Question

obtain a relation between youngs modulus bulk modulus and poissons ratio with explaination​

Answer 1

Answer:

K =Y / 3(1 - 2/μ)

Where,

K is the Bulk modulus.

Y is Young’s modulus.

μ is the Poisson’s ratio.

Relation Between Young’s Modulus And Bulk Modulus derivation

Young’s modulus is the ratio of longitudinal stress to longitudinal strain. Represented by Y and mathematically given by-

Y=σϵ

On rearranging-

ϵ=σY

When the deforming force is ling x direction-

ϵx=σY−1mσY−1mσY

Here negative sign represents the reduction in diameter when longitudinal stress is along the x-axis.

1m arise due to compression along other two direction.

When the deforming force is ling y-direction-

ϵy=σY−1mσY−1mσY

When the deforming force is ling z-direction-

ϵz=σY−1mσY−1mσY

The volumetric strain is given by-

ϵv=ϵx+ϵy+ϵz

Substituting the corresponding values to ??x ,??y , ??z we get-

ϵv=3σY[1−2m]

The Bulk modulus is the ratio of volumetric/bulk strain to volumetric/bulk stress, represented by K and mathematically given by-

K=σϵv

Substituting ϵv=3σY[1−2m] in above equation we get-

K=σ3σY[1−2m] ⇒K=Y3[1−2m]

Hope you understood the relation and conversion between Young’s modulus and the Bulk modulus of an object.

PLS MARK ME BRAINLIEST!