Elasticity

Concepts of Elasticity
Is the tendency of a substance to regain its original form or volume when external force that deformed it, is removed; or the property by virtue of which a body resists and recovers from a deformation performed by an external force.

Elasticity Limit
The property of elasticity however, works only within certain limits. The smallest value of the stress required to produced a permanent distortion in a body is called the Elastic Limit. When=a stress in excess of this limit is applied, the body will not return to its original state after the stress is removed.\

Stress
Is a measure of the strength of the agent that is causing deformation. Precisely, if a force F is applied to a surface of area A then,

Stress = force / area = F / A

Strain
Is a measure of the deformation.

Strain = change in dimension / original dimension

Hooke’s Law
States that the strains (deformation) are proportional to the stresses that produce them. We then define a constant, called modulus of elasticity by the relation:

Modulus of elasticity = stress / strain

Young’s Modulus
Young’s modulus (Y) is the proportionality constant that relates the compressive or tensile stress and the strain of a particular type of material.

Stress = applied force / cross section = F / A

Strain = elongation / original length =L / L

Bulk Modulus
The bulk modulus (B) is due to a compressing stress, and it is particularly applied to liquids and gasses which cannot be subjected to tensile stress. Since in liquids and gasses the stress is numerically equal to the pressure, we have

B = pressure change / volume strain = - P / V / V

Shear Modulus : Modulus of Rigidity
The modulus of rigidity is due to a shearing stress. If you place your hand on the top over of a book and gently push it to the side, tour hand generates a shear stress. The resulting distortion of the book as the pages slide across each other is a shear strain. If the object being sheared is elastic, there is proportionality between the shear strain and the shear stress. The proportionality constant that relates the shear stress and strain is called the shear moduls. Thus, for shearing stress (S) of elastic materials:

Shear stress = shear modulus x shear strain
S = FL / A x


Referrence:
page 104 Physics Committee
Far Eastern University
2004