A Novel Approach to Thermo-Mechanically Coupled, Gradient-Enhanced Damage Modeling

Thermo-mechanical damage, such as thermal shock, is a common engineering problem. It constitutes a challenging problem that damage and temperature are conversely interacting with each other: Material damage leads to an increase in temperature due to energy dissipation; temperature also influences damage evolution. On the one hand, an increase in temperature decreases the damage threshold, which makes damage more likely to occur. On the other hand, a non-uniform temperature distribution can cause internal stresses within the material, leading to the occurrence of damage. Taking all of the above points into account, we introduce a novel approach based on the Hamilton principle for thermo-mechanically coupled, gradient-enhanced damage modeling. To accelerate the computation speed, we adopt the Neighbored Element Method to calculate the Laplace operator in the governing equation of both the damage variable and temperature. The numerical examples show the robustness and efficiency of our method.