A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity

Abstract

We propose a displacement-based approach to solve problems in compressible and nearly incompressible plane elasticity that combines a nodal integration technique and the virtual element method (VEM), wherein the strain is averaged around nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements.We refer to these new elements as node-based uniform strain virtual elements (NVEM). A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations thereby providing room for further development of this novel approach. Through several benchmark problems in plane elasticity, we demonstrate that the NVEM is accurate and optimally convergent, and devoid of volumetric locking in the nearly incompressible limit.