Virtual Element Method: an equilibrium-based stress recovery procedure

TL;DR

This paper introduces an equilibrium-based stress recovery procedure within the Virtual Element Method to improve stress field accuracy in plane elasticity problems, using a simple and efficient approach validated by numerical tests.

Contribution

It presents a novel stress recovery method based on Compatibility in Patches that enhances stress accuracy in VEM without complex modifications.

Findings

Improved stress field accuracy demonstrated in numerical tests.

The method is simple to implement in existing VEM codes.

Enhanced stress recovery for complex polygonal elements.

Abstract

Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable operator which maps to the strain field is introduced in order to allow the calculation of the stiffness matrix. The stress field is then computed using that strian field, by using the constitutive law. Considering for example a first-order formulation for a homogeneous material, strains are locally mapped onto constant functions, and stresses are accordingly piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons which are not triangles. In this paper, Recovery by Compatibility in Patches is used in order to mitigate such an effect and, thus, enhance the accuracy of the recovered stress field. The procedure is simple, efficient and can be readily implemented in existing codes. Numerical tests confirm the soundness of the proposed approach.