Peridynamic simulation of transient heat conduction problems in functionally gradient materials with cracks

In this article, a modified state-based peridynamic (PD) method is proposed to solve transient heat conduction problems in functionally gradient materials (FGMs) with extending insulated cracks. The PD formulation of transient heat conduction has been derived by using the time integration through the forward difference technique. Numerical simulations have been performed to verify the accuracy and effectiveness of the proposed method. The analytical solution and the finite element method results are used for comparison. In this work, the material properties of functionally graded materials are assumed to vary exponentially in z-direction. Our PD results show good agreement with analytical solutions and results from the finite element method. Hence the proposed PD method is suitable to deal with the transient heat conduction problem in FGMs with extending insulated cracks.