Non-linear generalized elasticity of icosahedral quasicrystals

Abstract

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 Γ 4 -symmetry can be obtained by phonon stress, which is impossible in linear elasticity.

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“…Icosahedral quasicrystals, besides a phonon phase, also have a phason phase, so in general their energy density function is characterized by 5 second-order elastic constants (2 due to the phonon field, 2 due to the phason field, and 1 associated with phonon-phason coupling) [15] and 20 third-order elastic constants (4 due to phonon fields, 5 due to phason fields, 4 due to phonon-phonon-phason coupling, and 7 due to phonon-phason-phason coupling) [16]. Of these third-order constants only four are independent, and, moreover, the following relations are satisfied (see [17] with corrections from [18]):…”