Minimal dissipation theory and shear bands in biaxial tests

TL;DR

This paper develops a minimal dissipation theory for granular materials in biaxial tests, linking microscopic structure changes to macroscopic steady states and shear band behavior, validated through contact dynamics simulations.

Contribution

It introduces a minimal dissipation framework to explain steady states and shear band angles in biaxial tests, incorporating wall friction effects.

Findings

Steady states have constant stress ratios and volume due to minimal dissipation.

Shear band angles remain constant across structures.

Wall friction reduces shear band structure degeneracy, enabling calculable stress ratios.

Abstract

True biaxial tests of granular materials are investigated by applying the principle of minimal dissipation and comparing to two dimensional contact dynamics simulations. It is shown that the macroscopic steady state manifested by constant stress ratio and constant volume is the result of the ever changing microscopic structure which minimizes the dissipation rate. The shear band angle in the varying shear band structures is found to be constant. We also show that introducing friction on the walls reduces the degeneracy of the optimal shear band structures to one for a wide range of parameters which gives a non-constant stress ratio curve with varying aspect ratio that can be calculated.