Quantifying concave particle morphology for granular materials: a computational and geometric approach

Understanding concave particle morphology is essential for characterizing granular materials and their mechanical behavior. This study introduces a unified computational framework for quantifying concavity in three-dimensional (3D) rock, sand, and rubber particles. The framework integrates algorithms for identifying convex and concave surface points, quantifying local concavity, and performing optimized concavity-driven convex decomposition without conventional pocket and bridge operations. A novel descriptor, three-dimensional Concavity Driven Weight (3D CDW), measures morphological complexity through the minimum number of dominant convex components required to represent a prescribed proportion of particle volume. Sensitivity analyses examine the effects of computational parameters and cumulative volume thresholds on decomposition and particle ranking. Relationships between 3D CDW and conventional descriptors, including concavity number, depth, and surface complexity, are investigated to assess its geometric significance. Mechanical relevance is explored through associations between 3D CDW and a von Mises stress-based localization index under external loading. Evaluation across rock, rubber, and coral sand particles supports the framework’s applicability to complex particle geometries. The proposed algorithms have been verified, providing a foundation for improved morphological characterization and future investigations of shape-dependent mechanical responses in granular materials.