The incorporation of mesh quality in the stabilization of virtual element methods for nonlinear elasticity

This work constitutes a further contribution to developing convergent, locking-free virtual element formulations for problems of large-deformation nonlinear elasticity. Earlier work by the authors and others has introduced simple and effective forms of stabilization. This work investigates the approximation properties of the virtual element method for problems with domains having a high aspect ratio, and for alternative forms of stabilization: an existing approach, and two modifications, which account for high element aspect ratio and element distortion. The results in all cases demonstrate the locking-free convergence of the approach, with the newer modifications leading to improvements in accuracy. •A lowest-order displacement-based VEM is formulated for linear- and hyper-elasticity.•A novel approach to the scaling of the stabilization term is proposed and evaluated.•The scaling accounts for the aspect ratio and the degree of element distortion.•The proposed method exhibits superior performance to the standard VEM formulation.•The well-known locking-free behaviour of the lowest-order VEM is preserved.