The analogy of the elastic and dielectric spherical inhomogeneity for cubic and isotropic media

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Abstract
The elastic spherical inhomogeneity in an infinite medium is treated in analogy to the dielectric inhomogeneity. In the isotropic and cubic cases the formulas for the homogeneous internal field and the induced dipole are analogous to those for the electric case except for the sign of the polarization. In the isotropic elastic case octopoles are induced in addition to the dipoles, whereas in the cubic case an infinite series of multipoles appears. The electric and elastic Clausius‐Mossotti formulas for polarizable and for reorienting dipoles are very similar. However in the cubic medium the elastic dipoles in the Lorentz sphere contribute always to the strain in the centre.

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