How Does A Strain Tensor Transform?

In summary, the conversation is about the theory of elasticity and the transformation laws for a (0,2) tensor. The person is having trouble understanding how a strain tensor can be transformed and is asking for clarification. It is suggested that the transformation may only work for Cartesian coordinates and will only be correct for global rotations with an orthogonal matrix.
  • #1
antarctic
4
0
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.
 
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  • #2
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 [itex]x'^i=R^i_{\phantom{i}j}x^j[/itex] where R is an orthogonal matrix.
 

FAQ: How Does A Strain Tensor Transform?

1. How is strain tensor defined?

The strain tensor is a mathematical representation of the deformation of a material due to applied forces or stresses.

2. What is the difference between strain tensor and stress tensor?

The strain tensor describes the deformation of a material, while the stress tensor describes the forces or stresses applied to the material.

3. How does a strain tensor transform under a change of coordinate system?

A strain tensor transforms according to the rules of tensor transformation, which involves multiplying the tensor by the transformation matrix and its transpose.

4. What is the physical significance of the components of a strain tensor?

The components of a strain tensor represent the magnitude and direction of the deformation of a material in different directions.

5. How is the strain tensor related to the material's elastic properties?

The strain tensor is directly related to the material's elastic properties through the elastic modulus, which represents the material's resistance to deformation.

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