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

- General Virtual Element Method (VEM) framework for finite elasticity.
- The VEM displacement spaces allow exact computation of element-level volume changes.
- New stabilization term captures large and highly localized deformations.
- Convergence and accuracy of the VEM are verified.
- An engineering application of the VEM is demonstrated.

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.