#hookeslawandelasticity

Introduction:

Mechanical properties tell us how a solid responds to forces. Two core ideas are stress and strain. They help predict strength, elasticity, and failure. This guide from VAVA Classes explains definitions, types, formulas, the stress–strain curve, and real-world uses in clear language.

What Are Mechanical Properties of Solids?

These properties describe how materials behave under load: whether they are rigid, ductile, brittle, or tough. Key measures include elasticity, plasticity, strength, and toughness.

Stress:

Definition: Internal restoring force per unit area.

Formula: Stress = Force / Area

Types of Stress:

• Tensile Stress: stretching action • Compressive Stress: squeezing action • Shear Stress: tangential force causing layers to slide

Strain:

Definition: Relative deformation (dimensionless).

Formula: Strain = Change in dimension / Original dimension

Types of Strain:

• Longitudinal Strain: change in length per original length • Volumetric Strain: change in volume per original volume • Shear Strain: angular distortion

Hooke’s Law and Elastic Constants:

Within the elastic limit, stress is proportional to strain.

Formula: Stress ∝ Strain

Elastic Moduli:

• Young’s modulus (E): ratio of normal stress to longitudinal strain • Shear modulus (G): ratio of shear stress to shear strain • Bulk modulus (K): ratio of pressure change to volumetric strain • Poisson’s ratio (ν): lateral strain / longitudinal strain

Stress–Strain Curve:

1. Proportional limit: Hooke’s law holds 2. Elastic limit: end of reversibility 3. Yield point: start of plastic flow 4. Ultimate tensile strength: maximum stress 5. Fracture: necking and break

Applications and Examples:

• Bridges and buildings: beams using E and yield strength • Machine parts: torsion and shear modulus • Pressure vessels: hoop stress and bulk modulus • Sports gear: flexibility and strength tuning

Conclusion: