Hello Chagron:



thanks for your comments



To answer right away to your question (regarding Fig. 11A and Fig. 12A):



I say somewhere at the beginning (chap 1) that I would assume (which is mostly true) that granular material behaves like a Prandtl material (visco-elastic-plastic) in which the elastic response is very very small (negligible)



Hence the only relationships that holds is (because the Prandtl behavior):



Stress vs. rate-of-strain





In the figures we have:



Shear Stress vs. rate-of-Shear-strain





If we had a relationship of this kind: Shear stress vs. Shear-strain (or Stress vs. Strain) then it would make a sort of bizarre purely linear-elastic material (or Hookean material), which does not apply to granular material



So, your question was very good and not at all "minor" as you said ....



So, in a nutshell, the reason of the "rate-of-strain" rather than "strain" is dictated by the inner rheological nature of the material (e.g., I beleive that cold rock somehow display a very nice Hookean behavior, hence linear-elastic, hence stress vs strain ... so if you are more familiar with rock behavior you must see more often a stress vs strain relationship)



anyway thanks for asking



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SEb

Sebastien Dartevelle