M. Kato et al., ELASTIC STRAIN ENERGIES OF SPHERE, PLATE AND NEEDLE INCLUSIONS, Materials science & engineering. A, Structural materials: properties, microstructure and processing, 211(1-2), 1996, pp. 95-103
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.