Self-stabilized virtual element modeling of 2D mixed-mode cohesive crack propagation in isotropic elastic solids

Abstract

A comprehensive strategy for the simulation of mixed-mode cohesive crack propagation in a mesh of originally self-stabilized Virtual Elements (VEs) is proposed. Exploiting the VEs substantial insensitivity to mesh distortion, the propagating cohesive crack is accommodated within existing self-stabilized first-order quadrilateral VEs by simply adding new edges separated by a cohesive interface. The added edges make however the VE unstable and a new procedure for the stabilization of initially stable VE is developed. The method is formulated within a recently proposed Hu–Washizu variational framework, allowing for a higher order, independent modeling of stresses. In this way, a more accurate estimate of the stress at the tip of the cohesive process zone can be achieved allowing for a more accurate assessment of crack propagation conditions and direction. The proposed method is validated by application to several benchmark problems.