Quasi-static thermoelastic fracture: Adaptive phase-field modeling with variable-node elements

Although robust in handling different fracture processes such as nucleation, branching and coalescence, the phase-field method (PFM) is computationally very expensive because it requires extremely fine meshes to resolve the necessary physics. This paper presents a hybrid adaptive PFM discretized by using finite element method to model quasi-static fracture of thermoelastic solids and quenching. Based on a user-defined threshold on the phase field variable, the computational domain is local refined. The incompatibility between the meshes due to local refinement is directly handled by the variable-node elements, without the special handling of hanging-nodes. The coupled phase-field thermo-elastic equations are solved using the hybrid approach combined with a staggered solution scheme, and the robustness of the proposed framework in terms of capturing the crack morphology is demonstrated with several standard benchmark problems.