Page 502 - Introduction to Continuum Mechanics

486 Calculations of the Relative Deformation Tensor

Again, using the inverse functions of Eqs. (8.8.15), we can obtain the following components

The other components can be easily written down following the patterns given in the above
equations.

8.9 History of the Relative Deformation Tensor. Rivlin-Ericksen Tensors

The tensor C r(x,r) describes the deformation at time r of the element which is at x at
time t. Thus, as one varies r from r = - oo to r = tin the function C t (x,r), one gets the whole
history of the deformation from infinitely long time ago to the present time t.
If we assume that we can expand the components of C, in Taylor series about r = t, we
have,