For example, in uniaxial tension or compression experiments usually a specific resolution is used by the experimentalists for measuring load and displacement, from which they calculate stress and strain. In the same experiment the extacted data with lower resolution would lack details. A theoretical model can be used for modeling the data in one resolution, but most probably it would not be sufficient/proper for the other.
Does 'scale' mean specimen size ?
I don’t know the paper on the size dependence of strain-stress relation, but I know two following papers on the size dependence of compressive strength.
Bieniawski, Z.T.,1968, The effector specimen size on compressive strength of coal, Int.J. Rock Mech. Min. Sci. 5, 325-335.
Pratt, H.R.,A.D.Brace,W.S.Brown and W.F.Brace, The effect of specimen size on the mechanical properties of unjointed diorite, Rock Mech. Min. Sci., 9, 513-529.
The following is of my opinion.
The solid part without flaws may shows the same stress-strain behavior. The size dependence of stress-strain relation is thought to be characterized by the behavior of flaws in a specimen. The size dependence of strength is theoretically expressed in terms of the strength distribution for micro-fractures and the size effect of strength is explained by the same strength distribution independently of specimen size in a range of specimen volume. This suggests that the stress strain behavior is similar independently of specimen size for a range of specimen size, if the applied stress is normalized by the strength.
The theory of the size dependence of strength is presented in my paper: Estimation of Fracture Stress for Intact Rocks and Possibility of Long-Term Earthquake Prediction (In Japanese with English abstract and figure caption): in ‘contribution’ in my profile of RESEARCHGATE)
Certainly they have! Here are some that I have reported with collaborators for shale nanoindentation:
Bennett, K.C., Berla, L.A., Nix,W.D. and Borja, R.I. (2015) “Instrumented nanoindentation and 3D mechanistic modeling of a shale at multiple scales.” Acta Geotech. 10(1), 1-14, http://dx.doi.org/10.1007/s11440-014-0363-7.
- Badges
- Science topic
- Similar topics
- Biological Science
- Physiology
- Physiological Processes
- Stress