ELASTIC INCLUSIONS AND INHOMOGENEITIES IN TRANSVERSELY ISOTROPIC SOLIDS

A method that introduces a new stress vector function (the hexagonal s tress vector) is applied to obtain, in closed form, the elastic fields due to an inclusion in transversely isotropic solids. The solution is an extension of Eshelby's solution for an ellipsoidal inclusion in is otropic solids. The Green's functions for double forces and double for ces with moment are derived and these are then used to solve the inclu sion problem. The elastic field inside the inclusion is expressed in t erms of the newtonian and biharmonic potential functions, which are si milar to those needed for the solution in isotropic solids. Two more h armonic potential functions are introduced to express the solution out side the inclusion. The constrained strain inside the inclusion is uni form and the relation between the constrained strain and the misfit st rain has the same characteristics as those of the Eshelby tensor for i sotropic solids, namely, the coefficients coupling an extension to a s hear or one shear to another are zero. The explicit closed form expres sion of this tensor is given. The inhomogeneity problem is then solved by using Eshelby's equivalent inclusion method. The solution for the thermoelastic displacements due to thermal inhomogeneities is also pre sented.