Cauchy Stress Tensor in Applied Strength of Materials

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SUMMARY

The discussion centers on the relationship between the Cauchy stress tensor used in applied strength of materials and the stress-energy tensor in relativity. The Cauchy stress tensor is a 3D representation utilized for stress analysis, while the stress-energy tensor serves as a 4D extension incorporating a time component. The engineering application focuses on the space-space components of the stress-energy tensor in the material's rest frame, differing from the relativistic tensor by momentum terms. The recommended resource for further understanding is “Classical Field Theory” by Davison E. Soper, which addresses continuum mechanics and Lagrangian densities.

PREREQUISITES
  • Understanding of Cauchy stress tensor in mechanical engineering
  • Familiarity with stress analysis techniques such as Mohr's circles
  • Basic knowledge of continuum mechanics
  • Introduction to relativistic physics concepts
NEXT STEPS
  • Study the stress-energy tensor in relativity
  • Learn about Lagrangian densities and their applications
  • Explore the differences between 3D and 4D stress tensors
  • Read “Classical Field Theory” by Davison E. Soper for deeper insights
USEFUL FOR

Engineering students, mechanical engineers, and physicists interested in the applications of stress tensors in both classical and relativistic contexts.

dsaun777
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I am in a course in applied strength of materials and we often use the 3D stress tensor for stress analysis of materials i.e. Mohr's circles, bending, torsion, etc. Is the stress-energy tensor in relativity basically a 4-d extension to the Cauchy stress tensor commonly used in mechanical engineering? Cauchy with the addition of a time component? Are there any engineering courses that would use the relativistic energy tensor or is that more towards the theoretical side of things?
 
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The stress tensor used in engineering is the space-space components of the stress energy tensor in the rest frame of the material. In other words the engineering one is different from the corresponding components of the relativistic one by terms that represent the momentum carried by the bulk flow of matter across a surface.
 
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I might recommend a book, “Classical Field Theory” by Davison E. Soper. Dover 2008. The book covers areas like continuum mechanics while skipping things more of interest in quantum field theory. All things are derived from Lagrangian densities where Lorentz invariance is used. The development covers both 3 and 4 dimensional topics.
 
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