Answer to Question #247608 in Physics for Tithi

Question

What is meant by elasticity? Explain the elastic and plastic materials. Name the four elastic constants, and explain what they mean. Establish the expressions to show how they are related to each other for an isotropic medium. What is meant by Poisson’s ratio? Compute its limiting values.

Answer 1

Elasticity is a property of materials to return to their initial shape after some external force was applied. Elastic materials are materials that have elasticity, plastic materials are materials that do not keep the initial shape after the force is removed.

The four elastic constants:

• Young's modulus E. Makes bodies resist stretching or compression in axial direction.
• Bulk modulus K. Makes bodies resist volumetric compression or stretching.
• Rigidity modulus G. Makes bodies resist shear stress.
• Poisson's ratio μ. The ratio of lateral to longitudinal stress.

The relation:

$$\mu=\frac{3K-2G}{6K+2G},\\\space\\ -1<\mu<0.5.$$