# 体积模量

## 定义

${\displaystyle K=-V{\frac {\partial p}{\partial V}}}$

## 热力学关系

${\displaystyle K_{S}=\gamma \,p}$

${\displaystyle K_{T}=p\,}$

${\displaystyle c={\sqrt {\frac {K}{\rho }}}.}$

16×1010[1]

2.2×109[3]

## 注释与参考

1. 钟锡华、周岳明. 《力学》. 北京大学出版社. 2000年12月: 204. ISBN 978-7-301-04591-6.
2. ^ Phys. Rev. B 32, 7988 - 7991 (1985), Calculation of bulk moduli of diamond and zinc-blende solids
3. ^ http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html
4. ^ http://www3.interscience.wiley.com/cgi-bin/abstract/105558571/ABSTRACT

${\displaystyle (\lambda ,\,G)}$ ${\displaystyle (E,\,G)}$ ${\displaystyle (K,\,\lambda )}$ ${\displaystyle (K,\,G)}$ ${\displaystyle (\lambda ,\,\nu )}$ ${\displaystyle (G,\,\nu )}$ ${\displaystyle (E,\,\nu )}$ ${\displaystyle (K,\,\nu )}$ ${\displaystyle (K,\,E)}$ ${\displaystyle (M,\,G)}$
${\displaystyle K=\,}$ ${\displaystyle \lambda +{\tfrac {2G}{3}}}$ ${\displaystyle {\tfrac {EG}{3(3G-E)}}}$ ${\displaystyle {\tfrac {\lambda (1+\nu )}{3\nu }}}$ ${\displaystyle {\tfrac {2G(1+\nu )}{3(1-2\nu )}}}$ ${\displaystyle {\tfrac {E}{3(1-2\nu )}}}$ ${\displaystyle M-{\tfrac {4G}{3}}}$
${\displaystyle E=\,}$ ${\displaystyle {\tfrac {G(3\lambda +2G)}{\lambda +G}}}$ ${\displaystyle {\tfrac {9K(K-\lambda )}{3K-\lambda }}}$ ${\displaystyle {\tfrac {9KG}{3K+G}}}$ ${\displaystyle {\tfrac {\lambda (1+\nu )(1-2\nu )}{\nu }}}$ ${\displaystyle 2G(1+\nu )\,}$ ${\displaystyle 3K(1-2\nu )\,}$ ${\displaystyle {\tfrac {G(3M-4G)}{M-G}}}$
${\displaystyle \lambda =\,}$ ${\displaystyle {\tfrac {G(E-2G)}{3G-E}}}$ ${\displaystyle K-{\tfrac {2G}{3}}}$ ${\displaystyle {\tfrac {2G\nu }{1-2\nu }}}$ ${\displaystyle {\tfrac {E\nu }{(1+\nu )(1-2\nu )}}}$ ${\displaystyle {\tfrac {3K\nu }{1+\nu }}}$ ${\displaystyle {\tfrac {3K(3K-E)}{9K-E}}}$ ${\displaystyle M-2G\,}$
${\displaystyle G=\,}$ ${\displaystyle {\tfrac {3(K-\lambda )}{2}}}$ ${\displaystyle {\tfrac {\lambda (1-2\nu )}{2\nu }}}$ ${\displaystyle {\tfrac {E}{2(1+\nu )}}}$ ${\displaystyle {\tfrac {3K(1-2\nu )}{2(1+\nu )}}}$ ${\displaystyle {\tfrac {3KE}{9K-E}}}$
${\displaystyle \nu =\,}$ ${\displaystyle {\tfrac {\lambda }{2(\lambda +G)}}}$ ${\displaystyle {\tfrac {E}{2G}}-1}$ ${\displaystyle {\tfrac {\lambda }{3K-\lambda }}}$ ${\displaystyle {\tfrac {3K-2G}{2(3K+G)}}}$ ${\displaystyle {\tfrac {3K-E}{6K}}}$ ${\displaystyle {\tfrac {M-2G}{2M-2G}}}$
${\displaystyle M=\,}$ ${\displaystyle \lambda +2G\,}$ ${\displaystyle {\tfrac {G(4G-E)}{3G-E}}}$ ${\displaystyle 3K-2\lambda \,}$ ${\displaystyle K+{\tfrac {4G}{3}}}$ ${\displaystyle {\tfrac {\lambda (1-\nu )}{\nu }}}$ ${\displaystyle {\tfrac {2G(1-\nu )}{1-2\nu }}}$ ${\displaystyle {\tfrac {E(1-\nu )}{(1+\nu )(1-2\nu )}}}$ ${\displaystyle {\tfrac {3K(1-\nu )}{1+\nu }}}$ ${\displaystyle {\tfrac {3K(3K+E)}{9K-E}}}$