Extended virtual element method for two-dimensional linear elastic fracture

In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is extension of the standard (VEM), facilitates mesh-independent modeling crack discontinuities and crack-tip singularities on general polygonal meshes. For fracture in X-VEM, virtual element space augmented by additional basis functions that are constructed multiplying suitable enrichment fields, such as asymptotic mixed-mode solutions. The design X-VEM requires extended projector maps lying onto a set spanned polynomials fields. An efficient scheme to compute stress intensity factors using domain form interaction integral described. formulation permits integration weakly singular be performed over boundary edges element. Numerical experiments conducted benchmark problems demonstrate sound accuracy optimal convergence energy proposed formulation.