Continuum Mechanics: Stress on Opposite Sides of Infinitesimal Cube

In summary, the conversation is about the topic of Continuum Mechanics and specifically about the concept of stress. The person is asking why the stresses on opposite sides of an infinitesimal cube have to be the same and how to describe the stresses on a point. They also mention the difficulty of finding forums on this topic. The other person provides a link to Cauchy's lemma which is equivalent to Newton's third law and explains that body forces and surfaces of discontinuity can be accounted for in the momentum balance equation.
  • #1
vmtgomes
4
0
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
 
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  • #2
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?
 
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  • #3
Thank you, that certainly helps! I read this part of this textbook you linked here and it helped a lot.
 

1. What is continuum mechanics?

Continuum mechanics is a branch of physics and mechanics that studies the behavior of materials and fluids under the assumption that they are continuous and can be described by mathematical equations. It is used to analyze the effects of stress and deformation on a body, and is an important tool in many fields including engineering, materials science, and geology.

2. What is the concept of stress in continuum mechanics?

In continuum mechanics, stress refers to the internal forces that act within a material or fluid. These forces can be caused by external factors such as applied pressure or temperature changes, and they can result in deformation or movement of the material.

3. What does it mean for stress to be on opposite sides of an infinitesimal cube?

This refers to a specific scenario in continuum mechanics where a small cube of material is subjected to stress on two opposite sides. This can occur when the material is being compressed or stretched in one direction, causing stress to act in the opposite direction on the opposite sides of the cube.

4. How is stress calculated in continuum mechanics?

There are various mathematical equations and models used to calculate stress in continuum mechanics, depending on the specific scenario and type of material being analyzed. Generally, stress can be calculated by dividing the force acting on a material by its area or volume, and it is typically measured in units of pressure.

5. What are some practical applications of continuum mechanics?

Continuum mechanics is used in many real-world applications, including the design and analysis of structures like buildings, bridges, and aircraft. It is also used in the development of new materials and in understanding the behavior of fluids in geology and meteorology. Additionally, continuum mechanics is applied in the study of biological systems and processes, such as blood flow in the body.

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