Influence of heat transfer and fluid flow on crack growth in multilayered porous/dense materials using XFEM: Application to Solid Oxide Fuel Cell like material design

An advanced numerical model is developed to investigate the influence of heat transfer and fluid flow on crack propagation in multi-layered porous materials. The fluid flow, governed by the Navier–Stokes and Darcy’s law, is discretized with the nonconforming Crouzeix–Raviart (CR) finite element method. A combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods is used to solve the advection–diffusion heat transfer equation in the flow channel and in the fluid phase within the porous material. The crack is assumed to affect only the heat diffusion within the porous layer, therefore a time splitting technique is used to solve the heat transfer in the fluid and the solid phases separately. Thus, within the porous material, the crack induces a discontinuity of the temperature at the crack surfaces and a singularity of the flux at the crack tip. Conduction in the solid phase is solved using the eXtended Finite Element Method (XFEM) to better handle the discontinuities and singularities caused by the cracks. The XFEM is also used to solve the thermo-mechanical problem and to track the crack propagation. The multi-physics model is implemented then validated for the transient regime, this necessitated a post processing treatment in which, the stress intensity factors (SIF) are computed for each time step. The SIFs are then used in the crack propagation criterion and the crack orientation angle. The methodology seems to be robust accurate and the computational cost is reduced thanks to the XFEM.