Peridynamics model with surface correction near insulated cracks for transient heat conduction in functionally graded materials

Abstract

A peridynamic (PD) model of functionally graded materials (FGMs) is presented to simulate transient heat conduction in the FGM plate with insulated cracks. The surface correction is considered in the model to reduce the surface effect near the domain boundary and insulated cracks. In order to verify the proposed model, a numerical example for the FGM plate is carried out. The results show good agreement with the analytical solution. The convergence of the model with the surface correction for FGMs without cracks is then investigated. The results reveal that our model converges to the classical solutions in the limit of the horizon going to zero. The effects of two material points discretization schemes on the accuracy of numerical results are investigated. For transient heat conduction of FGMs with a static crack, the results obtained from the proposed PD model agree well with that from the finite element method. Finally, transient heat conduction of the FGM plate with a dynamic horizontal crack and intersecting cracks is simulated and discussed.