Page 218 - Introduction to Continuum Mechanics
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Stress Power 203
where Div denotes the divergence with respect to the material coordinates X and Eq. (4.11.5)
reads
where div denotes the divergence with respect to the spatial coordinates x.
4.12 Stress Power
Referring to the infinitesimal rectangular parallelepiped of Fig. 4.8 which is repeated here
for convenience, let us compute the rate at which work is done by the stress vectors and body
force on the particle as it moves and deforms.
Fig. 4.8 (repeated)
The rate at which work is done by the stress vectors t_ Cj and ^ on the pair of faces having
—QI and ej as their respective normal is:
where we have used the fact that t^-v = Te^v/e/ = v/e/'Tej = v/7/i , and dV=dxidx^dx^
denotes the differential volume. Similarly, the rate at which work is done by the stress vectors
Including the rate of work done by the body force (pBdV- v = pBiVjdV) the total rate of
work done on the particle is
