Abstract
The elastic field in the three-phase, spherically concentric solid due to a stress-free transformation strain in the inclusion is obtained. This analysis considers both homogeneous and a polynomial-type, nonlinear transformations. In the former case, the strain field in the inclusion is found to be also homogeneous under a hydrostatic transformation, but becomes heterogeneous under a deviatoric one. The mean fields are uncoupled between a hydrostatic and a deviatoric case, and even between one shear and the other. The elastic energies of the solid under these transformations are also derived. In light of this new development, a modification is suggested for the Mori-Tanaka method. The resulting effective shear modulus of a two-phase composite lies between the Hashin-Shtrikman bounds, and the predicted Young's modulus also compares well with the experimental data.
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