Stress response function from Voronoi tessellation of static granular layers

Abstract

A new technique to obtain the stress response function of static granular layers from the geometric properties of the corresponding Voronoi tessellations is presented. We measured the vertex displacements of the Voronoi polygons due to the application of a vertical force located on the surface of the layer. A protocol to obtain the stress response function is proposed by establishing a gauge between the geometric measurements and the contact forces, which allows to calculate the stress components indirectly. We show that the Voronoi tessellation response function—VTRF—exhibits the elastic characteristics of additivity, reversibility and linearity as the stress response function. Thus, we applied this protocol to calculate the stress response profiles of two different preparations and to compare them with the results obtained from microscopic measurements, that is, the stress response calculated using contact forces.