Class 12 > Unit # 20:AC Circuits > Deformation in One Dimension

Talha's Physics Academy

Deformation, Stress, Strain, and Hooke's Law

Video Lecture

"Watch the complete lecture on deformation in one dimension, exploring the concepts of stress, strain, and their direct proportionality under Hooke's Law."

Watch on YouTube: Deformation in One Dimension | Talha's Physics Academy

1. Deformation

"In material science, deformation refers to modifications of the shape or size of an object due to applied forces or a change in temperature."

Common examples of deformation include:

1. Stretching a rubber band, which causes an elastic deformation.
2. Squishing a metal drink can.
3. Bending a metal bar permanently beyond its flexibility limit.
4. Breaking a piece of chalk.

2. Stress

Stress in physics is defined as the force exerted per unit area of a substance. It quantifies the magnitude of the external force responsible for causing material deformation.

• Tensile Stress: Occurs when a pulling force is applied, resulting in elongation.
• Compressive Stress: Occurs when a pushing force is applied, producing compression.

$$\text{Stress } (\sigma) = \frac{F}{A}$$

Unit: $\text{N/m}^2$ (or Pascals, $\text{Pa}$)

3. Strain

Strain is the measure of how much a material deforms relative to its original dimensions when a force is applied. For one-dimensional deformation, it is evaluated as the change in length per unit original length.

$$\text{Strain } (\epsilon) = \frac{\Delta L}{L_0}$$

Where $\Delta L$ is the change in length and $L_0$ is the original length.

Unit: It has no unit (dimensionless ratio, as length units cancel out).

4. Relation Between Stress and Strain (Hooke’s Law)

The relationship between stress and strain is direct proportionality up to a specific threshold known as the elastic limit. This is governed by Hooke’s Law, which states that within the elastic limit, the strain produced in a solid is directly proportional to the applied stress.

$$\text{Stress} \propto \text{Strain}$$ $$\text{Stress} = E \times \text{Strain}$$ $$\frac{\text{Stress}}{\text{Strain}} = \text{Constant}$$

Where the constant of proportionality represents the elastic modulus of the material. If the applied stress exceeds the elastic limit, the material permanently deforms and fails to return to its original shape.

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