How are stress and strain different?

Stress is a measure of the internal resistance of a material to deformation when subjected to external forces. It is defined as the force acting on an object per unit area. Mathematically, it can be represented as: \[ \sigma = \frac{F}{A} \] where, \( \sigma \) = Stress, \( F \) = Force acting on the object, and \( A \) = Area over which the force is acting.

Strain is a measure of the deformation experienced by an object subjected to external forces. It is a dimensionless quantity, defined as the relative change in shape or size of an object due to the applied forces. Mathematically, strain can be represented as: \[ \epsilon = \frac{\Delta L}{L} \] where, \( \epsilon \) = Strain, \( \Delta L \) = Change in length, and \( L \) = Original length.

Stress and strain, both are essential concepts in the study of material deformation. However, they are different in several aspects: 1. Stress is the measure of resistance, while Strain is the measure of deformation. 2. Stress has units and dimensions, whereas Strain is a dimensionless quantity. 3. Stress depends on the applied force and the cross-sectional area of the material, while Strain depends on the change in length and the original length of the material.

The unit of stress in the International System of Units (SI) is Pascal (Pa), where 1 Pascal is equal to 1 Newton force per square meter (1 Pa = 1 N/m²). In the Imperial system, stress can be measured in pounds-force per square inch (psi). For strain, since it is dimensionless, it does not have any units. It is usually represented as a ratio or as a percentage. In conclusion, stress and strain are related concepts as they are vital in understanding the deformation of materials subjected to external forces. However, they have different meanings, applications, and units. While stress deals with the internal resisting force per unit area, strain measures the relative change in shape or size of an object due to applied forces.