Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites

Abstract

An elliptical inclusion embedded in an infinite 1D hexagonal piezoelectric quasicrystal matrix is analysed in the framework of linear piezoelasticity of quasicrystals. Using the technique of conformal mapping, the closed-form solutions of the complex potentials, all the field quantities in the matrix and the inclusion are obtained under far-field antiplane mechanical loads of the phonon and phason fields and an inplane electrical load. Several special cases, such as a homogeneous material, a soft and permeable inclusion, an impermeable inclusion, a line inclusion, a rigid inclusion and a crack are reduced by the present results. Some numerical examples are provided to shows the variations of the stresses of the phonon and phason fields and the electric field with the shape of hole/inclusion, the dielectric permittivity and the distance from the hole/inclusion.

Keywords:

• Piezoelectric quasicrystal composites
• inclusion
• hole
• crack
• conformal mapping

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11262012], [grant number 11502123], [grant number 11462020], [grant number 11262017]; the Natural Science Foundation of Inner Mongolia Autonomous Region of China [grant number 2015JQ01], [grant number 2015MS0129].