Three-dimensional nonlocal damage modelling of fractures in quasi-brittle materials using the octree polyhedral scaled boundary finite element method

Abstract

This paper extends the recently proposed nonlocal macro–meso-scale damage (NMMD) model to the 3D, incorporating spatial interaction and energy degradation to simulate crack propagation. By unifying key features of peridynamics and phase-field approaches, the model automatically evolves crack paths without the cumbersome explicit tracking of complex 3D fracture surfaces. Unlike earlier 2D NMMD formulations, each macroscopic material point is now equipped with a spherical influence domain that characterizes the underlying mesostructure. To achieve accurate crack simulation, an octree polyhedral mesh and boundary trimming technology are used to ensure smooth mesh size transition and boundary adaptability. This study capitalizes on the inherent advantage of the polyhedral scaled boundary finite element method (SBFEM), which can effectively handle arbitrary polyhedral elements without restrictions on the shape of the boundary faces and seamlessly combine with the octree polyhedral mesh. A 3D patch test confirms that Wachspress or Laplace shape functions coupled with the octree polyhedral mesh deliver markedly higher accuracy than the mean value shape function alternative in polyhedral SBFEM analyses does. The reliability of the coupled NMMD–polyhedral SBFEM framework is validated through three classical examples and a typical engineering failure problem. The numerical results indicate that the proposed model accurately captures the entire cracking process and provides quantitative predictions of the load–deformation response. The combination of the NMMD model and polyhedral SBFEM enables efficient and robust nonlinear solutions, providing a new approach for the 3D fracture simulation of quasi-brittle materials such as concrete.