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Bulk modulus and poisson's ratio

  1. Mar 31, 2009 #1
    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. jcsd
  3. Mar 31, 2009 #2
    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.
  4. Mar 31, 2009 #3
    Perhaps this will bring the answer out.

    A body subjected to a uniform hydrostatic pressure all three stress components are equal to a -p.
  5. Mar 31, 2009 #4
    i see. so the total hydrostatic pressure is the sum of all components, and that's where the factor of 3 comes in, right?
  6. Mar 31, 2009 #5
    Yes that is right. But it is a negative 3. You are in compression.
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