On energy-consistency principle of PFM for thermal fracturing in thermoviscoelasticity solids and its application for modeling thermal response due to crack growth based on adaptive mesh technique

The study of thermal response in the crack tip due to crack growth is very important to study the material behavior. Actually, the thermal response in the crack tip is generated by the mechanical dissipation energy properties, e.g., the viscous energy dissipation in viscoelasticity solids. Therefore, we proposed the PFM for crack propagation in thermoviscoelasticity solids and demonstrated several numerical examples. Our present model is derived from the Francfort–Marigo energy with the Ambrosio–Tortorelli regularization, and thermal energy. Our study aims to numerically investigate the thermal response in materials due to crack growth using the proposed model. In the numerical method, we apply the adaptive finite element method because the mesh needs to be fine enough to capture the damage variable z. Several interesting numerical examples are demonstrated, such as Mode I crack propagation and scalar Mode III crack propagation in non-isothermal and adiabatic processes. Numerical experiments demonstrate the capability of the proposed model to capture the temperature increasing around crack tips which is consistent with the viewpoint of laboratory experiments in the literature.