Page 234 - Introduction to Continuum Mechanics

Mechanical Properties 219

(equal to M/d), we find that the ratio -B d/e a is a constant if the strains are small. We call this
constant Poisson's ratio and denote it by v. A typical value of v for steel is 0.3.

Fig. 5.2

So far we have only been considering a single specimen out of the block of material. It is
conceivable that the modulus of elasticity Ey, as well as Poisson's ratio v may depend on the
orientation of the specimen relative to the block. In this case, the material is said to be
anisotropic with respect to its elastic properties. Anisotropic properties are usually exhibited
by materials with a definite internal structure such as wood or a rolled steel plate or composite
materials. If the specimens, cut at different orientations at a sufficiently small neighborhood,
show the same stress-strain diagram, we can conclude that the material is isotropic with respect
to its elastic properties in that neighborhood.
In addition to a possible dependence on orientation of the elastic properties, we may also
find that they may vary from one neighborhood to the other. In this case, we call the material
inhomogeneous. If there is no change in the test results for specimens at different neighbor-
hoods, we say the material is homogeneous.
Previously, we stated that the circular cross-section of a bar can remain circular in the
tension test. This is true when the material is homogeneous and isotropic with respect to its
elastic properties.
Other characteristic tests with an elastic material are also possible. In one case, we may be
interested in the change of volume of a block of material under hydrostatic stress a for which
the stress state is