Thermal Response due to Crack Growth in Viscoelasticity

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. 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 investigate the thermal response in the material due to crack growth numerically using the proposed model.  In the numerical method, since we need the mesh which has to be fine enough to capture the damage variable $z$, we apply the adaptive finite element method. Several interesting numerical examples are demonstrated, such as; Mode I crack propagation, Mixed Mode I+II crack propagation, and scalar Mode III crack propagation in the 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.