# Re: [deal.II] Re: Easy way to calculate second-deviatoric tensor

On 10/17/2016 03:36 AM, Daniel Arndt wrote:



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).



You can also compute it directly: if you have the symmetric gradient eps(u) already computed, then
  Pi_gamma = std::sqrt (2*eps*eps);

Best
W.

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Wolfgang Bangerth          email:                 bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

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