A coupled FEM-VEM approach for crack tracking in quasi-brittle materials

The numerical simulation of crack propagation in quasi-brittle materials has historically been mainly faced by means of consolidated approaches in the framework of the finite element method (FEM). However, the very recently developed virtual element method (VEM) is a new promising technique whose strong point is the possibility to model polygonal meshes, characterized by any number of edges. This paper proposes a new approach, coupling FEM and VEM for crack tracking in quasi-brittle materials. In these materials, diffuse degradation is followed by high deformation bands localizing in certain regions of the structure. To best exploit the potentialities of FEM and VEM, in this work the structure is initially entirely modeled through a FEM mesh. Then, when a diffuse damage meets the requirements for a localized band formation, the involved finite elements are converted into virtual sub-elements among which a thin layer is introduced. The thin layer is modeled through interphase (IPH) elements, which are advanced mechanical devices with respect to the common interface elements since internal strains and stresses are added to the contact ones. The portion of the structure modeled using VEs and IPHs is called substructure. Structure and substructure are solved through two nested iterative procedures. The proposed numerical and crack tracking strategy are illustrated in detail and the results on three benchmark examples show its applicability as an alternative strategy to the full FEM approach.