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Li, X. F.; Xie, L. Y.; Fan, T. Y.

Elasticity and dislocations in quasicrystals with 18-fold symmetry. (English) Zbl 1301.74013

Phys. Lett., A 377, No. 39, 2810-2814 (2013); corrigendum ibid. 380, No. 41, 3444 (2016).
Summary: Elasticity problems of quasicrystals with 18-fold rotational symmetry are studied. Constitutive equations and governing equations are obtained. For static elasticity problems, the displacement vectors in two phason fields are expressed in terms of two pairs of associated harmonic functions or two analytic functions. For dynamic problems, the displacement vectors can be represented in terms of an auxiliary function satisfying a fourth-order partial differential equation. A general solution of phasons is given by the solution of two diffusion equations. Phason elastic fields induced by a dislocation in a quasicrystal with 18-fold symmetry are determined and exhibit an inverse singularity.

Cited in 1 Review
Cited in 4 Documents

MSC:

74E15 Crystalline structure
74B99 Elastic materials
35Q74 PDEs in connection with mechanics of deformable solids
74N05 Crystals in solids

Keywords:

quasicrystal; elasticity; phason; dislocation; 18-fold symmetry; constitutive equation
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References:

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