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Poissons ratio close-packed spheres

  1. Oct 6, 2013 #1
    Hello,

    See question 7.4 from the link.

    http://books.google.com/books?id=0N...CfU3U1qlbfJCRXsRow1xzu7hxEWOjYCow&w=685&w=800

    "Assuming that atoms are hard elastic spheres, show that Poisson's ratio for a close-packed array of spheres is 1/3"

    I am having trouble explaining the proof for this.

    I know the that the volume modulus, K, = E(elastic modulus) / ((3(1-2[itex]\upsilon[/itex])) where [itex]\upsilon[/itex] is the elastic modulus.

    K = E / (3(1-2[itex]\upsilon[/itex]))

    When [itex]\upsilon[/itex] = 1/3, K=E.

    I'm thinking that since for a hexagonal close packed structure, HCP, the angles between lattice sites is 120°, or 1/3 of the plane of a full crystal structure.

    Refer to:
    http://www.science.uwaterloo.ca/~cchieh/cact/fig/hcp.gif
    http://www.chem.ufl.edu/~itl/2045/lectures/h1.GIF [Broken]

    Therefore the elastic properties for a given volume is split in thirds? It seems like a misleading argument, but I can't find a way to explain it with math!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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