Enhanced Brittle Fracture Modeling in Heterogeneous Materials: A Variational Phase Field Approach Integrating XFEM and Level-Set Methods

Crack initiation and propagation analysis in brittle two-dimensional isotropic materials are conducted using the damage Phase Field Method (PFM) following the variational approach. Here, we study two-dimensional (2D) structures that contain material heterogeneities (e.g., interfaces and inclusions) as well as geometric ones (e.g., cracks and voids) when subjected to quasi-static uniaxial tensile loading. The adopted methodology combines Extended Finite Element Method (XFEM) and Level-Set couple with PFM in order to investigate both the case of heterogeneous materials (composite or porous) as well as the case of interfacial cracks between two different materials for their interest and relevance as practical examples. Among many others, one can, for example, argue that: (a) the regular hexagonal arrangement of heterogeneities leads to a significantly higher strength than any random arrangement, for both the composite material (containing fibers) and the porous material (containing voids), (b) the effects of contrasting stiffness and toughness between two materials along with their respective impacts on the interfacial crack trajectory, on energy balance and on reaction force are in favor of toughness.