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Double dot product in Cylindrical Polar coordinates

  1. Jul 31, 2014 #1
    Hello,

    I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows:

    2W = σijεij

    Where σ and ε are symmetric rank 2 tensors.

    For cartesian coordinates it is really easy because the metric is just the identity matrix, hence:

    2W = σxxεxx + σyyεyy + σzzεzz + 2 σxyεxy + 2 σxzεxz + 2 σzyεzy

    My question is how the expression should be for cylindrical polar coordinates (r,θ,z)

    Thanks!
     
  2. jcsd
  3. Jul 31, 2014 #2
    Since cylindrical polar coordinates are likewise orthogonal, it's going to be pretty much analogous.

    Chet
     
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