Hooke’s
Law / Poisson’s Ratio, ν
In a Nut Shell: Properties of engineering
materials vary widely. Common examples
of engineering materials
with differing stress-strain 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. |
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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). |
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Stress-strain Relation for Brittle and Ductile Materials The stress-strain diagram
for a brittle and a ductile material may be idealized to simplify the stress-strain
model. In both cases the slope of the
stress-strain curve in the linear range is
Young’s Modulus. Click here to view
typical stress-strain diagrams for a brittle material and
the idealized, linear-elastic stress-strain 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 linear-elastic model the
strain continues to increase with no change in the stress beyond the yield stress in this
idealized model of the stress-strain relationship. |
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Values of Modulus of Elasticity, E, and Poisson’s Ratio, ν
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Return to Notes on Solid Mechanics |
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