Elasticity is a change in its volume or shape, length occurs when an external force acts on a rigid body. The body appears to restore its original size and shape as an external force is released. Such a characteristic of a body is called elasticity since a body appears to recover its original form or size when an external load is removed.
Many solid materials exhibit an elastic nature to a lesser or greater degree, but the force acting and the resulting deformation with which any material recovers elastically is still restricted. This threshold, known as the elastic limit, is the maximum stress or force per unit of an area within such solid that can occur before the appearance of permanent deformation. To prepare for the JEE main examination, elasticity is a very important topic. Refer to the Previous Year JEE Main Problems on Elasticity to score good marks in the particular topic.
Elastic Stress and Strain
Stress
Forces inside the body are brought into action when the body is deformed by the influence of external forces. Due to some internal regeneration forces, elastic bodies recover their original form. In the same way, the internal forces & external forces are the opposite. If a force F is uniformly enforced over a surface area (A) the stress is described as the force per unit area. The S.I unit of stress is Nm-2.
| Stress = Force(F) / Area(A) |
Stress Types
Three kinds of stress are
- Bulk Stress or volume stress
- Shear stress or tangential stress
- Longitudinal stress
Strain
A body gets deformed under stress. The fractional shift in the dimension of a body generated by the external stress on which it operates is called strain. The charge ratio of any dimension to its original dimension is regarded as strain. Since strain is the ratio of two physical quantities which are identical, it is just a number. There is no unit or dimension for strain.
| Strain = (Change in dimension)/ (Initial dimension) |
Strain types
The three kinds of strain are listed below.
- Volume strain
- Longitudinal strain
- Tangential strain or shearing strain
Modulus of elasticity
The measurement of the elasticity of a material is the modulus of elasticity, also recognized as Elastic Modulus or simply Modulus. The modulus of elasticity measures the resistance of a material to non-permanent, or elastic, deformation. Materials will first show elastic properties when under stress: stress can cause them to deform, but once the stress is released, the material will recover to its previous condition. Materials reach a plastic environment after moving via the elastic region and via their yield point, whereby they show permanent deformation after the tensile stress is released.
Definition of the Elasticity Modulus
As per Hooke’s law, up to the proportional restriction “for minor deformation, stress is directly proportional to strain”.
Hooke’s Law mathematically interpreted as
| σ = E ε |
Where
σ = Stress
ε = Strain
E = Constant known as modulus elasticity.
Modulus of elasticity can be expressed as
| E = (F ✕ L)/ (A ✕ δL) |
The modulus of Elasticity can be defined as the ratio of normal stress to longitudinal strain.
