Page 495 - Introduction to Continuum Mechanics

Non-Newtonian Fluids 479

From Eq. (8.7,1), we clearly also have

and

The relative right Cauchy-Green deformation tensor C,is defined by

and the relative left Cauchy-Green deformation tensor B, is defined by

and these two tensors are related by

1
1
The tensors C t and E t are often encountered in the literature. They are known as the
relative Finger deformation tensor and the relative Piola deformation tensor respectively.
We note that

Show that if dbc ' and cbc > are two material elements emanating from a point P at time t
and dx'' ' and dx'' ' are the corresponding elements at time r, then

and

Solution. From Eq. (8.6.1), we have

By the definition of the transpose