|
[Sponsors] |
February 19, 2013, 09:06 |
Magnitude of a tensor
|
#1 |
Member
M Mallikarjuna Reddy
Join Date: Jul 2012
Posts: 91
Rep Power: 13 |
Dear all,
I would like to share your opinion on my doubt. - The rate of strain tensor is written as(if i have not understand wrongly): E=symm(grad(U))=1/2[grad(U)+grad(U)^T].......................(1) - According to linear algebra the magnitude of any tensor S is: |S|=sqrt(2S:S) .........................(2) - According to Eq. (2) the magnitude of rate of strain tensor is: |E| = sqrt(2E:E). ..............................(3) = sqrt(2*(E_ij*E_ij))...................... (4) - In OpenFOAM notation the magnitude of rate of strain tensor can be written as: |E|=sqrt(2*symm(grad(U))).......................(5) But for the testing purpose i defined a Tensor Q as [1 0 0 0 0.8 0 0 0 0.5]. According to Eq. (2), it's magnitude is 1.944222. But the OpenFOAM is giving 1.3747727. So the definition of the magnitude of tensor according to OpenFOAM is: |S| = sqrt(S:S)=sqrt(S_ij*S_ij)...........................(6) Which contradicts Eq. (2). Can any one clarify my doubt and how to write rate of strain tensor in OpenFOAM notation. Thanks in advance. yours Mallikarjuna Reddy |
|
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Magnitude of the strain tensor | didomenico | OpenFOAM | 1 | August 7, 2011 03:02 |
Stresseq vs stress magnitude | watashiwa | OpenFOAM | 1 | October 14, 2010 12:02 |
curvature correction term, material derivative of a tensor | volker | OpenFOAM Programming & Development | 7 | June 3, 2010 08:08 |
About deformation gradient tensor | ZHANG | Main CFD Forum | 0 | June 18, 2007 12:51 |
second invariant of rate-of-strain tensor | Chun Min Chew | Main CFD Forum | 3 | December 10, 2003 11:34 |