Relations between the Material Mechanical Parameters and the Inter-particle Potential in Amorphous Solids

TL;DR

This paper develops a scaling theory linking inter-particle potentials to the shear modulus and yield stress in amorphous solids, enabling predictions of mechanical properties based on microscopic interactions.

Contribution

It introduces a novel scaling approach that predicts how mechanical parameters depend on density and inter-particle potential in amorphous materials.

Findings

Predicts yield stress and shear modulus from inter-particle potential and density.

Identifies conditions under which predictions are valid across densities.

Provides insights for designing materials with tailored mechanical properties.

Abstract

The shear-modulus and yield-stress of amorphous solids are important material parameters, with the former determining the rate of increase of stress under external strain and the latter being the stress value at which the material flows in a plastic manner. It is therefore important to understand how these parameters can be related to the inter-particle potential. Here a scaling theory is presented such that given the inter-particle potential, the dependence of the yield stress and the shear modulus on the density of the solid can be predicted in the athermal limit. It is explained when such prediction is possible at all densities and when it is only applicable at high densities. These results open up exciting possibilities for designing in principle new materials with desirable mechanical properties.