This paper proposes a new 3D continuous-discontinuous heat conduction model to consider the thermal resistance effect of cracks and dynamic crack propagation during heat transfer. Combining this heat conduction model and the finite-discrete element method (FDEM), we construct a coupled thermomechanical model for solving thermal cracking problems in brittle materials. The mechanical fracture calculation utilizes virtual joint elements between adjacent solid elements for fracture simulation. On the other hand, virtual joint elements are not included in the heat conduction model to improve numerical efficiency. When new cracks are generated, the node sharing relationship is dynamically updated in the heat conduction calculation to consider the thermal resistance effect of cracks. In this study, the proposed models are verified by simulating heat transfer, coupled thermomechanical, and thermal cracking problems in brittle materials. The numerical simulations are consistent with analytical solutions, and a complex thermal crack process can be realistically captured. These numerical examples verify the correctness of the proposed models, which can be powerful tools for solving heat transfer, coupled thermomechanical, and thermal cracking problems in brittle materials.

本文提出了一种新的 3D 连续-不连续热传导模型，以考虑传热过程中裂纹的热阻效应和动态裂纹扩展。结合这种热传导模型和有限离散元方法 (FDEM)，我们构建了一个耦合热机械模型，用于解决脆性材料中的热裂纹问题。机械断裂计算利用相邻实体单元之间的虚拟连接单元进行断裂模拟。另一方面，热传导模型中不包含虚拟关节单元以提高数值效率。当新裂纹产生时，在热传导计算中动态更新节点共享关系，以考虑裂纹的热阻效应。在这项研究中，通过模拟脆性材料中的传热、热机械耦合和热裂纹问题，对所提出的模型进行了验证。数值模拟与解析解一致，可以真实地捕捉到复杂的热裂纹过程。这些数值例子验证了所提出模型的正确性，它可以成为解决脆性材料中的传热、热机械耦合和热裂纹问题的有力工具。