4
$\begingroup$

$C=F^TF$ is called the "Right" Cauchy-Green tensor, and $b=FF^T$ is called the "Left" Cauchy-Green tensor.

I suppose in $C=F^TF$ the non-transposed $F$ stands on the right, and in $b=FF^T$ it stands on the left, but I guess there's gotta be more to it? Is there any reason for why they are called "right" and "left" specifically?

$\endgroup$

1 Answer 1

4
$\begingroup$

I would guess that it has to do with the polar decomposition of the deformation gradient ($\mathbf{F}$)

$$\mathbf{F} = \mathbf{R} \mathbf{U} = \mathbf{V}\mathbf{R}\, ,$$

with $\mathbf{R}$ an orthogonal tensor, $\mathbf{U} = \mathbf{C}^{1/2}$ the right stretch tensor, and $\mathbf{V} = \mathbf{b}^{1/2}$ the left stretch tensor.

Both, $\mathbf{C}$ and $\mathbf{b}$, should be positive definite tensors for the square root to be well defined.

$\endgroup$
1
  • $\begingroup$ Slightly related concept, but definitely more convincing than my version. I'll take it :) $\endgroup$
    – MaxD
    May 27 at 20:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.