Three-dimensional fundamental thermo-elastic field in an infinite space of two-dimensional hexagonal quasi-crystal with a penny-shaped/half-infinite plane crack

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

“…We get a set of material properties of a particular 2D hexagonal piezoelectric QCs satisfying the positive definite condition from Refs. [14,20,27], whose material properties are tabulated in Table 1. Based on the material constants given in Table 1, we obtain the material parameters ( = 1, 2, 3, 4), ′ ( = 1, 2) of the 2D hexagonal piezoelectric QCs as follows, which are positive and different with each other:…”

“…Based on the 2D fundamental solutions, Hou [26] investigated the piezoelectric coated functional devices under external force and electrical loads, and proved that the method was accurate and efficient. Li et al [27] studied the crack problem of 2D hexagonal thermo-elastic QCs with a penny-shaped/half-infinite plane crack by general solutions and potential theory. Although the influences of the piezoelectric effect on the behaviors of QCs were studied, it needs to be further studied to benefit the practical application of QCs.…”

Thermo‐electric response in 2D hexagonal QC exhibiting piezoelectric effect

“…Numerical examples are presented to analyze the change rules of each field components of a semi‐infinite space of 2D hexagonal thermo‐electric QC. A group of elastic constants [22, 24, 28] of 2D hexagonal QC material under thermo‐electric loading is shown in Table 1. The numerical examples in this section are discussed on the plane .…”

“…Furthermore, since the QCs have the potential to be used as components in drilling and nuclear storage facilities, it is very necessary to study the influence of temperature on QCs. So, piezoelectricity and thermoelasticity in QC materials have, thus, also attracted extensive attention from researchers [20‐29]. Li et al.…”

“…The elastic‐plastic problems of the two‐dimensional (2D) hexagonal QC under thermal loading [21] and piezoelectric loading [25, 26] were also concerned. Based on the fundamental solutions and potential theory of QC, the cracks problem [28, 29] and contact problem [27] of QC were studied, and the variations of each field component were analyzed. To the best of the authors’ knowledge, thermal response problem of 2D hexagonal QC with piezoelectric effect was not reported and deserves to be addressed to give further insight into the multi‐fields coupling behaviors of QC.…”