Nonlocal stress and J-integral approaches for cohesive crack growth within enhanced DodeQuad virtual element

Abstract

The aim of this paper is to present a numerical procedure for reproducing the crack growth in two-dimensional (2D) cohesive solids. Two approaches are proposed to determine the direction of crack propagation. One approach is based on the evaluation of the nonlocal stress around the tip of the fracture, while the other on the computation of the J-integral. Once the direction of crack propagation has been determined, a cohesive interface is introduced. The crack evolution is performed by developing a new 12-node quadrilateral enhanced virtual element (VE), denoted as DodeQuad, presenting three different formulations of the element. The new VE is characterized by features that make it particularly suitable for reproducing the crack growth, including its stabilization-free nature, its high degree of accuracy in determining the strain and stress fields, its suitability for the J-integral evaluation, and its ability to define a numerical procedure that does not require the variation of the number of nodes and degrees of freedom during the analysis. This leads to a minimal remeshing requirement for crack propagation. To illustrate the performance of the developed numerical procedure, some numerical applications are performed, including comparisons with available experimental evidence and with other numerical techniques.