<p>Peridynamics (PD) suffers from computational inefficiencies, surface effects, and inaccuracies in non-uniform discretization. Establishing a finite element-analogous format for PD can eliminate these problems. The governing equations of PD are reformulated into the finite element-analogous format via the Galerkin approach, wherein shape functions serve as the pivotal mediator for this transformation. In this study, A novel approach is proposed by incorporating the shape function of the scaled boundary finite element method (SBFEM). The scaled boundary shape function is derived by solving Laplace’s equation. It maintains the essential interpolation characteristics of conventional finite element shape functions while fundamentally overcome their inherent geometric topology constraints. The proposed method realizes a unified representation of shape functions for different mesh types. This establishes a theoretical foundation for coupled modeling of PD and SBFEM in complex unstructured meshes, demonstrating significant advantages in handling non-conventional mesh configurations. Six numerical case studies validate the computational accuracy, mesh flexibility, and engineering applicability of the coupled method. Results demonstrate that the coupled algorithm effectively predicts crack paths across varying mesh densities and types, with triangular meshes and hybrid meshes showing superior uniformity in complex models. The coupled algorithm exhibits robust convergence characteristics and stability, as evidenced by consistent force-displacement responses and damage evolution patterns under different loading conditions. By bridging the theoretical gap between SBFEM and PD, this study advances the field of computational fracture mechanics, offering a flexible and accurate alternative for modeling complex fracture phenomena without the constraints of conventional mesh-dependent approaches.</p>