A multigrid coupled (FE-EFG) approach to simulate fatigue crack growth in heterogeneous materials

Abstract

In the present work, a multigrid coupled finite element (FE) and element free Galerkin (EFG) approach has been proposed to evaluate the fatigue life of cracked heterogeneous plate under plane stress condition. The discontinuities located away from the major crack have negligible effect on the fatigue life. Therefore, discontinuities are modeled only in a small region near the major crack. This small region is modeled by meshfree EFGM as a heterogeneous medium whereas FEM is utilized in the rest of the domain to exploit the advantages of both the methods. The transition from EFG to FE domains is accomplished by interface elements. A ramp function is employed in the interface elements to maintain displacement continuity in the results. In the multigrid coupled approach, the domain is discretized by a non-uniform mesh. The region containing multiple discontinuities is modeled by fine-mesh while rest of the region is modeled by a coarse mesh with equivalent homogeneous material properties. In order to maintain the displacement continuity at the junction of the coarse and fine mesh, special transition elements are employed. Several problems with discontinuities spread over a 20% region of the domain are solved by the proposed approach, and the results are compared with those obtained by EFG containing discontinuities in the entire problem domain. © 2014 Elsevier Ltd.