Stress and Strain

Stress and Strain Notes

Stress:

1. Definition: Stress is the force acting on a material per unit area. It is a measure of
the internal resistance of a material to deformation under an applied force.
2. Types of Stress:
○ Normal Stress (σ): The stress acting perpendicular to the cross-sectional
area of the material.
○ Shear Stress (τ): The stress acting parallel to the cross-sectional area of
the material.
3. Formulas:
○ Normal Stress: σ=AF
○ Shear Stress: τ=AF
4. Units: Stress is measured in Pascals (Pa) or N/m².
5. Stress-Strain Curve: Materials exhibit different behaviors under stress. The
stress-strain curve illustrates how a material deforms under increasing stress.

Strain:

1. Definition: Strain is the measure of deformation or change in shape of a material
in response to stress. It is a dimensionless quantity.
2. Types of Strain:
○ Normal Strain (ε): The change in length per unit original length of the
material.
○ Shear Strain (γ): The change in shape per unit original shape of the
material.
3. Formulas:
○ Normal Strain: ε=LΔL
○ Shear Strain: γ=tan(θ), where θ is the angle of deformation.
4. Units: Strain is a dimensionless quantity.
5. Relationship between Stress and Strain:
○ Hooke's Law: In the elastic region of a material, stress is proportional to
strain. σ=Eε, where E is the Young's Modulus.
6. Plastic Deformation: Beyond a certain stress, materials undergo plastic