A new weight-function enrichment in meshless methods for multiple cracks in linear elasticity

A new enriched weight function for meshless methods is proposed for the numerical treatment of multiple arbitrary cracks in two dimensions. The main novelty consists in modifying the weight function with an intrinsic enrichment which is discontinuous over the finite length of the crack, represented by a segment, but continuous all around the crack tips. An analytical function is used to introduce discontinuities that are incorporated in the kernel in a simple, multiplicative manner. The resulting method allows a more straightforward implementation and simulation of the presence of multiple cracks, crack branching and crack propagation in a meshless framework without using any of the existing algorithms such as visibility, transparency, and diffraction and without using additional unknowns and additional equations for the evolution of the level-sets, as in extrinsic partition of unity-based methods. Stress intensity factors calculated using the J-integral demonstrate excellent agreement with analytical solutions for classical fracture mechanics benchmarks.