Jaekwang, >From this symmetric gradient tensor, do we have one easy way to calculate > the following "the second invariant of rate-of-strain tensor"? > There is SymmetricTensor::second_invariant [1] which is defined as I2 = 1/2[ (trace sigma)^2 - trace (sigma^2) ] and SymmetricTensor::first_invariant [1] which just the trace I_1=trace sigma. According to Wikipedia [2], your \Pi_\gamma can then be expressed as \Pi_\gamma^2 = 1/2(I1^2 -2 I2).
Best, Daniel [1] https://www.dealii.org/8.4.0/doxygen/deal.II/classSymmetricTensor.html#a7bbdfc57da6931de6a1757a0fa7ee982 [2] https://en.wikipedia.org/wiki/Invariants_of_tensors > > <https://lh3.googleusercontent.com/-k8SKQzE3aEk/WAQQnorR5lI/AAAAAAAAA60/4XJBD25ZRSAa2IYsdK4NCMOuY3QXJydmwCLcB/s1600/Screen%2BShot%2B2016-10-16%2Bat%2B6.42.40%2BPM.png> > > > > Regards, > > Jaekwang Kim > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
