Non-linear generalized elasticity of icosahedral quasicrystals

TL;DR

This paper develops a third-order non-linear elasticity theory for icosahedral quasicrystals, linking phonon stress to phason strains with specific symmetry, advancing understanding of their complex elastic behavior.

Contribution

It introduces the third-order strain invariants and elastic constants for icosahedral quasicrystals, enabling phason strains to be induced by phonon stress in non-linear elasticity.

Findings

Determined third-order strain invariants and elastic constants.

Established that phason strains can be generated by phonon stress in non-linear regime.

Connected strain invariants with 20 independent elastic constants.

Abstract

Quasicrystals can carry, in addition to the classical phonon displacement field, a phason displacement field, which requires a generalized theory of elasticity. In this paper, the third-order strain invariants (including phason strain) of icosahedral quasicrystals are determined. They are connected with 20 independent third-order elastic constants. By means of non-linear elasticity, phason strains with icosahedral irreducible Gamma^4-symmetry can be obtained by phonon stress, which is impossible in linear elasticity.