Why are the traction vectors on each surface independent?

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SUMMARY

The discussion centers on the independence of traction vectors on each surface of an infinitesimal cube in the context of stress tensor derivations. It is established that while the sum of all traction vectors is zero, each vector acts independently on its respective surface due to the nature of stress distribution within the material. The concept of the infinitesimal cube as a free body diagram is crucial for understanding this independence, as it allows for the analysis of forces acting on individual surfaces without assuming direct opposition between them.

PREREQUISITES
  • Understanding of stress tensor concepts in continuum mechanics
  • Familiarity with free body diagrams and their applications
  • Basic knowledge of traction vectors and their role in material stress analysis
  • Concept of equilibrium in mechanics
NEXT STEPS
  • Study the derivation of the stress tensor in detail
  • Learn about the role of free body diagrams in analyzing forces in materials
  • Explore the concept of traction vectors and their mathematical representation
  • Investigate examples of stress distribution in different materials
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Students and professionals in mechanical engineering, materials science, and applied physics who are looking to deepen their understanding of stress analysis and the behavior of materials under load.

itamar123
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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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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?
 

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