Physics deformation

Deformation is the change in the shape, size, or volume of a body when external forces act on it. In physics, we study how materials respond to forces—whether they stretch, compress, bend, or twist—and whether they return to their original form or remain permanently changed.

1. Types of Deformation

• Elastic deformation: Temporary change. The body returns to its original shape and size when the deforming force is removed. This occurs within the elastic limit of the material.

• Plastic (or permanent) deformation: Permanent change. The body does not return fully to its original shape/size after the force is removed. This happens beyond the elastic limit.

• Brittle fracture: Some materials (e.g., glass, cast iron) break with little or no plastic deformation.

• Ductile behaviour: Materials that can undergo significant plastic deformation before breaking (e.g., copper, aluminium, mild steel).

2. Stress and Strain

Stress is the internal restoring force per unit area set up inside a body when external forces try to deform it.

$\text{Stress} = \frac{F}{A}$

• Unit: $N\,m^{-2}$ or pascal ($Pa$)

• Types of Stress:

  • Tensile stress: Force tends to stretch the body (pulling).

  • Compressive stress: Force tends to shorten the body (pushing).

  • Shear (tangential) stress: Force is parallel to the surface and tends to twist or slide layers.

  • Bulk (volume) stress: Force acts uniformly from all directions (e.g., pressure on a submerged object).

Strain is the measure of deformation produced. It is a ratio (dimensionless, no unit).

• Longitudinal (tensile/compressive) strain:

$\text{Longitudinal strain} = \frac{\Delta L}{L}$

(change in length / original length)

• Shear strain:

$\text{Shear strain} = \frac{\text{lateral displacement}}{\text{original length}} = \tan(\theta) \approx \theta$

(in radians for small angles)

• Volume strain:

$\text{Volume strain} = \frac{\Delta V}{V}$

(change in volume / original volume)

3. Hooke’s Law

Within the elastic limit, stress is directly proportional to strain.

$\text{Stress} \propto \text{Strain} \quad \Rightarrow \quad \frac{\text{Stress}}{\text{Strain}} = \text{constant}$

The constant is called the modulus of elasticity (or elastic modulus).

Hooke’s law can also be written for springs as:

$F = k x$

where $k$ is the spring constant (stiffness) and $x$ is the extension.

4. Moduli of Elasticity

Different moduli describe different types of deformation:

• Young’s modulus ($Y$ or $E$): For longitudinal stress and strain (stretching or compressing a wire/rod).

$Y = \frac{\text{longitudinal stress}}{\text{longitudinal strain}} = \frac{F/A}{\Delta L/L} = \frac{F L}{A \Delta L}$

• Unit: $Pa$ or $N\,m^{-2}$

• High $Y$ means the material is stiff (hard to stretch). Example: steel has a much higher $Y$ than rubber.

  • Shear modulus ($G$ or $\eta$): For shear stress and strain.

$G = \frac{\text{shear stress}}{\text{shear strain}} = \frac{F/A}{\theta}$

• Bulk modulus ($K$ or $B$): For volume stress and strain (change under uniform pressure).

$K = \frac{\text{volume stress}}{\text{volume strain}} = -\frac{\Delta P}{\Delta V / V}$

(The negative sign shows that volume decreases when pressure increases.) The reciprocal of bulk modulus is compressibility.

5. Stress–Strain Curve (Typical for a Ductile Metal)

A graph of stress against strain shows important points:

• Proportional limit: Up to this point Hooke’s law is obeyed (straight line).

• Elastic limit: Beyond this, permanent deformation begins. The material may still recover partially but not fully.

• Yield point: Sudden increase in strain with little or no increase in stress (material starts to flow).

• Ultimate tensile strength (UTS): Maximum stress the material can withstand.

• Breaking point (fracture): Material finally breaks.

Beyond the elastic limit, the material enters the plastic region. Work hardening can occur as the material is further deformed.

6. Factors Affecting Deformation / Elasticity

• Nature of the material (molecular structure, bonding)

• Temperature (most materials become less elastic / more plastic at higher temperatures)

• Cross-sectional area and length of the specimen

• Magnitude and duration of the applied force

• Presence of impurities or defects

• Heat treatment / annealing (can restore elasticity in some metals)

7. Energy Stored in a Stretched Wire (Elastic Potential Energy)

When a wire is stretched within the elastic limit, the work done is stored as elastic potential energy:

$U = \frac{1}{2} F \times \Delta L = \frac{1}{2} \times \text{stress} \times \text{strain} \times \text{volume}$

$U = \frac{1}{2} Y \times (\text{strain})^2 \times \text{volume}$

8. Important Practical Points (SHS Context)

• Elastic limit and breaking stress are crucial in engineering design (bridges, buildings, cables must stay well below the elastic limit under normal loads).

• Rubber has a low Young’s modulus and a large elastic range; steel has a high Young’s modulus and a smaller elastic range.

• Hooke’s law is the basis of spring balances and many measuring instruments.

• Thermal expansion can also cause deformation if a material is constrained.

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