The action exerted on a defect or inclusion in an elastic solid by the surrounding medium can be expressed by means of the space-like part of the Noether energy momentum tensor, the so-called Eshelby tensor 1 . The theory by Eshelby is variational in essence and has been formulated for materials of grade n. It is based on Noether theorem that establishes the existence of a second order tensor quantity which is invariant along the trajectories, under conditions of homogeneity, if the equations of motion are satisfied. As well known, this theorem (a central result in Hamiltonian mechanics) states that every group of transformations under which the Lagrange density function is invariant generates a conserved quantity 2 .Gurtin has proved the validity of Eshelby relation in non conservative setting 3 . His argument is based on • the time variation of a reference control volume, interpreting the evolution of defects or interface surfaces, and the action of the associated material observer 4 ; • a mechanical version of the second law of thermodynamics;• the requirement of invariance under re-parametrization of the boundary of the reference control volume. It applies to phenomena implying addition or subtraction of material points to the reference control volume, as for example cases in which there is crack growth 5 or evolution of a surface across which phase transitions occur. In such a way, 1 [Eshelby, 1975] 2 [Marsden and Hughes, 1983] 3 [Gurtin, 1995] 4 [Gurtin, 1997] 5 Podio-Guidugli, 1996] [Gurtin andYatomi, 1980]