Rise and fall of void population governs the porous-to-solid transition in soft granular materials

Abstract

Soft granular materials are porous packings of highly deformable particles found in systems ranging from blood clots and tissue scaffolds to starchy foods and 3D-printing inks. They start as collections of discrete, loosely packed motifs, but then transition to a coherent solid under load. Understanding when that {\it granular-to-continuum} transition occurs is critical because it controls whether a biomaterial can be injected through a needle, how easily cells and drugs infiltrate a healing wound, and how nutrients are transported through engineered tissue. Classical approaches rely on counting inter-particle contacts, but this becomes rather ambiguous as contact points evolve into contact surfaces when soft grains undergo large, nonlinear changes in size and shape. Here, we present a paradigm shift: instead of tracking the granular material, we track the empty space between them. Through computational simulations, we discover that porosity evolves through a universal sequence: as the material compresses, interstitial voids undergo a stereotyped cascade of fragmentation (proliferation) followed by collapse (elimination). We identify a topological marker that marks the exact onset of solid-like rigidity and stress homogenization. The critical threshold of this topological marker is independent of the particle size distribution or elasticity, offering a robust geometry-based descriptor for the solidification of soft matter.