Modeling quasi-static and dynamic thermo-elastic coupled brittle fracture using an adaptive isogeometric hybrid phase-field method

Thermal shocks are ubiquitous in engineering applications. Due to the multi-field nature, numerical simulation of thermally induced cracking and subsequent propagation is challenging. Thanks to the recent introduction of variational phase-field model of fracture, it is now possible to numerically model the complex behavior of damage nucleation, growth, bifurcation and coalescence within one unified framework. Despite its popularity, one of the difficulties that hinder its practical application is the heavy computational requirement. In this paper, we propose a space adaptive framework based on locally refined non-uniform rational B-splines (LR NURBS) with generalized-α method for temporal discretization for studying the crack growth in brittle materials subjected to combined thermo-mechanical loading under quasi-static and dynamic loading conditions. The coupled three-field problem, viz., temperature, displacement and phase fields is solved using a staggered scheme. Adaptive refinement is done in the vicinity of evolving damage based on user-defined threshold on the critical damage variable. The accuracy in predicting the crack path and morphology with the proposed framework is demonstrated with a few examples that involve quasi-static and dynamic loading conditions. It is opined that the adaptive framework yields comparable results similar to uniformly refined mesh, but with less computational effort.