Hooke’s
Law / Poisson’s Ratio, ν
In a Nut Shell: Properties of engineering
materials vary widely. Common examples
of engineering materials
with differing stressstrain relations include concrete, glass, steel, wood, aluminum,
composites, and others. A basic
mechanical property is the relationship between stress and strain for a
given material under axial loading. Also, as you stretch a rubber
band in one direction it contracts in
the other two directions. This response gives rise
to the Poisson Ratio effect. 

Hooke’s Law for an Axial Member undergoing Tensile Loading For an axial member under
load with stress. σ, and (extensional) strain, ε, Hooke’s Law (in the linear range) gives σ = E
ε where E
is Young’s modulus (modulus of
elasticity) or proportionality constant. Since strain is
dimensionless, the common units for Young’s modulus are psi (English units) or GPa (metric units). 

Stressstrain Relation for Brittle and Ductile Materials The stressstrain diagram
for a brittle and a ductile material may be idealized to simplify the stressstrain
model. In both cases the slope of the
stressstrain curve in the linear range is
Young’s Modulus. Click here to view
typical stressstrain diagrams for a brittle material and
the idealized, linearelastic stressstrain model. Note for a test involving
a brittle material, the stress increases in a linear manner to its proportional limit and then continues in a nonlinear fashion
to failure at its ultimate strength. For a ductile material,
the stress increases in a linear manner to its yield point. For a linearelastic model the
strain continues to increase with no change in the stress beyond the yield stress in this
idealized model of the stressstrain relationship. 

Values of Modulus of Elasticity, E, and Poisson’s Ratio, ν

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