Computational Approaches for Crack Propagation in Materials and Structures: Comparison Between Linear Elastic Fracture Mechanics (LEFM) and Peridynamics (PD) Based Strategies

In solid mechanics, the defects and imperfections of materials (e.g., cracks, dislocations, etc.) play a key role on the overall mechanical behaviour of the structure despite their localized character. In this paper, the phenomenon of crack propagation under tension (Mode I) has been investigated considering two different approaches: linear elastic fracture mechanics (LEFM) and bond-based peridynamics (PD). For the former, the progression of crack path is simulated with the aid of extended finite element method (XFEM), which eliminates the need to have conforming mesh with crack geometry by locally enriching the nodes located in the influence domain of discontinuity and singularity. For the latter, a classical continuum mechanics-peridynamics (CCM-PD) coupling strategy is utilized to combine the ability of peridynamics in handling the displacement field׳s discontinuity with the computational efficiency of continuum-based modeling approaches. All the formulations are developed within two-dimensional (2D) linearized framework, and implemented through in-house codes. The correspondence between LEFM based XFEM and CCM-PD coupled models is discussed through a benchmark problem of practical importance: a uniaxially deformed finite plate with an edge crack, focusing on the variation of fracture parameters and comparing the computational costs.