A FEM-VEM crack tracking algorithm using the Desmorat’s anisotropic damage model

When a structure or a specimen is subjected to loading up to failure, strains localize in narrow bands leading to the formation of macroscopic cracks. The nucleation and propagation of fractures, even in isotropic media, can induce anisotropy and guide the fracture towards directions different from the corresponding isotropic damage model. From a computational standpoint, the accurate simulation of fracture in isotropic and anisotropic media remains challenging, especially when complex crack paths and distorted meshes are involved. In this work, a numerical strategy for the simulation of crack initiation and propagation in isotropic quasi-brittle materials is proposed within the framework of the Virtual Element Method (VEM), employing Desmorat’s anisotropic damage model. The approach builds upon a continuum damage description with anisotropic damage variables, capable of capturing direction-dependent stiffness degradation and strain localization. Crack onset is detected through localization criteria based on the concept of critical damage, while crack orientation emerges from the spectral analysis of a fracture tensor. Once localization is detected, discontinuities are represented through interphase elements, allowing the transition from a continuous to a discontinuous description without remeshing. The use of VEM enables flexible handling of polygonal sub-elements generated during crack evolution, ensuring numerical robustness even in the presence of highly distorted geometries. The global equilibrium problem is iteratively solved by accounting for the internal forces arising from the anisotropic damaged substructures. Benchmark examples are presented to illustrate the effectiveness of the method in capturing anisotropic fracture patterns.