Characterizing granular networks using topological metrics

Abstract

We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range from microscopic through mesoscopic to systemwide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between microscales and macroscales. We report two main findings: (1) The number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress-tensor-derived measures and contact numbers depend in a universal manner on the fraction of nonrattler particles, f_{NR}. (2) The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both f_{NR} and topological metrics are useful measures to consider when quantifying the state of a granular system.

Upscaling critical state considering the distribution of meso‐structures in granular materials

“…In the 2D granular assembly, the meso loop enclosed by a set of particles was commonly considered as the basic structure element to analyze the rearrangement of particles and local characters during the loading and at the critical state. [38][39][40] The evolutions of meso-characters of granular materials during the shearing toward the critical state were presented in many investigations [41][42][43][44][45][46][47][48] to account for the macro dilatancy, anisotropy and mechanical properties of critical state. For example, Zhu 46,47 described the evolution of quantitative proportion and volume ratio for different loops to analyze the dilatancy of granular materials, and Liu 48 suggested that the macro volume changing during loading is the consequence of mutual transformation for higher-order loops and lower-order loops which reaches a dynamic equilibrium at critical state.…”

The devil is in the mesoscale: Mechanical and behavioural heterogeneity in collective cell movement

“…Promising experimental methods for disentangling intrinsic from extrinsic influences include the stretching of suspended cell monolayers in vitro [91] and the mesoscale control of cellular mechanical properties and interactions in vivo using optogenetics [95]. New analytical tools rease in measured heterogeneity odel of collective cell migration A B could come from the theory of granular materials [96], percolation theory for modelling force chains, correlation functions for separating objects of different shape [97] and statistical identification of mesoscopic correlations. We anticipate considerable interest in measuring, understanding and modelling mesoscale structures in the coming years, without which the mechanisms of collective cell behaviour will remain opaque.…”

Correlating the force network evolution and dynamics in slider experiments

“…the present work, we will consider application of persistent homology (PH), which allows for formulating precise and objective measures of static and dynamic properties of the force networks. This approach has been used extensively in analysis of the data obtained via discrete element simulations in the context of dry granular matter [19,20] and suspensions [21], but its application to experimental data has so far been rather sparse [22,23]. We show that this method allows to develop clear correlations between the static and dynamic properties of the force networks on micro-and meso-scale and the macro-scale system dynamics.…”