CroninProjects.org/ Vince/ Course/ IntroStructGeol/3445-Lect-Stress19.html

John Logan looking at the Large Sample Rig in the rock-deformation lab at the Center for Tectonophysics, Texas A&M University, on the occasion of the 50th anniversary of the Center in 2018. Dr. Logan designed the LSR and joined countless students and colleagues in conducting great scientific investigations using this tool.

John Logan looking at the Large Sample Rig in the rock-deformation lab at the Center for Tectonophysics, Texas A&M University, on the occasion of the 50th anniversary of the Center in 2018. Dr. Logan designed the LSR and joined countless students and colleagues in conducting great scientific investigations using this tool. Photo by Vince Cronin.

Introductory Structural Geology, Stress


This page is under construction!

Refer to Ben van der Pluijm and Steve Marshak, Processes in Structural Geology and Tectonics (psgt.earth.lsa.umich.edu), chapter 2, pages 41-60.

Terms you should work to understand and use properly

anisotropic anisotropic stress body force compressive stress confining pressure
continuum mechanics deviatoric stress differential stress eigen value eigen vector
ellipse ellipsoid force gravity greatest principal
compressive stress
homogeneous hydrostatic intermediate principal
stress		 isotropic isotropic stress
least principal
stress		 lithostatic stress mean stress Mohr diagram newton (unit)
normal stress pascal (unit) pressure principal plane principal stress
scalar σ1 σ2 σ3 shear stress
stress stress ellipsoid stress field stress matrix stress tensor
tensile stress traction vector -- --

Some questions provided by students that are related to this material

  1. How do you calculate the deviatoric stress?
  2. What type of stress would change the size (but not the shape) of an isotropic, homogeneous, linear-elastic object?
  3. According to Ben van der Pluijm, what are the four fundamental quantities used to describe the physical properties of materials?
  4. Which of the four basic forces act(s) over large distances and is/are always attractive?
  5. What type of principal stress has a positive value?
  6. What is an example of a 0th rank tensor?
  7. What is an example of a 1st rank tensor?
  8. What is an example of a 2nd rank tensor?
  9. What is an example of a 4th rank tensor?
  10. What is an example of a body force that is relevant to geology?
  11. What is a common term that is approximately equivalent to "isotopic stress" (although this term is properly applied only to liquids or gases -- materials without shear strength -- rather than to solids)?

Other notes

The Mohr diagram is a very clever graphical computer, but it was devised at a time when electronic calculators did not exist. We now have access to powerful electronic computers, so it is reasonable to ask how one might solve for the principal stresses given the tractions on a randomly oriented cube within an anisotropic stress field. The Mathematica notebook EigenDecomposition3D.nb is one example of how this problem might be solved. That notebook is accessible online via http://CroninProjects.org/Vince/Course/IntroStructGeol/EigenDecomposition3D.nb and a non-executable PDF of that notebook is available via http://CroninProjects.org/Vince/Course/IntroStructGeol/EigenDecomposition3D.pdf.

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