Hook's Law
The Stress is directly proportional to strain.
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| Hook's Law |
Elastic constants are those factor which determine the deformation produced by given a stress acting on a material.
- Modulus of elasticity(E) = Normal stress / Normal strain
- Modulus of rigity (G) = Shear Stress / Shear Strain
- Bulk Modulus (K) = Direct stress / Volumetric strain
Poisson’s Ratio (µ)
µ = - (Transverse Strain) / (Axial Strain)
- µ = 0 to 0.5 under uni-axial loading
- µ = 0 for cork
- µ = 0.5 for perfectly plastic
- -1 < µ < 0.5
Volumetric Strain (ev)
Here, sx , syand sz are stress in x, y, and z- direction.
ev = ex + ey + ez
| ev = (sx + sy + sz)(1 - 2µ) / E |
If sx = sy = sz = s,
| ev = 3s(1 - 2µ) / E |
- Volumetric strain of cylinder bar = longitudinal strain + (2 x diametric strain)
- Volumetric strain of sphere = 3 x diametric strain
Relation Between E, G, K, µ
| Material | Number of independent Elastic constant |
| Homogeneous & Isotropic | 2 |
| Orthotropic | 9 |
| Anistropic | 21 |
Axial elongation of a prismatic bar due to external load
Equivalent young's modulus of parallel composite bar
Strain Energy
It is the ability of material to absorb energy when it is strained.
U = Pxδ / 2 = Txϴ / 2
Where P = Applied load
δ = Elongation due to applied load
T = Applied Torque
ϴ = Angle of twist due to applied torque
Resilience
Ability of a material to absorb energy in the elastic region when it is strained.
Resilience = Area under P- δ curve = Pxδ / 2
The maximum strain energy that can be stored in a material is known as proof resilience.
Modulus of Resilience (u) = Strain energy / Volume
Thermal Stress and Strain
Stress which is induced in a body due to change in the temperature is known as thermal stress and the corresponding strain is called thermal strain.
T is the Temperature change.
- When bar is free to expand, there will be no thermal stress due to temperature change.
- airon = 11.8 µm/m·K
- aAluminium > aBrass > a Copper > airon
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