查看“︁Template:弹性模量”︁的源代码

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{{noteTA
|1=zh-cn:模量;zh-tw:模數;
|2=zh-cn:各向同性;zh-tw:等向性;
}}
</noinclude>{{Navbox
| name  = 弹性模量
| title = 均质各向同性材料的[[弹性模量|彈性模數]]
| list1 = [[体积模量]] (<math>K</math>) • [[杨氏模量|楊氏模數]] (<math>E</math>) • [[拉梅参数|拉梅常數]] (<math>\lambda</math>) • [[剪切模量|剪切模數]] (<math>G</math>) • [[泊松比|蒲松比]] (<math>\nu</math>) • [[P波模量]] (<math>M</math>)
}}
{| class="wikitable collapsible" width="100%" style="font-size:smaller; background:white" align=center
! colspan=11 | 换算公式
|-
| colspan=11 | 均质各向同性线弹性材料具有独特的弹性性质，因此知道弹性模量中的任意两种，就可由下列换算公式求出其他所有的弹性模量。
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| align=center | <math>(\lambda,\,G)</math>
| align=center | <math>(E,\,G)</math>
| align=center | <math>(K,\,\lambda)</math>
| align=center | <math>(K,\,G)</math>
| align=center | <math>(\lambda,\,\nu)</math>
| align=center | <math>(G,\,\nu)</math>
| align=center | <math>(E,\,\nu)</math>
| align=center | <math>(K,\, \nu)</math>
| align=center | <math>(K,\,E)</math>
| align=center | <math>(M,\,G)</math>
|-
| align=center | <math>K=\,</math> 
| align=center | <small><math>\lambda+ \tfrac{2G}{3}</math> </small>
| align=center | <math>\tfrac{EG}{3(3G-E)}</math> 
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|
| align=center | <math>\tfrac{\lambda(1+\nu)}{3\nu}</math> 
| align=center | <math>\tfrac{2G(1+\nu)}{3(1-2\nu)}</math> 
| align=center | <math>\tfrac{E}{3(1-2\nu)}</math>
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| align=center | <math>M - \tfrac{4G}{3}</math>
|-
| align=center | <math>E=\, </math> 
| align=center | <math>\tfrac{G(3\lambda + 2G)}{\lambda + G}</math> 
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| align=center | <math>\tfrac{9K(K-\lambda)}{3K-\lambda}</math> 
| align=center | <math>\tfrac{9KG}{3K+G}</math> 
| align=center | <math>\tfrac{\lambda(1+\nu)(1-2\nu)}{\nu}</math> 
| align=center | <math>2G(1+\nu)\,</math> 
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| align=center | <math>3K(1-2\nu)\,</math> 
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| align=center | <math>\tfrac{G(3M-4G)}{M-G}</math>
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| align=center | <math>\lambda=\,</math> 
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| align=center | <math>\tfrac{G(E-2G)}{3G-E}</math> 
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| align=center | <math>K-\tfrac{2G}{3}</math>
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| align=center | <math>\tfrac{2 G \nu}{1-2\nu}</math> 
| align=center | <math>\tfrac{E\nu}{(1+\nu)(1-2\nu)}</math>
| align=center | <math>\tfrac{3K\nu}{1+\nu}</math> 
| align=center | <math>\tfrac{3K(3K-E)}{9K-E}</math> 
| align=center | <math>M - 2G\,</math>
|-
| align=center | <math>G=\, </math> 
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| align=center | <math>\tfrac{3(K-\lambda)}{2}</math> 
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| align=center | <math>\tfrac{\lambda(1-2\nu)}{2\nu}</math> 
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| align=center | <math>\tfrac{E}{2(1+\nu)}</math>
| align=center | <math>\tfrac{3K(1-2\nu)}{2(1+\nu)}</math> 
| align=center | <math>\tfrac{3KE}{9K-E}</math>
|  
|-
| align=center | <math>\nu=\,</math> 
| align=center | <math>\tfrac{\lambda}{2(\lambda + G)}</math> 
| align=center | <math>\tfrac{E}{2G}-1</math> 
| align=center | <math>\tfrac{\lambda}{3K-\lambda}</math>
| align=center | <math>\tfrac{3K-2G}{2(3K+G)}</math> 
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| align=center | <math>\tfrac{3K-E}{6K}</math>
| align=center | <math>\tfrac{M - 2G}{2M - 2G}</math>
|-
| align=center | <math>M=\,</math> 
| align=center | <math>\lambda+2G\,</math> 
| align=center | <math>\tfrac{G(4G-E)}{3G-E}</math> 
| align=center | <math>3K-2\lambda\,</math> 
| align=center | <math>K+\tfrac{4G}{3}</math> 
| align=center | <math>\tfrac{\lambda(1-\nu)}{\nu}</math> 
| align=center | <math>\tfrac{2G(1-\nu)}{1-2\nu} </math> 
| align=center | <math>\tfrac{E(1-\nu)}{(1+\nu)(1-2\nu)}</math> 
| align=center | <math>\tfrac{3K(1-\nu)}{1+\nu}</math> 
| align=center | <math>\tfrac{3K(3K+E)}{9K-E}</math> 
| 
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[[胡克定律|虎克定律]]中的刚度矩阵（按[[Voigt notation]]为9乘9或6乘6）可由同类且各向同性材料的任意两个参数来确定，表中列出了可能的换算关系。

== 参考文献 ==
* G. Mavko, T. Mukerji, J. Dvorkin. ''The Rock Physics Handbook''. Cambridge University Press 2003 (paperback). ISBN 0-521-54344-4

[[Category:弹性模量|*]]
[[Category:连续介质力学|*]]
[[Category:物理学导航模板|{{PAGENAME}}]]
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