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

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

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