A kinetic theory of plastic flow in soft glassy materials

TL;DR

This paper develops a kinetic model describing the elasto-plastic flow of soft glassy materials, revealing non-local effects, diverging correlation lengths near yielding, and finite size influences on flow behavior.

Contribution

It introduces a non-local kinetic equation for stress distribution and derives a constitutive law incorporating spatial correlations and plastic event rates, advancing understanding of soft glassy material flow.

Findings

Correlation length diverges near yielding

Finite size effects influence flow behavior

Absence of intrinsic local flow curves

Abstract

A kinetic model for the elasto-plastic dynamics of a flowing jammed material is proposed, which takes the form of a non-local -- Boltzmann-like -- kinetic equation for the stress distribution function. Coarse-graining this equation yields a non-local constitutive law for the flow, introducing as a key dynamic quantity the local rate of plastic events. This quantity, interpreted as a local fluidity, is spatially correlated, with a correlation length diverging in the quasi-static limit, i.e. close to yielding. We predict finite size effects in the flow behavior, as well as the absence of an intrinsic local flow curves. These features are supported by recent experimental and numerical observations.