This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M + N. By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem.

No abstract

No abstract

In this paper, a new method to analytically carry out the exterior elastic fields of a class of non-elliptical inclusions, i.e., those characterized by Laurent polynomials, is developed. Two complex variable fields, which exactly characterize the Eshelby's tensor, are explicitly achieved for the hypocycloidal and the quasi-parallelogram inclusions. Numerical examples show that the exterior fields near the inclusion are dominated by the boundary shape, but the fields far away from the inclusion tend to be convergent and can be well approximated by those of its equivalent circular/elliptical inclusion. These solutions are firstly reported, and largely make up for the deficiency in the list of the analytical results of non-elliptical inclusions in 2D isotropic elasticity.