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Engineering Mechanics (ENGGEN121) 4.3 Volumetric Strain

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University of Auckland

Engineering Mechanics (ENGGEN121)

4.3 Volumetric Strain
The volumetric strain is defined as follows:
Volumetric Strain:
The volumetric strain is the unit change in volume, i.e. the change in volume divided by
the original volume.
4.3.1 Two-Dimensional Volumetric Strain
Analogous to Eqn 3.5.1, the strain invariants are
Strain Invariants (4.3.1)
Using the strain transformation formulae, Eqns. 4.2.2, it will be verified that these
quantities remain unchanged under any rotation of axes.
The first of these has a very significant physical interpretation. Consider the deformation
of the material element shown in Fig. 4.3.1a. The volumetric strain is
(4.3.2)
If the strains are small, the term
xx yy
will be very much smaller than the other two
terms, and the volumetric strain in that case is given by

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Engineering Mechanics (ENGGEN121) 4.3 Volumetric Strain

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