Micro-origin of Macro-strength: Friction

TL;DR

This paper develops an analytical framework linking micro-scale contact forces and fabric to macro-scale stress and strength in granular materials, providing insights into frictional behavior and material strength.

Contribution

It introduces explicit expressions connecting micro-parameters to macro-constitutive properties and proposes an optimization method to determine maximum internal friction angle from micro-scale data.

Findings

Derived relations between micro-contact forces and macro stress.

Established connection between micro-parameters and Mohr-Coulomb friction angle.

Proposed optimization for maximum internal friction angle.

Abstract

This paper presents an analytical study about the behavior of arbitrary shaped and sized non-cohesive two-dimensional granular materials. Several mechanical properties and relations are unraveled by connecting micro and macro scales in an explicit fashion that, at the same time, provides the basis of an analytical-theoretical framework for the development of new multi-scale techniques. Furthermore, the work herein presented is based on three main ideas that are developed and connected progressively; namely, the obtention of explicit expressions that enable us to relate micro-scale parameters, such as contact forces and fabric, to stress as a macro (continuum) physical property. Then, with these powerful tools, physical connections and relations between the mentioned micro-parameters and macro-constitutive parameters, in specific, Mohr-Coulomb's mobilized internal friction angle, are established. Finally, a non-linear optimization problem, which includes physical constraints at the contact point level, is proposed and solved in order to find the limit (maximum) internal friction angle in terms of the aforementioned micro-parameters. Thus, throughout this theoretical study, some important features about strength, anisotropy, contact buckling, and non-uniqueness of systems of contact forces are extracted, allowing us to have a deeper insight, as well as, a better understanding of the mechanical behavior of such complex-to-model materials.