A PD-FEM coupling approach for modeling thermal fractures in brittle solids

Abstract

A novel approach coupling peridynamic (PD) and finite element method (FEM) is initiated to investigate the onset and development of thermal fractures in brittle solids. In this technique, the analysis domain is divided into two separate layers, of which the thermal diffusion equation is solved in the FEM layer, while the solid deformation, even fracturing, is represented by the peridynamics layer. The temperature related quantities are applied locally within the FEM layer, and the resulting thermal strain is then used in the PD layer. The noteworthy features of the proposed PD-FEM coupling approach include: (1) it is a straightforward application of classical thermal diffusion equation using the FEM, and thus it is free of any calibration procedure to determine the PD micro-conductivity coefficients, and (2) it is computationally flexible in the sense that the discretization of each layer is not necessarily identical. The coupled model is solved by a staggered solution scheme. By comparing with available closed-form solutions and reference solutions by the pure FEM model, the accuracy of the coupling approach is evaluated firstly. Then the coupled model is used for modeling a notched cruciform specimen under mechanical-thermal loading and ceramics under thermal shock to demonstrate its ability to reproduce the complex crack patterns involving heat transfer.