Bulk modulus

1. Mar 31, 2009

ABoul

1. The problem statement, all variables and given/known data
derive the equation for the bulk modulus, K = E/3(1 - 2v), where v is poisson's ratio.

2. Relevant equations
E = stress/e, where e is strain

3. 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?

2. Mar 31, 2009

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.

3. Mar 31, 2009

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.

4. Mar 31, 2009

ABoul

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

5. Mar 31, 2009

CFDFEAGURU

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