On material-uniform elastic bodies with disclinations and their homogenization

TL;DR

This paper investigates the properties of material-uniform hyperelastic bodies with disclinations and dislocations, revealing how symmetry constraints limit defect sizes and informing models with distributed defects.

Contribution

It provides a rigorous analysis of how symmetry groups restrict disclination sizes and discusses implications for homogenization of bodies with continuous defect distributions.

Findings

Disclination size is limited by the body's symmetry group.

Discrete symmetry groups prevent arbitrarily small disclinations.

Results inform the derivation of models with continuous defect distributions.

Abstract

In this note, we define material-uniform hyperelastic bodies (in the sense of Noll) containing discrete disclinations and dislocations, and study their properties. We show in a rigorous way that the size of a disclination is limited by the symmetries of the constitutive relation; in particular, if the symmetry group of the body is discrete, it cannot admit arbitrarily small, yet non-zero, disclinations. We then discuss the application of these observations to the derivations of models of bodies with continuously-distributed defects.