Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 318, Issue -, Pages 148-192Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.12.020
Keywords
Virtual element method (VEM); Finite elasticity; Mixed variational principle; Filled elastomers
Funding
- US National Science Foundation (NSF) [162423, 1437535]
- European Research Council (ERC) under the European Unions Horizon research and innovation programme [681162]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1624232] Funding Source: National Science Foundation
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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. (C) 2016 The Authors. Published by Elsevier B.V.
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