Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect

Fundamental solutions and frictionless contact problem in a semi‐infinite space of 2D hexagonal piezoelectric QCs

“…According to Refs. [13,16], the generalized deformable geometric equations for 2D hexagonal piezoelectric QCs are…”

“…Without body forces and free charges, the equilibrium equations for 2D hexagonal piezoelectric QCs are [13,16]…”

“…[8][9][10] Chen [11] firstly obtained the fundamental solutions of one dimensional (1D) hexagonal QCs in the elastic field by means of potential theory and the generalized Almansi's theorem. Subsequently, some researchers obtained the 3D fundamental solutions of 1D hexagonal QCs in the thermo-elastic field, [12] in the piezoelectric field, [13] and in the thermo-electro-elastic field, [14] and the 3D fundamental solutions of 2D hexagonal QCs in the elastic field [15] and in the thermo-elastic field. [16] Because of the brittleness of the QCs, [5] the mechanical behavior of QCs with defects, such as crack, dislocation, void, inclusion, etc., has aroused the attention of many researchers'.…”

General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics

“…For an antiplane shear crack in other 1D QCs, the solutions can be obtained to utilize the rigorous operator theory [38][39] .…”

Fundamental elastic field in an infinite medium of two-dimensional hexagonal quasicrystal with a planar crack: 3D exact analysis

“…Owing to his great discovery, Shechtman was awarded the 2011 Nobel Prize in Chemistry and the International Union of Crystallography (1992) changed the official definition of a crystal. In the past three decades, the mechanical behaviors of QCs have stimulated much scientific interest and a variety of topics have been discussed, such as, dislocation (Lazar and Agiasofitou, 2014;Li and Liu, 2012), indentation (Wu et al, 2013;Li et al, 2014b), bending of layered plate , self-action in phason field (Colli and Mariano, 2011;Mariano and Planas, 2013), fundamental elastic fields in infinite and/or half infinite spaces Li et al, 2013;Li et al, 2014a), and so forth. As a class of novel materials, which have a lower friction coefficient, lower adhesion, higher wear resistance and lower porosity in comparison with traditional media, QCs have been found a plenty of potential industrial applications (Kenzari et al, 2012).…”