Some basic formulations of the virtual element method (VEM) for finite deformations

By Heng Chi, L. Beirão da Veiga, Glaucio H. Paulino. 2017

191 citations recorded by the source corpus.

Abstract 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.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/303d608c7f82548f577f3acbe0b2677d4d908bb2

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions (2018, background): “We here mention, in addition to the ones above, a sample of papers [1, 9, 18, 4, 12, 16, 26, 22] and refer to [24] for a more complete survey of the existing VEM literature.”
A low order 3D virtual element formulation for finite elasto–plastic deformations (2017, methodology): “The use of VEM for nonlinear problems has been discussed recently in [6] for inelastic materials at small strains and in [7,8] for hyperelastic materials at finite deformations as well as in [9] for two-dimensional deformations at finite plastic strains and in [10,11] for anisotropic materials at”