Spatial Connectivity of Force Chains in a Simple Shear 3D Simulation Exhibiting Shear Bands

Abstract

Force chains within a granular material are the major load carriers responsible for the strength of a material. The authors study the spatial distribution of force chains across length scales in a three-dimensional (3D) assembly of spherical particles subject to simple shear. Specifically, the authors network sets of force chains by basing connectivity on the distance between chain particles. The authors quantify the connectivity of networked force chains at different length scales using ideas employed in landscape ecology. The authors find a geometric transition in force chain connectivity and observe a change in the character of this transition with respect to force chains restricted to the shear band. The spatial distribution of force chains in the shear band exhibits two dominant length scales: force chains are separated by lateral support, on average, by one particle diameter in one direction and two particle diameters in a second direction. The existence of two dominant length scales in the lateral support around those force chains within shear bands suggests improvements to predictive constitutive models by explicitly incorporating such variation in, for example, in-plane and normal to shear directions.