Virtual Element Method: an equilibrium-based stress recovery procedure
For researchers using VEM in computational mechanics, this provides a simple and efficient method to improve stress accuracy, though it is an incremental improvement over existing techniques.
The paper addresses the problem of inaccurate stress evaluation in displacement-based Virtual Element Method (VEM) for plane elasticity. It proposes a recovery procedure based on compatibility in patches to enhance stress accuracy, with numerical tests confirming its effectiveness.
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.