The Stress Transmission Universality Classes of Periodic Granular Arrays

TL;DR

This paper investigates how stress propagates through static periodic arrays of rigid grains, revealing universal classes and the influence of geometrical disorder on stress transmission.

Contribution

It introduces a universal classification of stress transmission in periodic granular arrays and analyzes the effects of geometrical disorder on stress distribution.

Findings

Stress transmission can be classified into universality classes.

Stress distribution is linear in non-degenerate cases.

Geometrical disorder significantly affects stress transmission coefficients.

Abstract

The transmission of stress is analysed for static periodic arrays of rigid grains, with perfect and zero friction. For minimal coordination number (which is sensitive to friction, sphericity and dimensionality), the stress distribution is soluble without reference to the corresponding displacement fields. In non-degenerate cases, the constitutive equations are found to be simple linear in the stress components. The corresponding coefficients depend crucially upon geometrical disorder of the grain contacts.