Benchmark data for validating coupled fluid-solid models was obtained through underwater drop experiments involving circular, rectangular, and L-shaped objects. Image processing was used to analyze the motion of these objects, and each experiment was repeated 10–15 times to ensure reproducibility. Four types of coupled methods (SPH-DEM, LBM-DEM, FDM-DEM and FVM-DEM) were used to simulate the experiments and evaluate the dynamics of the underwater drops as a validation approach. To facilitate validation and improve the accuracy of coupled fluid-solid models for other researchers, the resulting benchmark data will be published as an appendix to this paper.

This paper proposes a method for transforming damage behavior into discontinuous deformation by utilizing the duality between Voronoi diagrams and Delaunay triangulation (Voronoi-Delaunay duality). Continuum damage models, which replace fracture by the degradation of material stiffness, are well-suited for unstructured meshes composed of triangular or tetrahedral finite elements. Based on this compatibility, the proposed approach converts an unstructured Delaunay mesh into a Voronoi diagram, enabling the representation of damage behavior as discontinuous deformation. This transformation allows continuum-based numerical analyses to capture fracture phenomena in a discontinuous manner. After demonstrating the effectiveness of the proposed method through several numerical examples, the approach is applied to a mesoscale fracture simulation of reinforced concrete. The results show that the proposed method can successfully reproduce (visualize) complex three-dimensional fracture behavior at the mesoscale.