Template:Elastic moduli
Revision as of 00:33, 24 March 2012 by imported>YFdyh-bot (r2.7.2) (Robot: Adding zh:Template:弹性模量; modifying fr:Modèle:Modules élastiques)
| Conversion formulas | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these, thus given any two, any other of the elastic moduli can be calculated according to these formulas. | ||||||||||
| <math>(K,\,E)</math> | <math>(K,\,\lambda)</math> | <math>(K,\,G)</math> | <math>(K,\, \nu)</math> | <math>(E,\,G)</math> | <math>(E,\,\nu)</math> | <math>(\lambda,\,G)</math> | <math>(\lambda,\,\nu)</math> | <math>(G,\,\nu)</math> | <math>(G,\,M)</math> | |
| <math>K=\,</math> | <math>\tfrac{EG}{3(3G-E)}</math> | <math>\tfrac{E}{3(1-2\nu)}</math> | <math>\lambda+ \tfrac{2G}{3}</math> | <math>\tfrac{\lambda(1+\nu)}{3\nu}</math> | <math>\tfrac{2G(1+\nu)}{3(1-2\nu)}</math> | <math>M - \tfrac{4G}{3}</math> | ||||
| <math>E=\, </math> | <math>\tfrac{9K(K-\lambda)}{3K-\lambda}</math> | <math>\tfrac{9KG}{3K+G}</math> | <math>3K(1-2\nu)\,</math> | <math>\tfrac{G(3\lambda + 2G)}{\lambda + G}</math> | <math>\tfrac{\lambda(1+\nu)(1-2\nu)}{\nu}</math> | <math>2G(1+\nu)\,</math> | <math>\tfrac{G(3M-4G)}{M-G}</math> | |||
| <math>\lambda=\,</math> | <math>\tfrac{3K(3K-E)}{9K-E}</math> | <math>K-\tfrac{2G}{3}</math> | <math>\tfrac{3K\nu}{1+\nu}</math> | <math>\tfrac{G(E-2G)}{3G-E}</math> | <math>\tfrac{E\nu}{(1+\nu)(1-2\nu)}</math> | <math>\tfrac{2 G \nu}{1-2\nu}</math> | <math>M - 2G\,</math> | |||
| <math>G=\, </math> | <math>\tfrac{3KE}{9K-E}</math> | <math>\tfrac{3(K-\lambda)}{2}</math> | <math>\tfrac{3K(1-2\nu)}{2(1+\nu)}</math> | <math>\tfrac{E}{2(1+\nu)}</math> | <math>\tfrac{\lambda(1-2\nu)}{2\nu}</math> | |||||
| <math>\nu=\,</math> | <math>\tfrac{3K-E}{6K}</math> | <math>\tfrac{\lambda}{3K-\lambda}</math> | <math>\tfrac{3K-2G}{2(3K+G)}</math> | <math>\tfrac{E}{2G}-1</math> | <math>\tfrac{\lambda}{2(\lambda + G)}</math> | <math>\tfrac{M - 2G}{2M - 2G}</math> | ||||
| <math>M=\,</math> | <math>\tfrac{3K(3K+E)}{9K-E}</math> | <math>3K-2\lambda\,</math> | <math>K+\tfrac{4G}{3}</math> | <math>\tfrac{3K(1-\nu)}{1+\nu}</math> | <math>\tfrac{G(4G-E)}{3G-E}</math> | <math>\tfrac{E(1-\nu)}{(1+\nu)(1-2\nu)}</math> | <math>\lambda+2G\,</math> | <math>\tfrac{\lambda(1-\nu)}{\nu}</math> | <math>\tfrac{2G(1-\nu)}{1-2\nu} </math> | |
The stiffness matrix (9 by 9, or 6 by 6 in Voigt notation) in Hooke's law (in 3D) can be parametrized by only two components for homogeneous and isotropic materials. One may choose whichever pair one prefers among the elastic moduli given below. Some of the possible conversions are listed in the table.
References
- G. Mavko, T. Mukerji, J. Dvorkin. The Rock Physics Handbook. Cambridge University Press 2003 (paperback). ISBN 0-521-54344-4
</include> da:Skabelon:Parametre for materialers elasticitet es:Plantilla:Módulo de elasticidad eo:Ŝablono:Elastaj moduloj fa:الگو:مدولهای کشسانی fr:Modèle:Modules élastiques zh:Template:弹性模量