1.4. TYPES OF ELASTIC MODULI
Figure 1.14: Uniform compression from initial volumeV to final volume (V≠ V) due
to pressureP acting on all sides.
The negative sign represents the decrease in volume with increasing pressure. Bulk mod-
uli of a few common materials can be seen in Table1.1. Bulk Modulus K relates changes
in pressure and volume of fluids and solids. Reciprocal of Bulk Modulus is called Com-
pressibility (—).
—=1
K
Worked out Example 1.4.3A uniform pressure of 5. 0 ◊ 104 Pa is exerted on a copper block having a volume of
10 ≠^3 m^3. What is the change in volume of the block? Bulk Modulus of Cu is 11 ◊ 1011
Pa.Solution:Bulk Modulus (K) =≠PV
V
)Magnitude of change in volume =PV
K
=
(5. 0 ◊ 104 Pa)(10≠^3 m^3 )
(11◊ 1011 Pa)=4. 5 ◊ 10 ≠^10 m^31.4.4 Poisson’s Ratio
A deforming force invariably produces changes in dimensions of a solid objects not only
along the direction of its application, but along other directions too^2. For example, when
a rubber band is stretched, it becomes noticeably thinner. Consider the cylindrical metal
specimen in Figure1.15having original lengthl 0 , diameterd 0 and cross-sectional areaA 0.
Assume that a longitudinal forceFis applied to the cylinder in the z-direction (i.e., along
(^2) This is known as thePoisson e ect, the phenomenon in which a material tends to contract in
directions perpendicular to the direction of tensile forces while it gets elongated parallel to the force.
Similarly, materials tend to expand in directions perpendicular to compressive forces while they contract
in directions parallel to the forces. Poisson’s Ratio is a measure of the Poisson e ect.