Approximating Perfection by Lebedev Leonid P

Author:Lebedev, Leonid P.
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2015-03-14T16:00:00+00:00

with respective faces parallel to the principal directions, then after deformation it becomes a rectangular parallelepiped with sides

The volumes of the cube and the corresponding parallelepiped are

Thus, keeping in mind that we consider the tensor of small deformation so that all higher powers of εij are neglected in comparison with linear terms, the change in the volume due to deformation is

The relative change in volume is

This is the first invariant for the strain tensor, and it measures the relative change of volume not only for a cube but for any elementary volume containing the point of interest. It can be expressed in any Cartesian frame as

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