Why are the traction vectors on each surface independent?

In summary, the conversation discusses the concept of stress tensor and the independence of traction vectors on each surface. The question of why traction vectors are independent is raised and it is explained that they are placed on the surfaces of an infinitesimal cube in a free body diagram. The reason why the sum of all the traction vectors is zero is also addressed. However, further clarification is requested with a specific example and figure.
  • #1
itamar123
1
0
Hey y'all, my first thread here,
Got a burning question that has been disturbing my serenity.
In all derivations of the stress tensor that I've seen they didn't explain it that much,
So my question is, why do the traction vectors on each surface are independent?
From what I understood, the infinitesimal cube is actually a free body diagram of a small cube taken from a material, and so you put force (or traction) vectors acted on the surfaces that you cut,
But the sum of all the force (or traction) vectors is zero, why can't I just present it as two opposing and equal vectors?
 
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  • #2
itamar123 said:
Hey y'all, my first thread here,
Got a burning question that has been disturbing my serenity.
In all derivations of the stress tensor that I've seen they didn't explain it that much,
So my question is, why do the traction vectors on each surface are independent?
From what I understood, the infinitesimal cube is actually a free body diagram of a small cube taken from a material, and so you put force (or traction) vectors acted on the surfaces that you cut,
But the sum of all the force (or traction) vectors is zero, why can't I just present it as two opposing and equal vectors?
I don't quite understand your question. Can you please give a specific example with a figure?
 

1. Why do traction vectors on each surface need to be independent?

The independence of traction vectors on different surfaces is necessary for accurately analyzing the forces acting on a body. If the traction vectors were not independent, it would be difficult to determine the specific forces acting on each surface and their effects on the body's motion.

2. What happens if the traction vectors on each surface are not independent?

If the traction vectors on different surfaces are not independent, it would result in an inaccurate analysis of the forces acting on a body. This can lead to incorrect predictions of the body's motion and hinder our understanding of the underlying physical principles.

3. How do we ensure that the traction vectors on each surface are independent?

To ensure the independence of traction vectors on different surfaces, we must consider the orientation and position of each surface relative to the forces acting on the body. This allows us to accurately determine the magnitude and direction of each traction vector and their effects on the overall motion of the body.

4. Can the independence of traction vectors on each surface change?

The independence of traction vectors on different surfaces can change depending on the forces acting on the body. For example, if a body is in a state of equilibrium, the traction vectors on each surface will be independent. However, if the body is accelerating, the independence of traction vectors may change.

5. Are there any exceptions to the independence of traction vectors on each surface?

In certain cases, such as when a body is in contact with a frictional surface, the independence of traction vectors on each surface may be compromised. This is because the presence of friction introduces additional forces that must be considered in the analysis of the body's motion. However, in most cases, the independence of traction vectors on each surface holds true.

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