Explicit phase-field material point method for thermally induced fractures

Thermally induced fractures in solids pose significant challenges in various fields, such as aerospace, deep underground, and civil engineering structures. Numerical methods are effective for addressing such problems, with recent advancements in phase-field and material point methods demonstrating notable advantages in crack simulation. This paper presents a computational approach within an explicit material point method framework for coupling the solutions of temperature, displacement, and phase (damage) fields. The displacement and phase fields are intricately linked through a history-dependent strain field and degradation function. The model incorporates temperature-induced strains from temperature gradients for coupling the temperature and displacement fields. In addition, the model accounts for the detrimental effects of cracks on heat conduction, ensuring a comprehensive representation of the coupled system. Two numerical examples involving thermomechanical coupling and dynamic crack branching were used to validate the effectiveness of the proposed method. Finally, the proposed method was applied to simulate the thermal shock and large deformations of thin circular ceramic specimens, successfully replicating the initiation and propagation of cracks observed during the experiment. The simulated thermally induced fractures exhibited periodic and hierarchical characteristics consistent with the experimental findings.