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 p olyhedral inclusion with uniform eigenstrains is investigated. Exact soluti ons are obtained for the stress field in and around a fully general polyhed ron, i.e., an arbitrary bounded region of three-dimensional space with a pi ecewise planner boundary. Numerical results are presented for the stress fi eld and the strain energy for several major polyhedra and the effective sti ffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eig enstrain do not coincide with those for a spherical inclusion (Eshelby's so lution) except for dodecahedron and icosahedron which belong to icosidodeca family, i.e., highly symmetrical structure.