Page 498 - Introduction to Continuum Mechanics

482 Calculations of the Relative Deformation Tensor

and

The inverse of Eqs.(i) are

(B) Cylindrical Coordinates
The procedures described below for obtaining the formulas for computing the components
for the relative right Cauchy-Green tensors, are the same as those used in Section 3.30 of
Chapter 3.
We have

But from calculus

Thus, we have

Similarly, one can obtain