Lecture Notes on Elasticity

Review of Elasticity Concepts

• Elasticity: Ability of a material to return to its original shape after deformation (temporary deformation).
• Plasticity: Permanent deformation when material does not return to original shape after force is removed.
• Types of Deformation:
  • Elastic Deformation (Temporary)
  • Plastic Deformation (Permanent)

Properties of Materials

• Hardness
• Brittleness
• Malleability
• Ductility
• Elasticity
• Density
• Feasibility
• Conductivity

Hooke's Law

• States that force applied is proportional to the change in length or extension (F = -kx).
• Negative sign indicates a restoring force.
• Restoring Force: Force that brings a material back to its original shape.
• Elastic limit: Maximum stress that can be applied without causing permanent deformation.

Stress and Strain

• Stress: Force over area.
• Strain: Change in length over original length.
• Types of Stress:
  • Tensile Stress: Equal and opposite forces stretching an object.
  • Compressive Stress: Equal and opposite forces compressing an object.

Modulus of Elasticity

• Ratio of stress to strain.
• Types:
  • Young's Modulus (E or Y)
  • Shear Modulus
  • Bulk Modulus
• Formula: E = FL / AΔL

Shear Modulus

• Describes resistance to shear deformation.
• Formula: Shear Stress / Shear Strain
• Example: Tilting a table top without changing its shape.

Bulk Modulus

• Response to change in volume under pressure.
• Formula: Bulk Stress / Bulk Strain
• Negative sign denotes volume decrease.

Energy Stored in Elastic Materials

• Potential Energy stored when a material is deformed.
• Formula: Energy = 1/2 kx²

Relationship Between Moduli

• All related through stress and strain ratios.
• Poisson's Ratio connects the moduli.

Examples

• Calculation of shear modulus, bulk modulus.
• Practical examples solving for stress, strain, energy.

Practice Questions

• Multiple-choice questions provided for further practice.

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Next Class: Wednesday, 10 to 11 AM. Have a great weekend!