Enriched virtual elements for plane elasticity with corner singularities

We construct a nonconforming virtual element method for the approximation of singular solutions to isotropic linear elasticity problems on polygonal domains. Standard nonconforming virtual element spaces are enriched with suitable singular functions. The enrichment is based on the nonconforming structure of the discrete spaces and not on partition of unity techniques. We prove optimal convergence and assess numerically the theoretical results of the method. The proposed scheme naturally paves the way for an efficient linear elastic fracture solver.