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Understanding the strain energy function invariant term

  1. May 24, 2012 #1
    Hi, Dear all,

    Facing problem to understand strain energy function invariant terms
    A typical strain energy function consist of strain invariant can be defined as followed
    I1 and I4 are so called invariants of Green's strain tensor. (large deformation)

    here is the complete link taken http://www.engin.umich.edu/class/bme456/ch6fitelasticmodelconstant/bme456fitmodel.htm [Broken]

    1. I read from article that N is a unit vector along the stretch direction, so can i conclude that
    I4 consist of unit vector multiply with principal stretch?

    2. the lamda in the formula is stretch ratio or principal stretch?
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 27, 2012 #2
    After giving it a quick read,

    2)[itex]\lambda_1 ,\lambda_2 ,\lambda_3[/itex] are the "normal stretch", where the link calls them that. but I think they are just the stretch coefficients for force in the same direction as the normal plane vector.

    1) Yes, It seems so then, assuming you have "principle"[itex]\iff[/itex]"normal"

    That's my take on it.
  4. May 30, 2012 #3
    Hi, jfy4,

    I actually try to read more, but cannot find resources.
    1. so all the N1, N2, N3,should always equal to 1? or under any condition they will change?
    2. or can I call them as right stretch tensor?sorry, as i cannot differentiate left and right stretch tensor, so cannot evaluate more for you.
  5. May 30, 2012 #4
    well, [itex]N_i[/itex] is a unit vector, a vector whose magnitude is 1. That is [itex]N_i N_i=N_{1}^{2}+N_{2}^{2}+N_{3}^{2}=1[/itex]. But, it is a vector, not a constant, so it's direction can vary. It says:
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