The Moving Plane Inhomogeneity Boundary with Transformation Strain

Abstract

Within the context of linear elastodynamics, the radiated fields (including inertia) for a plane inhomogeneous inclusion boundary with transformation strain (or eigenstrain), moving in general motion under applied loading, have been obtained on the basis of Eshelby’s equivalent inclusion method, by using the strain field of a moving homogeneous inclusion boundary previously obtained. This dynamic strain field, obtained from the dynamic Green’s function (for an isotropic material), is unique, and has as initial condition the limit of the spherical Eshelby inclusion, as the radius tends to infinity, which is the minimum energy solution for the half-space inclusion. With the equivalent dynamic eigenstrain (which is dependent on the velocity of the boundary), the radiated fields for the inhomogeneous plane inclusion boundary can be obtained, and from them the driving force on the moving boundary can be computed, consisting of a self-force (which is the rate of mechanical work (including inertia) required to create an incremental region of inhomogeneity with eigenstrain), and of a Peach-Koehler force associated with the external loading. While for an expanding plane homogeneous inclusion boundary the Peach-Koehler force is independent of the boundary velocity, in the case of an inhomogeneous one it is not.