Dynamic thermal shock resilience of functionally graded materials: An adaptive phase-field approach

This work presents a phase field model for dynamic fracture under thermo-mechanical loads to analyze functionally graded material (FGM). Coupled governing equations are derived by minimizing the total energy consisting of kinetic energy and elastic strain energy, along with the energy due to the external heat source. To overcome the computational expense associated with the standard finite element analysis for implementing the phase field model, an adaptive approach based on the quadtree algorithm is employed that enhances computational efficiency while preserving accuracy. The hanging nodes within the element are treated as polygonal elements. The governing equations are solved using a staggered solution algorithm, following a hybrid phase field implementation strategy. The notch location, temperature variation, and gradation profile of FGM are carefully examined and investigated using numerous examples. It is observed that these parameters significantly influence the behavior of FGM. The results align well with the existing literature, validating our methodology within the examples explored. Additionally, the computational efficiency of adaptive meshing techniques is assessed, demonstrating the significant reductions in computational overhead while preserving accuracy and versatility in handling multi-physics fracture scenarios.