A computational meshfree RPIM approach for phase-field modeling of brittle fracture

Modeling failure mechanisms in solids by using sharp crack discontinuities suffers various shortcomings that can be diminished by diffusive crack conception or phase-field method. The phase-field method describes sharp crack surfaces with a continuous field variable evaluated through a differential evolution equation. This study deals with the discretization and solution of equilibrium and crack evolution equations by the meshless radial point interpolation method (RPIM). A simple equation is proposed to evaluate the average distance between the field nodes distributed/scattered non-uniformly in the solution domain. A novel meshless scheme is proposed to select the field nodes around the quadrature points placed near the crack tip. A modified Newton–Raphson method is applied to restore the iterative convergence of the proposed method. Error analysis of the developed RPIM is carried out, and the RPIM results are compared with finite element method (FEM). The model verification is performed through four well-known benchmark tests, and the computed results are then compared with the solutions reported in the literature or derived from FEM.