Phase-field cohesive zone modeling of multi-physical fracture in solids and the open-source implementation in Comsol Multiphysics

Despite the popularity of phase-field models for fracture in purely mechanical problems, their application to the modeling of fracture in multi-physics problems is much less reported. This might be attributed, on the one hand, to the theoretical complexity involved in multi-physical phenomena, and on the other hand, to the cumbersome implementation of these coupled models in home-made platforms. In this work, the phase-field cohesive zone model (PF-CZM) is adopted as the prototype model to address fracture in various multi-physics problems, e.g., the thermo-mechanical, chemo-mechanical, chemo-thermo-mechanical, electro-mechanical, etc. The relevant theoretical and numerical aspects are categorized into modular structures, and the open-source implementations in the software platform Comsol Multiphysics are presented in details. In order to validate the PF-CZM for fracture in multi-physics problems and its numerical implementation, a number of representative benchmark examples are considered. Not only the qualitative crack patterns but also the quantitative global responses are compared against available experimental test data. It is found that the typical characteristics of fracture in all the considered multi-physics problems are well captured. Moreover, as in the purely mechanical counterpart, the predicted crack pattern and global responses are insensitive to the phase-field length scale, making the PF-CZM promising for modeling fracture in other more involved multi-physics problems.