拉梅参数

• 拉梅参数λ，又称拉梅第一参数
• 剪切模量μ，又称拉梅第二参数，也可记为${\displaystyle G}$

${\displaystyle \sigma =2\mu \varepsilon +\lambda \;\mathrm {tr} (\varepsilon )I}$

参考文献

• F. Kang, S. Zhong-Ci, Mathematical Theory of Elastic Structures, Springer New York, ISBN 0-387-51326-4, (1981)
• G. Mavko, T. Mukerji, J. Dvorkin, The Rock Physics Handbook, Cambridge University Press (paperback), ISBN 0-521-54344-4, (2003)

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