A coupled FEM–Bernstein approach for computing the J k integrals

Abstract

The stress intensity factors of mixed mode I-II crack loading are often evaluated numerically via FEM implementation combined with the equivalent domain integral method to derive the J k integrals. Mesh refinement or singular elements are classic techniques for reproducing the sharp stress gradient due to material fracture. In this context, high-order Bernstein shape functions are proposed for a model that couples a radial spectral expansion for the stress field around crack tip with a finite element mesh in the outer regions. Lagrange multipliers are used to enforce the coupling in displacements along the FEM-Bernstein approximations interface, in which non-matching nodal patterns are allowed.