Stress and Strain

When a force is applied to a body, it causes a deformation (change in shape or size). Inside the body, restoring forces are immediately set up to oppose this change. These internal forces try to bring the body back to its original state. The concepts of stress and strain are used to describe the elastic properties of a body under these conditions.

The internal restoring force per unit area of a body is called stress.

OR

The internal restoring force acting per unit area of a deformed body is called stress.

• SI Unit: N/m² (pascal, Pa)
   Dimensions: [M¹L⁻¹T⁻²]

Strain is defined as the ratio of the change in dimensions of the body to its original dimensions.

OR

The ratio of change in configuration to the original configuration is called strain.

• It has no unit and no dimensions (pure ratio).

The elastic properties of a body are characterized by its response to an applied force, which leads to stress and strain.

1. Deformation: When an external force, called the deforming force, is applied to a body, it causes a temporary or permanent change in the body's shape or size.
2. Restoring Force: As the body starts to deform, internal restoring forces are set up within the material. These forces are directed to oppose the deformation.
3. Equilibrium: When the body is in equilibrium in its altered shape or size, the magnitude of the deforming force and the internal restoring force are equal and opposite.
4. Stress: Stress is the measure of these internal restoring forces acting per unit area. It represents the intensity of the forces trying to restore the body to its original state.
5. Strain: Strain is the measure of the deformation itself. It quantifies how much the body has changed relative to its original size or shape, specifically as a ratio of the change in dimension to the original dimension. This deformation occurs when two equal and opposite forces are applied to an elastic body.

The ratio of change in length of the body to its initial length is called longitudinal strain: ε = ΔL/L.

The ratio of change in volume of the body to its original volume is called volume strain: ΔV/V.

The angular displacement of the surface in direct contact with the applied shear stress from its original position is called shear strain: τ = W/L = tan ⁡θ.

When there is an increase in the length or extension of the body in the direction of the applied force, the stress produced is called tensile stress.

When there is a decrease in the length or compression of the body due to the applied force, the stress produced is called compressive stress.

When equal normal forces are applied on every surface of a body causing a change in volume, the restoring force opposing this change per unit area is called hydraulic stress (also called volume stress).