Nonlinear elasticities of octagonal and dodecagonal quasicrystals

The nonlinear elasticities are analyzed for octagonal and dodecagonal quasicrystals. All the third-order elastic constants are determined. According to Hermann's theorem, quasicrystal anisotropy may be revealed by the nonlinear elasticities due to the coupling between phonons and phasons. The summary on isotropy or anisotropy of all quasicrystal elasticities is given.