Three-dimensional computational homogenization of cracked composite materials using state-based peridynamics and MPI parallelization

This paper presents a scalable three-dimensional computational framework for the homogenization of cracked composite materials using the ordinary state-based peridynamic formulation. The method integrates a generalized bond-breaking algorithm, based on a modified Möller-Trumbore raytracing scheme, which transforms arbitrary crack surfaces into triangle mesh representations, enabling robust and geometry-independent fracture detection. Volumetric periodic boundary conditions are implemented to ensure energetic consistency and compatibility with the Hill–Mandel macro-homogeneity condition. To address the substantial computational cost of 3D nonlocal models, the framework employs MPI-based domain decomposition combined with PETSc iterative solvers, achieving strong parallel scalability for representative volume elements (RVEs) containing millions of material points. Numerical experiments on fibre-reinforced composite RVEs, both intact and pre-cracked, demonstrate the framework’s ability to capture complex three-dimensional fracture patterns and accurately predict effective stiffness properties. The proposed approach offers a robust, general purpose, and high performance solution for microscale fracture analysis and homogenization in composite materials, with potential applicability to broader classes of heterogeneous and damage-prone materials.