An extended coupling method integrating NURBS and meshfree RPIM for accurate 2D crack modeling

Abstract

Accurately modeling cracks in two-dimensional (2D) solids with complex geometries remains a significant challenge in fracture mechanics. Traditional coupling methods for crack analysis often require complex domain partitioning and boundary condition imposition, limiting computational efficiency. Recently, a novel method known as N-RPIM, which integrates non-uniform rational B-splines (NURBS) and radial point interpolation (RPIM), has demonstrated promise for plane stress simulations in web structures with openings, where the presence of curved boundaries highlights its advantages in geometric representation and numerical accuracy. However, its application to crack analysis remains unexplored, necessitating further development to capture crack behaviors. Building on this framework, this paper develops an extended N-RPIM method (XN-RPIM), incorporating the partition-of-unity technique to accurately model cracks in 2D cases of elastic solids. NURBS basis functions represent domain shapes with precision, while RPIM approximates the displacement field. The Heaviside and branch functions capture surface discontinuities and crack tip singularities, respectively. Unlike existing coupling approaches, the proposed method eliminates the need for subdomain divisions and additional boundary conditions, streamlining the simulation process. Benchmark studies on mixed-mode cracks and intricate configurations demonstrate that XN-RPIM can achieve errors of the stress intensity factor (SIF) below 1% while requiring significantly fewer nodes than the extended finite element method (XFEM) in the best-performing cases. These findings highlight the potential of XN-RPIM as a robust and efficient tool for advanced crack analysis.