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On Continuum Mechanics

  1. Oct 18, 2011 #1
    Hello, I'm not sure if this is the right place to ask about Continuum Mechanics or if the right place would be the engineering forums, but since Continuum Mechanics is a branch of Classical Mechanics, I thought it might be the place.

    My question is about Stress. Why does the stresses on opposite sides of an infinitesimal cube have to be the same? I know about the equilibrium. But what if the continuum is accelerating (for example if it is part of a fluid)? How can you describe the stresses on a point? If usually we use a stress tensor with nine components with respect to three orthogonal interfaces at a point, now this wouldn't be possible since we would have eighteen different stresses at that point.

    I can't find any continuum mechanics forums on the internet. If you know of anyone, please tell me and sorry for the amount of questions.

    Thanks,
    Vítor Mussa T. Gomes
     
  2. jcsd
  3. Oct 19, 2011 #2

    Andy Resnick

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    I think you are asking about Cauchy's lemma:

    http://www3.esc.auckland.ac.nz/people/staff/pkel015/SolidMechanicsBooks/Part_III/Chapter_3_Stress_Mass_Momentum/Stress_Balance_Principles_03_The_Cauchy_Stress_Tensor.pdf [Broken]

    Which is equivalent to Newton's third law (action-reaction).

    If there is a body force present, that is accounted for in the momentum balance equation- which can also account for surfaces of discontinuity.

    Does that help?
     
    Last edited by a moderator: May 5, 2017
  4. Oct 21, 2011 #3
    Thank you, that certainly helps! I read this part of this text book you linked here and it helped a lot.
     
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