Elastic Energy Momentum Tensor and Defects

[muzialis]

Hi All,

I am reading the seminal paper by Eshelby on the elastic energy-momentum tensor, which I attach for your convenience.
It is all beautiful but equation 4.4 at the beginning. He considers a surface S in the undeformed configuration of a body. The surface is translated by a vector u to a surface S', and the claim is made that the difference in the energies of the portions of the body enclosed by S, S' equals the energy of the portion included by S times the vector u, I really do not see that, albeit the fact it must be obvious...it does not even seem dimensionally consistent to me ...Can anybody help?, I am sure many of you read the paper and/or are familiar with these concepts, I would not hope that you read a new paper just to answer a post.

Thank you very much

 

[Andy Resnick]

4.4 looks like an alternate way of writing ∇E = F (equivalently, ΔE = Δx * F).

 

[muzialis]

Andy, many thanks. sometimes I get stuck and an obviousity becomes a wall.