Calculation of the incremental stress-strain relation of a polygonal packing

TL;DR

This paper uses molecular dynamics simulations to derive the incremental stress-strain relation of polygonal packings, revealing how micro-contact rearrangements influence stiffness and plasticity under quasi-static deformation.

Contribution

It introduces a method to calculate the constitutive relation of polygonal packings and links micro-contact changes to macroscopic stress-strain behavior.

Findings

Stress remains stable within a failure surface with power law dependence on pressure.

Stiffness tensor relates directly to micro-contact rearrangements.

Plasticity follows a non-associated flow rule with a distinct plastic limit surface.

Abstract

The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure surface, that shows a power law dependence on the pressure. Below the failure surface, non linear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results shows that the stiffness tensor can be directly related to the micro-contact rearrangements. The plasticity obeys a non-associated flow rule, with a plastic limit surface that does not agree with the failure surface.