# 体积模量

## 定义

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

## 热力学关系

$K_S=\gamma\, p$

$K_T=p\,$

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

16×1010[1]

2.2×109[3]

## 注释与参考

1. ^ 1.0 1.1 1.2 1.3 钟锡华、周岳明. 《力学》. 北京大学出版社. 2000-12: 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

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