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?
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.
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?