Elastic fields in a polyhedral inclusion with uniform eigenstrains and related problems

In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of three-dimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain energy for several major polyhedra and the effective stiffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eigenstrain do not coincide with those for a spherical inclusion (Eshelby's solution) except for dodecahedron and icosahedron which belong to icosidodeca family, i.e., highly symmetrical structure.