1. Introduction
This very brief write up attempts to explain the physical interpretation of elastic constants: elastic modulus, poisson's ratio, bulk modulus, shear modulus, thermal expansion coefficient.
This very brief write up attempts to explain the physical interpretation of elastic constants: elastic modulus, poisson's ratio, bulk modulus, shear modulus, thermal expansion coefficient.
2. Physical meaning of elastic constants
It is important to have a feel for
the physical significance of the elastic constants:
elastic modulus, poisson's ratio, bulk modulus, shear modulus, thermal expansion coefficient.
Young’s modulus (E)
is the slope of the stress—strain curve in uniaxial tension. It has dimensions
of stress ( N/m2 ) and is usually large – for steel, E=210×10^9 N/m2.
You can think of E as a measure of the stiffness of the solid. The
larger the value of E, the stiffer the solid. For a stable
material, E>0.
Poisson’s ratio ν
is the ratio of lateral to longitudinal strain in uniaxial tensile stress. It
is dimensionless and typically ranges from 0.2—0.49, and is around 0.3 for most
metals. For a stable material, −1<ν<0.5.
It is a measure of the compressibility of the solid. If ν=0.5, the solid is incompressible –
its volume remains constant, no matter how it is deformed. If ν=0, then stretching a specimen
causes no lateral contraction. Some
bizarre materials have ν<0 --
if you stretch a round bar of such a material, the bar increases in diameter!!
Thermal
expansion coefficient quantifies the change in volume of a
material if it is heated in the absence of stress. It has dimensions of
(degrees Kelvin)-1 and is usually very small. For steel, α≈6^-10×10^-6 K^-1
Bulk modulus
quantifies the resistance of the solid to volume changes. It has a large
value (usually bigger than E).
Shear modulus
quantifies its resistance to volume preserving shear deformations. Its
value is usually somewhat smaller than E.
