Bulk modulus and poisson's ratio

[ABoul]

Homework Statement

derive the equation for the bulk modulus, K = E/3(1 - 2v), where v is poisson's ratio.

Homework Equations

E = stress/e, where e is strain

The Attempt at a Solution

e_v = e_x + e_y + e_z
e_y = e_z = -v*e_x
e_v = (1 - 2v)*e_x

K = stress/e_v
therefore K = stress/[(1 - 2v)*e_x]

i am out by a factor of 1/3. where have i gone wrong?

 

[CFDFEAGURU]

Here is a hint. e = epsilon sub x + epsilon sub y + epsilon sub z. Look at the equations for epsilon sub x, epsilon sub y, and epsilon sub z.

For instance, epsilon sub x = (sigma sub x) / E - (v*sigma sub y) / E - (v*sigma sub z) / E.

 

[CFDFEAGURU]

Perhaps this will bring the answer out.

A body subjected to a uniform hydrostatic pressure all three stress components are equal to a -p.

 

[ABoul]

Perhaps this will bring the answer out.

A body subjected to a uniform hydrostatic pressure all three stress components are equal to a -p.

i see. so the total hydrostatic pressure is the sum of all components, and that's where the factor of 3 comes in, right?

 

[CFDFEAGURU]

Yes that is right. But it is a negative 3. You are in compression.