Page 221 - Introduction to Continuum Mechanics

206 Stress

Using the identity tr(ABCD) = tr(BCDA) = tr(CDAB) and the relation detF = ~~ Eq. (iii)
becomes

Example 4.12.2
Showjthat the stress power can be expressed in terms of the second Piola-Kirehhoff stress
tensor T and the Lagrange strain tensor E * as follows

Solution. From Eq. (3.13.6),

and Eq. (3.7.2)

we obtain

From Eq. (3.24.2), we obtain

so that

Compare Eq. (i) with Eq. (4.12.12), we obtain

Using Eq. (4.10.11), that is

we have for the stress power