Average moduli and velocity of minerals
Mineral aggregate averages
VRH Bounds
- Voigt bound (upper):
- Reuss bound (lower):
- Voigt-Reuss-Hill Average:
Hashin-Shtrikman (HS) Bounds
Polycrystalline averages
Bulk / shear moduli from elastic constants () based on polycrystalline averages.
Acoustic velocity
- Compressional velocity:
- Shear velocity:
References
- Watt, J. P. (1979). Hashin‐Shtrikman bounds on the effective elastic moduli of polycrystals with orthorhombic symmetry. Journal of Applied Physics, 50(10), 6290–6295. https://doi.org/10.1063/1.325768
- MPtutorial2 (berkeley.edu)
- Rock physics - SEG Wiki
- Microsoft Word - CijExercise.docx (colorado.edu)
- The cij calculator cij.core.calculator module — Cij documentation (mineralscloud.github.io)