Elasticity

Elasticity: Elasticity is the property of the body by virtue of which a deformed body regains its original shape, size, and position after removal of deformation.

Plasticity: The property of a body by virtue of which it does not regain its original size and shape after removal of an external applied force is called plasticity.

Deforming force: A force is said to be a deforming force if it can change the shape, size, and position of the object.

Restoring force: A force is said to be a restoring force if it brings the object back to its original shape, size, and position after the removal of a deforming force.

Types of objects on the basis of elasticity

1. Elastic object: An object is said to be elastic if it regains its original shape and position after the removal of the deforming force.
2. Plastic Object: An object is said to be plastic if it doesn’t regain its original shape and position after the removal of the deforming force.

Stress

Stress: Stress that occurs w/s defined the force acting per unit area of material. Mathematically, it can be expressed as

Types of Stress

i. Normal stress: Stress that occurs when a member is loaded by an axial force is known as normal stress. It represents the symbol σ. The SI unit of Normal stress is MPa. ​ Normal stress is also called Longitudinal and tensile stress.

ii. Bulk Stress: The stress by which the volume of an elastic body is changed is called bulk stress. The force is applied perpendicular to the whole surface of the body.

iii. Shear Stress: The stress by which the shape of an elastic body is changed is called shear stress.

Strain

Strain: The ratio of the change in size of object to its original size is called strain. We can also say that strain is the effect and stress is its cause.
The strain is dimensionless quantity because it is the ratio of two same physical quantities. So, it has no unit. Like stress it is a tensor.

Types of Strain:
i. Longitudinal or tensile or linear strain
ii. Bulk strain or volume strain
iii. Lateral strain
iv. Shear strain

Hooke’s Law

It states that the restoring force (deforming force) is directly proportional to the extension within the elastic limit. i.e.,

F  ∝  x     (where x=extension)

F=kx (where k is the constant of proportionality called the force constant)

Alternate Form of Hooke’s Law: Hooke’s Law can also be stated as: The stress is directly proportional to the strain within the elastic limit.

Stress  ∝   train

$$\text{Stress}=E\times \text{Strain}(\text{where }E\text{ is the modulus of elasticity})$$Therefore,

Stress-Strain Graph: Elastic limit

Modulus of Elasticity (E)

The Modulus of Elasticity, also known as Young’s Modulus, is a measure of the stiffness of a material. It defines the relationship between stress and strain in the elastic (reversible deformation) region of a material.
The modulus of elasticity is the ratio of stress to strain within the elastic limit of a material.

Types of Modulus of Elasticity:
The modulus of elasticity refers to the ratio of stress to strain in a material within its elastic limit. It measures the stiffness of a material under various types of deformation. There are three main types of modulus of elasticity:

1. Young’s Modulus (E): 
It is the ratio of longitudinal (tensile or compressive) stress to longitudinal strain within the elastic limit. Mathematically, it can be expressed as

Where:

• $F$ = Applied force
• $A$ = Cross-sectional area
• $\Delta L$ = Change in length
• $L$ = Original length
• Units: Pascal (Pa) or N/m²