Question

obtain a relation between Young's modulus,bulk modulus and poisson's ratio​

Answer 1

Answer:

Poisson's ratio is related to elastic moduli K (also called B), the bulk modulus; G as the shear modulus; and E, Young's modulus, by the following (for isotropic solids, those for which properties are independent of direction). The elastic moduli are measures of stiffness. They are ratios of stress to strain.

Answer 2

Answer:

This could be answered by simply providing the equations relating these elastic constants. But that’s not as interesting as demonstrating how these equations arise. Thus I’ll do that starting with the equation tying together bulk modulus K, Poisson’s ratio ν, and elastic modulus E.

The generalized Hooke’s law for the x-, y- and z-directions is

ϵx=1E[σx−ν(σy+σz)]

ϵy=1E[σy−ν(σz+σx)]

and

ϵz=1E[σz−ν(σx+σy)]

where ε is strain and σ is stress.