MIND GROW Magazine

Properties of Matter – Stage 1 (Page 7)

Elastic Energy, Resilience & Stress–Strain Curve (IIT-JEE Core)

1. Elastic Energy

When a body is deformed within elastic limit, work is done on it. This work is stored in the body as elastic potential energy.

Elastic Energy = Work Done during deformation

U = ½ × Stress × Strain × Volume

2. Elastic Energy in Terms of Young’s Modulus

Using Hooke’s law:

U = (½) × Y × (Strain)² × Volume

Valid only within elastic limit
Extremely important for numerical problems

IIT Tip:
Energy depends on square of strain, not directly on force.

3. Resilience

Resilience is the ability of a material to absorb energy when deformed elastically and release it upon unloading.

Resilience = Elastic Energy stored per unit volume

Resilience = ½ × Stress × Strain

4. Proof Resilience

The maximum elastic energy per unit volume that a body can store without permanent deformation is called Proof Resilience.

Proof Resilience = ½ × Elastic Limit × Corresponding Strain

JEE Favourite:
Area under stress–strain curve up to elastic limit = Proof Resilience

5. Stress–Strain Curve (Ductile Material)

O–A: Proportional limit
A–B: Elastic limit
B–C: Yielding region
C–D: Ultimate stress
D–E: Fracture point

Key Concept:
Beyond elastic limit → permanent deformation occurs.

6. Brittle vs Ductile Materials

Property	Ductile	Brittle
Plastic region	Large	Almost zero
Fracture	After large deformation	Sudden
Examples	Copper, Steel	Glass, Cast iron

7. Area under Stress–Strain Curve

The area under stress–strain curve gives elastic energy per unit volume.

Area = Elastic Energy Density

Numerical Shortcut:
Triangle area = ½ × Stress × Strain

Stage 1 – Page 7 Summary

Elastic energy formula
Resilience & proof resilience
Stress–strain curve interpretation
Ductile vs brittle comparison

Stage 1 – Page 7 Completed ✅
Next: Thermal Stress, Thermal Strain & Expansion – Page 8

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