On the dynamic generalization of the anisotropic Eshelby ellipsoidal inclusion and the dynamically expanding inhomogeneities with transformation strain

Abstract

The self-similarly dynamically (subsonically) expanding anisotropic ellipsoidal Eshelby inclusion is shown to exhibit the constant stress “Eshelby property” in the interior domain of the expanding inclusion on the basis of dimensional analysis, analytic properties and the proof for the static inclusion alone. As an example of this property and the application of the dynamic Eshelby tensor (constant in the interior domain), it is shown that the Eshelby equivalent inclusion method always allows for the determination of the equivalent transformation strain for a self-similarly dynamically expanding inhomogeneous spherical inclusion when the Poisson's ratio is in the real range (positive definiteness of the strain energy). Thus, the solution of dynamically self-similarly expanding inhomogeneities (chemical phase change) with transformation strain can be obtained, as well as the driving force per unit area of the expanding inhomogeneity.