N-sided polygonal smoothed finite element method (nSFEM) with non-matching meshes and their applications for brittle fracture problems

Abstract

In this work, an n-sided polygonal smoothed finite element method (nSFEM) based on gradient smoothing technique is presented for phase field fracture modelling. The phase field approach approximates the crack topology in a diffuse way through an exponential function. A coupled elastic displacement and phase field variational formulation is established by using a Smoothed Galerkin Weak form. Meanwhile, non-matching meshes for local refinement are considered in brittle fracture problems. Non-matching meshes at their interfaces are automatically converted to matching meshes by using present arbitrary sided polygonal elements. In other words, no interface constraint is needed here. In order to validate the feasibility of present nSFEM for brittle fracture problem with non-matching meshes, several numerical examples are employed. The nSFEM can discretize the computational domain in a very flexible manner. Arbitrary sided polygonal elements and non-matching meshes are adopted for comparison. Numerical results validate that the nSFEM shows great potential for phase field fracture problems due to its flexibility in dealing with complex elements shape and non-matching meshes.