A Peridynamic Model for Anisotropic Heat Conduction and Its Extension to Phase-Change Problems

An anisotropic heat conduction model and its corresponding phase change extension based on the Bond-Based Peridynamic (BB-PD) framework are proposed in this paper. A novel micro‑conductivity formulation is introduced that enforces positive definiteness of the conductivity tensor, thereby preventing material instabilities while remaining fully compatible with isotropic behavior. Based on the anisotropic heat conduction model, a phase change PD formulation for anisotropic materials is developed for the first time, incorporating direction-dependent thermal conductivities and latent heat effects. A series of numerical examples are presented to validate the accuracy and applicability of the two PD models in continuous and discontinuous media. The results demonstrate that the proposed anisotropic heat conduction PD model shows excellent agreement with Finite Element Method solutions and accurately captures the thermal behavior in highly anisotropic materials. Furthermore, the anisotropic phase change PD model can effectively track the solid-liquid interface and handle complex solidification processes even in the presence of crack propagation and intersection, thereby providing a rigorous foundation for the development of thermally coupled multiphysics simulation frameworks.