How Does A Strain Tensor Transform?

[antarctic]

Hello All,
I am trying to learn the theory of elasticity from Landau's book and from the very beginning I've run into trouble. As I learned it, a (0,2) tensor T_ij obeys the transformation law T_hk=T(dx_i/dx_h)(dx_j/dx_k). But I do not see how a strain tensor can be transformed in such a manner (I'm getting two extra terms at the end that don't seem to add to 0). How can you justify it being called a tensor then? Or does the transformation work, and I'm just not seeing something?
Any help appreciated.

 

[henry_m]

Hi,
I suspect that L&L have defined the strain tensor for Cartesian coordinates only. You will only get the correct transformation laws for global rotations $x'^i=R^i_{\phantom{i}j}x^j$ where R is an orthogonal matrix.