ELASTIC STRAIN ENERGIES OF SPHERE, PLATE AND NEEDLE INCLUSIONS

The inclusion problem of linear isotropic elasticity is applied to dis cuss the orientation and shape dependencies of the elastic strain ener gies of sphere, plate and needle inclusions with general misfit strain s. The strain-energy minimization criterion is adopted and difference in elastic constants between the inclusion and the surrounding medium is taken into account. Regardless of the types of the misfit strains, it is generally found that the plate shape is most favorable for soft inclusions. For hard inclusions, however, the minimum-energy shape dep ends on the signs of the three principal misfit strains, a sphere when the three misfit strains have the same sign and a needle when they ha ve different signs. Some other new and general characteristics on the strain energies of the coherent inclusions are newly found. Stresses a nd strain energies of incoherent inclusions after the occurrence of pl astic accommodation are also evaluated.