Mechanical Properties of Solids - Important Formulas, Definitions, and Examples | 11th Physics

Chapter 6: Mechanical Properties of Solids

Chapter 6: Mechanical Properties of Solids

Formulas: Stress, Strain, Hooke’s Law, Young’s Modulus, Bulk Modulus, Shear Modulus

Introduction

This chapter explores the mechanical behavior of solid materials when subjected to different types of forces. The study of the mechanical properties of solids includes concepts like stress, strain, and elastic behavior, governed by Hooke's Law. These properties are essential for understanding how materials deform under force and how they return to their original shape when the force is removed.

1. Stress and Strain

Definition:

Stress is the internal restoring force per unit area that develops within a material when an external force is applied. It is measured in Pascals (Pa).

  • Formula: Stress (σ) = Force (F) / Area (A)

Strain is the relative change in the shape or size of a material as a response to stress. It is a dimensionless quantity.

  • Formula: Strain (ε) = Change in Length (ΔL) / Original Length (L)

2. Hooke’s Law

Definition:

Hooke's Law states that within the elastic limit, the stress applied to a solid is directly proportional to the strain produced in the solid.

  • Formula: Stress ∝ Strain or σ = E × ε, where E is the Young's Modulus.

Elastic Limit:

  • The point beyond which a material no longer behaves elastically and may deform permanently.

3. Elastic Moduli

Young's Modulus (E):

Young’s Modulus measures the stiffness of a material and is defined as the ratio of tensile stress to tensile strain.

  • Formula: E = Stress / Strain = (F/A) / (ΔL/L)
  • Materials with a high Young’s Modulus are more rigid.

Bulk Modulus (K):

The Bulk Modulus measures a material's resistance to uniform compression. It is the ratio of volumetric stress to the volumetric strain produced.

  • Formula: K = - (ΔP) / (ΔV / V), where ΔP is the change in pressure and ΔV/V is the fractional change in volume.

Shear Modulus (G):

Shear Modulus, also known as Modulus of Rigidity, measures a material's response to shear stress.

  • Formula: G = Shear Stress / Shear Strain

4. Poisson's Ratio

Definition:

Poisson's Ratio is the ratio of lateral strain to longitudinal strain when a material is stretched.

  • Formula: ν = - (lateral strain) / (longitudinal strain)

Key Points:

  • It has no units.
  • Most materials have a Poisson’s ratio between 0 and 0.5.

5. Elastic and Plastic Behavior

Elastic Behavior:

When a material returns to its original shape after the removal of stress, it is said to exhibit elastic behavior. This behavior is governed by Hooke’s Law.

Plastic Behavior:

When a material undergoes permanent deformation and does not return to its original shape after the removal of stress, it is said to exhibit plastic behavior.

Yield Point:

The point at which a material transitions from elastic to plastic behavior.

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