Mechanical Properties of Solids

Elastic Behaviour of Materials, Stress and Strain

  • Elasticity deals with property of materials, its strength and ability to withstand against external forces which are acting on it.
  • The forces acting between the atoms due to Electrostatic interaction between the charges of the atoms are called interatomic forces.
  • Attractive forces between the nucleus of one atom and electrons of the other atom. These attractive forces tend to decrease the potential energy of the pair of atoms.
  • The force between molecules dues to Electrostatic interaction between the charges of the molecules are called inter molecular forces.
  • A body whose size and shape cannot be changed however large the applied forces may be is called rigid body
  • The External force which changes or ties to change the shape and size is called a deforming force.
  • The internal force which restores the size and shape of the body when deforming force is with drawn is called restoring force.
  • The magnitude of deforming force is equal to the Restoring force.
  • In a solid each atom or molecules are bonded together by inter atomic forces and in state position.
  • Elasticity is the property of a material by virtue of which it regains its original size and shape when deforming forces are withdrawn.
  • There is no perfect Elastic material exist in nature Quarts is nearly perfect Elastic body.
  • Plasticity is the property of material by virtue if which it does not regain the size and shape when deforming force is removed.
  • Steel is more Elastic than rubber.
  • The restoring force per unit area is called stress S = F/A
  • The stress Normal to the surface called Normal stress and tangential called tangential stress.
  • Shearing stress is defined as the Tangential restoring force per unit area of cross section.
  • Longitudinal stress and bulk stress are normal stress is which produce change in size, shearing stress is a tangential stress which produce change in shape.
  • Bulk stress is defined as the volume restoring force per unit area of cross section.
  • Strain is defined as the change in dimension per unit original dimension.
  • Linear strain is defined as the change in length to unit original length.
  • Shear strain is defined as the linear displacement of layer to distance between layers
  • Bulk strain is defined as the change in volume per unit original volume.

View the Topic in this video From 0:47 To 56:34

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1. Stress: The internal restoring force acting per unit area of a deformed body is called stress.
                         \tt Stress = \frac{Restoring\ force}{Area}=\frac{F}{A}

2. Strain
The fractional change in configuration is called strain.
                        \tt Strain = \frac{Change\ in\ configuration}{Original\ configuration}

3. Longitudinal strain = \tt \frac{Change\ in\ length}{Original\ length}=\frac{\Delta l}{l}

4. Volumetric strain = \tt \frac{Change\ in\ volume}{Original\ volume}=\frac{\Delta v}{v}

5. Shearing strain = Angular displacement of the plane perpendicular to the fixed surface. \tt \phi=\frac{x}{L}