10.13.2008
10.1
Elastic Deformations of Solids
Object in equilibrium
Zero net force
Zero net torque
Does not mean force and torques do no effect to object
Object is deformed when contact forces are applied to it
Deformation
Change in size or shape of object
Many solids are too stiff to see deformation with eye
Require microscope or other device to detect
When contact forces are removed
Elastic object returns to its original shape and size
Many objects are elastic as long as deforming forces are not too large
Other hand, many objects can be permanently deformed or broken if forces are
too large
Ie. Car crash
10.2
Hooke’s Law of Tensile and Compressive Forces
If stretched by same tensile forces and two wires get longer by proportional amount to
their original lengths then they have same fractional length change or strain.
Strain is dimensionless measure of degree of deformation
Strain = delta L / L
The force per unit area produces the same deformation on wires of same length and
composition. The force per unit area is stress.
Stress = F/A
SI units are same as pressure: N/m^2 or Pa
F = k delta L
Rewrite: stress proportional to strain
F/A = Y delta L/L
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Y is the proportionality constant and only depends on the inherent stiffness
K = Y A/L
Y is called elastic modulus or Young’s modulus
It has the same units as Pa or N/m^2, same as stress
Measures resistance of material to elongate or compress
Flexible and stretches easily such as rubber has low Y
Steel has high Y
Hooke’s law holds up to maximum stress called proportional limit.
10.3
Beyond Hooke’s Law
If tensile or compressive stress exceeds proportional limit, strain is no longer proportional
to stress.
The solid returns to original length when stress is removed as long as stress does not
exceed elastic limit.
If exceeded, material is permanently deformed.
When stress reaches breaking point, the solid fractures.
The maximum stress that can be withstood without breaking is called ultimate strength.
Ultimate strength can be diff for compressive or tensile strength of material
A ductile material continues to stretch beyond its ultimate tensile strength without
breaking. The stress then decreases from ultimate strength.
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 Spring '08
 Lloyd
 Force, Stress, Tensile strength, Shear modulus

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