Page 165 - Introduction to Continuum Mechanics

150 Components of Deformation Tensors in other Coordinates

Thus

i.e.,

We have already used this matrix for computing the components of F in a few examples above.
The situation is more complicated if the base vectors at the reference configuration are
different from those at the current configuration. Such situations arise not only in the case
where different coordinate systems are used for the two configuration ( for example, a
rectangular coordinate system for the reference and a cylindrical coordinates for the current
configuration, see (B) below), but also in cases where the same curvilinear coordinates are
used for the two configurations. The following are examples.
(A) Cylindrical coordinate system for both the reference and the current configuration
Let

be the pathline equations. We shall show in the following that

and