Gradient damage model for simulating thermo–mechanical coupling: Interaction between thermal degradation and mechanical damage

It is generally observed that extreme temperatures due to the application of a flux transforms sound combustible material into char, leading to the degradation of mechanical properties and a modification of initial thermal properties. Nevertheless, the coupling between thermal degradation and mechanical damage, remains underexplored in the literature. The objective of this study is to investigate the influence of mechanical and thermal degradation mechanisms on physical phenomena such as heat transfer, thermal decomposition, and cracking. The study aims to simulate the interaction between different degradation modes and their kinetics to assess their mutual impact on the material’s behavior. To achieve this, a rigorous thermodynamic approach is adopted, introducing internal variables corresponding to each physical phenomenon, as well as their gradients. This modeling approach combines two methods: on the one hand, a phase-field model is employed to describe thermal degradation, which evolves according to an Arrhenius law. This method is suitable for simulating phase transition phenomena and interface motion. On the other hand, a gradient damage model based on the principle of virtual powers avoids issues related to damage localization and mesh dependency. By coupling these two approaches, it becomes possible to simulate the interaction between mechanical damage and thermal degradation of the material. The results show that, on the one hand, charred regions become areas where damage and cracking are easily initiated due to the degradation of mechanical properties. On the other hand, damaged or cracked zones act as thermal barriers, delaying heat propagation. Indeed, the presence of cracks reduces thermal conductivity in these regions, thereby limiting the advance of the thermal front.