An irregular lattice-based numerical framework for implicit fracture analysis of structural concrete

This study presents an integrated in-house numerical framework for the implicit fracture analysis of structural concrete based on the Voronoi-cell lattice model (VCLM), unifying model generation, nonlinear damage analysis, sparse matrix assembly, iterative linear solution, and postprocessing within a single computational environment. To improve memory efficiency and scalability, the global stiffness matrix is assembled directly in compressed sparse row (CSR) format and solved with a diagonal-preconditioned conjugate gradient (D-CG) solver, with both the assembly and solution stages fully parallelized. Reinforcement is incorporated through a semi-discrete model that preserves the original lattice connectivity, avoiding an additional global sparsity pattern. The framework is validated through three-point bending simulations of a notched concrete beam, where results at two lattice resolutions confirm mesh-objective softening, and four-point bending simulations of a shear-critical reinforced concrete (RC) beam, where the nonlinear iteration count is shown to track the evolution of RC damage. The convergence of the D-CG solver, together with the parallel performance of both the nonlinear iteration process and the solver kernel, is evaluated across problem sizes and CPU thread counts, and compared against GPU offloading. The results demonstrate that the proposed approach reproduces representative fracture responses of structural concrete on a memory-efficient and computationally scalable framework, and that the relative benefit of GPU acceleration over CPU-based parallelization becomes more pronounced as the number of degrees of freedom increases, laying the groundwork for larger-scale 3-D lattice fracture simulations.