Interface material failure modeled by the extended finite-element method and level sets

Multi-phase materials are characterized by the fact that they possess a specific heterogeneous microstructure. This feature often necessitates complex formulations in order to obtain realistic mechanical behavior with macroscopic material models. Furthermore, such complex models cause substantial difficulties when the corresponding material parameters need to be identified and their physical meaning interpreted. In multiscale analyses, usually the microstructure of a material point is resolved directly. Thus, the material behavior at the material point can be modeled in an elegant, natural and simple way. The present contribution aims at a detailed geometric modeling of multi-phase materials, as well as at a local mechanical modeling of material interfaces and interfacial failure. The geometry of the material distribution within the microstructure is described through level set functions. The mechanical modeling of material interfaces and interfacial cracks is accomplished by the extended finite-element method (X-FEM). The combination of both, the level set method and the X-FEM, allows one to model such internal features of the microstructure without the adaptation of the mesh. Thus, expensive meshing procedures can be avoided and considerable flexibility is obtained with respect to the variation of the material design. In the X-FEM, the finite-element approximation is enriched by appropriate functions through the concept of partition of unity. Remarkably, the level set method cannot only be applied to describe the geometry of the material interfaces and cracks, respectively, but also to support and even to develop the corresponding enrichment function.