Topological Data Analysis of Emergent Networks in Dense Suspensions under Shear

Large contact networks naturally form in many soft materials, from gels assembled by nanoparticles to shear-thickened suspensions under strong deformation. Their microstructural sensitivity makes them highly programmable, making them important in technologies relevant from food to art conservation. Yet, how functionality emerges in these networks remains poorly understood.

In particle-based simulations, full access to particle positions and stresses allows direct probing of structure–rheology links. However, conventional geometric measures (e.g., mean coordination) often fail: minimal structural changes can trigger dramatic mechanical responses. I focus on networks self-organized under flow in shear-thickening suspensions.

Using a large-scale 3D model (φ = 56%) including lubrication and frictional forces, prior work from our group shows that intermittent percolation of specific particle subsets governs stress transmission. Here, topological invariants—especially the Euler characteristic (E.C.) profile—reveal distinct system-spanning contact clusters. These results suggest that a rigid backbone emerges through mesoscale self-organization, producing the sharp stress fluctuations that characterize Discontinuous Shear Thickening (D.S.T.).

This workflow bridges microscopic structure and macroscopic rheology, advancing graph-theoretic and topological analysis of networked materials.