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Fluids/tensors problem

  • Thread starter davcrai
  • Start date
  • #1
13
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Homework Statement


Going through a proof of uniqueness for stokes flow for a fluids class I'm taking. Part of it involves replacing the strain tensor (e) with the stress tensor (a), ie going from

(2u)*int(eij*eij)dV

to

int(eij*aij)dV


Homework Equations



aij = -p*dij + 2u*eij

dij = 1 if i=j, 0 otherwise.

The Attempt at a Solution



I can see you simply substitute for 2u*eij to the integral as follows,

int(eij*(eij*(p*dij + aij))dV

but why does eij*p*dij = 0 ????????

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
354
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Please try reposting this in the physics part of the forum.
 
  • #3
dextercioby
Science Advisor
Homework Helper
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Because the strain tensor e is traceless. The pressure term is exactly minus the trace of the stress tensor a.
 
Last edited:
  • #4
13
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Thank you very much!
 

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