Post-processing of 2D FEM Q1 models for fracture mechanics by radial basis functions and balance equations

In this paper a method to improve the stress state on a 2D finite element (FE) Q1 coarse mesh for fracture mechanics applications is shown. Radial Basis Functions (RBF) are employed synergically with balance equations to reduce the interpolation error and improve results extracted from the coarse FEM models. In addition to FE nodes, RBF interpolation embeds a certain number of additional points, for which displacements satisfy a minimization procedure of the error on balance equations. Derived fields (strain, stress) yield analytically from the constructed interpolator. Proposed method is validated with two 2D structural cases involving strong stress concentrations and applied on a mode I crack opening simulation in which the J-integral is extracted. Described procedure can be employed as a post-processing tool on meshes not suitable to be employed for fracture mechanics applications.