An element free Galerkin formulation for stable crack growth in an elastic solid

Abstract

The discrete formulation for stable crack growth in an elastic solid using the Element Free Galerkin (EFG) method based on the moving least-squares approximations has been established. The EFG method provides the ability to successfully model steep gradients, such as those that exist at a crack tip, through the introduction of an additional distribution of nodal points. In this formulation, the inertia force term in the momentum equation is converted into a spatial gradient term by employing the steady state conditions. A convective domain is employed to account for the analysis domain moving at the same speed as the crack front. A number of stable crack growth problems are examined and comparisons between the numerical predictions and analytical solutions are made for the near-tip fields, the crack opening profiles, as well as the global control parameters such as stress intensity factor K and energy release rate G.