Integration of hierarchical quadrature element method with a minimum-increment remeshing strategy for simulating coupled thermo-mechanical fracture in quasi-brittle materials

This paper presents a p-version finite element framework for analyzing the thermal fracture behavior of quasi-brittle materials under coupled thermo-mechanical loadings. The proposed formulation, based on the hierarchical quadrature element method (HQEM), enables accurate capture of temperature gradients even on relatively coarse meshes. Its accuracy in simulating heat conduction and thermally induced deformation is validated against ABAQUS results.

The HQEM is integrated with the virtual crack closure method to compute fracture parameters under combined thermal and mechanical loadings, significantly reducing mesh refinement and preprocessing effort compared to conventional h-version FEM. To efficiently track complex crack paths, a minimum-increment remeshing strategy is introduced, which controls element growth while preserving the geometric accuracy of crack paths during iterative crack propagation analysis, significantly reducing the computational cost associated with frequent remeshing. Applications to four representative numerical examples demonstrate excellent agreement with existing literature, confirming the reliability and accuracy of the proposed approach for coupled thermo-mechanical fracture analysis.