Calculation of Stress Intensity Factors Based on Force-Displacement Curve using Element Free Galerkin Method

An idea related to the calculation of stress intensity factors based on the standard appearance of the force-displacement curve is developed in this paper. The presented procedure predicts the shape of the graphics around the point under consideration form where indirectly the stress intensity factors are obtained. The numerical implementation of the new approach is achieved by using element free Galerkin method, which is a variant of meshless methods and requires only nodal data for a domain discretization without a finite element mesh. A MATLAB software code for two dimensional elasticity problems has been worked out, along with intrinsic basis enrichment for precise modelling of the singular stress field around the crack tip. One numerical example of a rectangular plate with different lengths of a symmetric edge crack is portrayed. The stress intensity factors obtained by the present numerical approach are compared with analytical solutions. The errors in the stress intensity factors for opening fracture mode I are less than 1% although the model mesh is relatively coarse.