Page 453 - Introduction to Continuum Mechanics

Principle of Conservation of Mass 437

(B) Alternatively, we can derive Eq. (7.4.2) in the following way:
Since [see Eq. (3,29.3) ]

where F is the deformation gradient and dV 0 is the volume at the reference state, therefore

Thus,

But from Eq. (vi) and Eq. (ii), we have,

therefore,

This is Eq. (7.4.2)

7,5 Principle of Conservation of Mass

The global principle of conservation of mass states that the total mass of a fixed part of
material should remain constant at all times. That is

Using Reynolds Transport theorem (7.4.1), we obtain