An enriched meshless method for non-linear fracture mechanics

This paper presents an enriched meshless method for fracture analysis of cracks in homogeneous, isotropic, non-linear-elastic, two-dimensional solids, subject to mode-I loading conditions. The method involves an element-free Galerkin formulation and two new enriched basis functions (Types I and II) to capture the Hutchinson–Rice–Rosengren singularity eld in non-linear fracture mechanics. The Type I enriched basis function can be viewed as a generalized enriched basis function, which degenerates to the linear-elastic basis function when the material hardening exponent is unity. The Type II enriched basis function entails further improvements of the Type I basis function by adding trigonometric functions. Four numerical examples are presented to illustrate the proposed method. The boundary layer analysis indicates that the crack-tip eld predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered, whether for the near-tip asymptotic eld or for the far-tip elastic eld. Numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the J -integral for the applied load intensities and material properties considered. Also, the crack-mouth opening displacement evaluated by the proposed meshless method is in good agreement with nite element results. Furthermore, the meshless results show excellent agreement with the experimental measurements, indicating that the new basis functions are also capable of capturing elastic–plastic deformations at a stress concentration e ectively