I Cauchy Stress Tensor in Applied Strength of Materials

[dsaun777]

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?

 

[Dale]

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.

 

[Paul Colby]

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.