Continuum Mechanics: Stress on Opposite Sides of Infinitesimal Cube

[vmtgomes]

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

 

[Andy Resnick]

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

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?

 

[vmtgomes]

Thank you, that certainly helps! I read this part of this textbook you linked here and it helped a lot.