From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials

Abstract Failure of quasi-brittle materials is governed by crack formation and propagation which can be characterized by two phases: (i) diffuse material degradation process with initial crack formation and (ii) severe localization of damage leading to the propagation of large cracks and fracture. While continuum damage mechanics provides an excellent framework to describe the first failure phase, it is unable to represent discontinuous displacement fields. In sharp contrast, cohesive zone models are poorly suited for describing diffuse damage but can accurately resolve discrete cracks. In this manuscript, we propose a coupled continuous/discontinuous approach to model the two failure phases of quasi-brittle materials in a coherent way. The proposed approach involves an integral-type nonlocal continuum damage model coupled with an extrinsic discrete interface model. The transition from diffuse damage to macroscopic cohesive cracks is made through an equivalent thermodynamic framework established in multidimensional settings, in which the dissipated energy is computed numerically and weakly matched. The method is implemented within the extended finite element framework, which allows for crack propagation without remeshing. A few benchmark problems involving straight and curved cracks are investigated to demonstrate the applicability and robustness of the coupled XFEM cohesive-damage approach. Force–displacement responses, as well as predicted propagation paths, are presented and shown to be in close agreement with available experimental data. Furthermore, the method is found to be insensitive to various damage threshold values for damage–crack transition, yielding energetically consistent results.