# Magnitude of the strain tensor

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 June 15, 2007, 09:37 Hi FOAMers, I would like to #1 New Member   Max Join Date: Mar 2009 Posts: 24 Rep Power: 17 Hi FOAMers, I would like to have your opinion about the following problem: - the strain tensor is defined as S = 2 * symm(grad(U)) = grad(U) + grad(U)^T (1) - and, according to the linear algebra, its magnitude is |S| = sqrt(.5 * (S_ij * S_ij)) (2) - now, if I let OpenFOAM to write out both the U gradients and S S = mag(2*symm(fvc:grad(U))) (3) I see that values coming from (3) and (2) (calculated manually) are different. I had a look to the vectorSpace class and what I can understand (with my little C++ knowledge), is that the magnitude of a tensor S is given by |S| = sqrt(Sij * Sij) (4) which differs from Eq. (2). Additionally, a manual check with the help of Eq.(4) does not return what is given by OF (Eq. (3)) and there is not any constant factor between their values... What am I missing? Thanks a lot, Massimiliano

 August 7, 2011, 03:02 #2 Senior Member   Claus Meister Join Date: Aug 2009 Location: Wiesbaden, Germany Posts: 241 Rep Power: 17 Hello Foamer, strain rate Tensor is defined by S:=1/2 [ grad(U)+gard(U)^T] Try it and give me respond if it's worked. Cheers