A texture tensor to quantify deformations

TL;DR

This paper introduces a statistical texture tensor that unifies microscopic and macroscopic descriptions of material deformation, capturing both elastic and fluid-like responses.

Contribution

It proposes a new formalism based on the texture tensor that extends elastic strain definitions to include fluid-like deformations from microscopic principles.

Findings

Defines the statistical texture tensor for deformation quantification

Links microscopic and macroscopic deformation descriptions

Extends elastic strain concept to fluid-like responses

Abstract

Under mechanical deformation, most materials exhibit both elastic and fluid (or plastic) responses. No existing formalism derived from microscopic principles encompasses both their fluid-like and solid-like aspects. We define the {\it statistical texture tensor} to quantify the intuitive notion of stored deformation. This tensor links microscopic and macroscopic descriptions of the material, and extends the definition of elastic strain.