Page 219 - Introduction to Continuum Mechanics

204 Stress

Since

Eq. (4.12.1) takes the form

However, we have from the equations of motion

therefore, we have

The first term in the right-hand side of Eq. (4.12.4) represents the rate of change of kinetic
energy of the particle as is seen from the following:

where we note that jr(pdV) = 0 on account of the mass conservation principle. Thus, from
Eq. (4.12.4)

where

is known as the stress power. It represents the rate at which work is done to change the volume
and shape of a particle of unit volume.

For a symmetric stress tensor