Weakly nonlocal continuum theories of granular media: restrictions from the Second Law

TL;DR

This paper demonstrates that Coulomb-Mohr type stress-strain relations in granular media can be derived solely from the Second Law of thermodynamics without assuming substructural interaction balances.

Contribution

It introduces a method to obtain classical stress-strain relations in granular media using thermodynamic restrictions alone, bypassing the need for substructural balance assumptions.

Findings

Stress-strain relations derived from thermodynamics alone.

Validation of classical models without substructural assumptions.

Enhanced understanding of granular media mechanics.

Abstract

The classical continuum mechanical model of granular media of rational thermodynamics results in a Coulomb-Mohr type equilibrium stress-strain relation. The proof is based on a two component material model introducing a scalar internal variable. Here we will show how one can get similar stress-strain relations without assuming a balance of substructural interactions, considering only the restrictions of the Second Law of thermodynamics.