Study On Relative Rigid-Body Displacement In Eshelby Problem Of A Polygonal Piezoelectric Inclusion In The Infinite Plane

In the research of electromechanical coupling effect in piezoelectric medium,the Eshelby problem of piezoelectric inclusions sometimes appear.For example,it intervenes in the nanostructure design of strained semiconductor devices involving strain-induced quantum dot(QD)and quantum wire(QWR)growth.Because the rigidbody displacement(rigid-body translation and rotation)of the inclusion relative to the matrix has been ignored in most previous studies,therefore,the Eshelby problem of polygonal piezoelectric inclusion is studied on the premise of considering the relative rigid-body displacement of the inclusion in this paper.By using the extended Stroh formalism and preset the relative rigid-body displacement term of inclusion,the analytical solution of two-dimensional arbitrary polygonal piezoelectric homogeneous inclusion under the uniform eigenstrain is derived again,and the rigid-body displacement of the inclusion relative to the matrix is obtained.By considering the piezoelectric material Ga As(110)as an example,the main conclusions are as follows:(1)In addition to the disturbance of the elastic field,the eigenstrain of the inclusion also causes the relative rigid body displacement between the inclusion and the matrix.In this paper,the expression of rigid-body displacement between the polygonal homogeneous inclusion and the matrix of piezoelectric materials under uniform eigenstrain is given.We have analyzed the relative rigid body displacement of regular polygon inclusion.With the increase of the number of regular polygon edges,the relative rigid body displacement tends to be stable.(2)By using the explicit solution of the characteristic function of the arbitrary polygon inclusion,the internal and external disturbance elastic strain and the distribution of the disturbance electric field of a particular inclusion are analyzed through an example.We discuss the characteristics of the jump of the perturbation field on the boundary of the inclusion and the concentration of the field quantity or the singularity of the tip at the top of the inclusion.The above results can provide some references for the researchers of anisotropic elastic theory,and hope that these works can play a certain role in the development of anisotropic Eshelby inclusion.