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We propose a combined nodal integration and virtual element method forcompressible and nearly incompressible elasticity, wherein the strain isaveraged at the nodes from the strain of surrounding virtual elements. For thestrain averaging procedure, a nodal averaging operator is constructed using ageneralization to virtual elements of the node-based uniform strain approachfor finite elements. We refer to the proposed technique as the node-baseduniform strain virtual element method (NVEM). No additional degrees of freedomare introduced in this approach, thus resulting in a displacement-basedformulation. A salient feature of the NVEM is that the stresses and strainsbecome nodal variables just like displacements, which can be exploited innonlinear simulations. Through several benchmark problems in compressible andnearly incompressible elasticity as well as in elastodynamics, we demonstratethat the NVEM is accurate, optimally convergent and devoid of volumetriclocking.

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