Generalized elasticity theory of quasicrystals

Elasto-Dynamics of Quasicrystals

“…Ding et al first proposed the elasticity of quasicrystals in [19]. The basic equations in deformation geometry are repressed by…”

“…So the total displacement field in a quasicrystal can be expressed by u = u ⊕ u ⊥ = u ⊕ w, in which u is in the parallel space, or the physical space; w is in the complement space, or the perpendicular space; which is an internal space and ⊕ denotes the direct sum. On the basis of the above physical framework and the extended methodology in mathematical physics from classical elasticity, the independent elastic constants for different symmetries of quasicrystals can be determined [16][17][18][19][20][21]. Then the mathematical elasticity theory of quasicrystals has been developed rapidly.…”

General Solutions for Three-Dimensional Thermoelasticity of Two-Dimensional Hexagonal Quasicrystals and an Application

“…In 2D QCs, a phason displacement field w n n = 1 2 exists in addition to a phonon displacement u i i = 1 2 3 . According to 2D QC linear elastic theory established by Ding et al [9] , the strain-displacement relations for 2D QCs are given by ij = j u i + i u j /2 w nj = j w n (1) where j = 1 2 3, repeated indices imply summation and j = / x j ij and w nj denote the phonon strain and phason strain, respectively. In the absence of body force, the balance laws require…”

“…Both phonons and phasons are considered as continuous medium filed variables within the elastic theory of QCs. Ding et al [9] established the generalized linear elastic theory of QCs, which provides us with a fundamental theory based on the notion of a continuum model to describe the elastic behavior of QCs. For comprehensive and detailed presentation for the linear elasticity of QCs, the review by Hu et al [10] and a monograph by Fan [11] are recommended.…”

The remarkable nature of one-dimensional quasicrystal

“…Within the framework of the Landau theory, the elastic energies of QCs were formulated (Bak, 1985;Levine et al, 1985). In particular, the field of linear elasticity theory of QCs has been investigated for many years (Ding et al, 1993;Wang et al, 1997). It provides us with a fundamental theory based on the notion of a continuum model to describe the elastic behavior of QCs.…”