Element-based Peridynamics for Heat Conduction Problems of Isotropic and Anisotropic Materials With Crack Propagation

Element-based peridynamics (EBPD) for transient and steady heat conduction of isotropic and anisotropic materials is proposed, which can conveniently study the thermal transfer problems with cracks. The interactions of EBPD are described using 2-node rod elements for one-dimensional (1D) problems, 3-node triangle elements for two-dimensional (2D) problems and 4-node tetrahedron elements for three-dimensional (3D) problems. An additional rule constructing elements in the EBPD is added to reduce element numbers and delete the low mesh quality elements. The EBPD transient heat conduction equations are derived from the Lagrangian formalism, and the steady heat conduction equations are obtained by the variation principle. The treatments of surface effects, boundary conditions and crack descriptions are provided in detail. The forward difference time increment scheme and Gauss elimination method are used to solve transient and steady heat conduction problems respectively. A series of numerical examples, including 1D, 2D and 3D transient and steady heat conduction problems, are used to validate the proposed EBPD model. The temperature fields of the model with cracks are solved by the proposed method, which has the potential to study thermomechanical and thermal shock problems.