Difference between revisions of "Template:Elastic moduli"
Jump to navigation
Jump to search
imported>Alan Liefting |
imported>YFdyh-bot m (r2.7.2) (Robot: Adding zh:Template:弹性模量; modifying fr:Modèle:Modules élastiques) |
||
| Line 114: | Line 114: | ||
[[Category:Physics templates|{{PAGENAME}}]] | [[Category:Physics templates|{{PAGENAME}}]] | ||
| + | </include><noinclude> | ||
[[da:Skabelon:Parametre for materialers elasticitet]] | [[da:Skabelon:Parametre for materialers elasticitet]] | ||
| + | [[es:Plantilla:Módulo de elasticidad]] | ||
[[eo:Ŝablono:Elastaj moduloj]] | [[eo:Ŝablono:Elastaj moduloj]] | ||
| − | |||
[[fa:الگو:مدولهای کشسانی]] | [[fa:الگو:مدولهای کشسانی]] | ||
| − | [[fr: | + | [[fr:Modèle:Modules élastiques]] |
| − | </ | + | [[zh:Template:弹性模量]] |
| + | </noinclude> | ||
Revision as of 00:33, 24 March 2012
| 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