Foundation (NSF) under Grant CMMI #1624232 (formerly #1437535). LBV was partially supported by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant Agreement No. 681162). This support is gratefully acknowledged. The information presented in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agencies.
Publisher Copyright:
© 2016 The Authors
PY - 2017/5/1
Y1 - 2017/5/1
N2 - We present a general virtual element method (VEM) framework for finite elasticity, which emphasizes two issues: element-level volume change (volume average of the determinant of the deformation gradient) and stabilization. To address the former issue, we provide exact evaluation of the average volume change in both 2D and 3D on properly constructed local displacement spaces. For the later issue, we provide a new stabilization scheme that is based on the trace of the material tangent modulus tensor, which captures highly heterogeneous and localized deformations. Two VEM formulations are presented: a two-field mixed and an equivalent displacement-based, which is free of volumetric locking. Convergence and accuracy of the VEM formulations are verified by means of numerical examples, and engineering applications are demonstrated.
AB - We present a general virtual element method (VEM) framework for finite elasticity, which emphasizes two issues: element-level volume change (volume average of the determinant of the deformation gradient) and stabilization. To address the former issue, we provide exact evaluation of the average volume change in both 2D and 3D on properly constructed local displacement spaces. For the later issue, we provide a new stabilization scheme that is based on the trace of the material tangent modulus tensor, which captures highly heterogeneous and localized deformations. Two VEM formulations are presented: a two-field mixed and an equivalent displacement-based, which is free of volumetric locking. Convergence and accuracy of the VEM formulations are verified by means of numerical examples, and engineering applications are demonstrated.
KW - Filled elastomers
KW - Finite elasticity
KW - Mixed variational principle
KW - Virtual element method (VEM)
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U2 - 10.1016/j.cma.2016.12.020
DO - 10.1016/j.cma.2016.12.020
M3 - Article
AN - SCOPUS:85012104108
SN - 0374-2830
VL - 318
SP - 148
EP - 192
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -