A thermal–mechanical coupled bond–based peridynamic model for fracture of anisotropic materials

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Thermal fracture analysis of anisotropic materials is a serious challenge in peridynamics (PD). This challenge arises from the need to incorporate anisotropy into both the thermal and mechanical constitutive relationships. While some previous research has explored anisotropy in mechanical field for specific materials, there has been a lack of emphasis on anisotropic materials in the thermal field. This gap creates a significant obstacle for the resolution of thermal fracture, a complex problem involving intricate thermal–mechanical coupling. To address this issue, an anisotropic bond–based PD (BB–PD) heat conduction equation was derived for the thermal analysis of anisotropic materials. In addition, a thermal–mechanical coupled BB–PD model with complete thermal–mechanical anisotropy was developed by integrating an anisotropic mechanical BB–PD model. Governed by a staggered coupling strategy, the pivotal parameters in the two physical fields can be timely updated, facilitating precise computation of the mechanical behavior in the thermal and mechanical fields. To validate the efficacy of the presented model, several numerical examples were performed, including the analysis of anisotropic heat conduction, the deformation analysis under purely mechanical loading, the deformation analysis in specific temperature fields, and two simulations of thermal fracture. The results show that the proposed model can accurately capture the temperature variation and deformation of anisotropic materials. Moreover, the proposed model demonstrates an excellent ability to predict thermal fracture.