在线性弹性力学中,拉梅常数包括以下两个参数: 拉梅常数λ,又称拉梅第一常数 剪切模量μ,又称拉梅第二常数,也可记为 G {\displaystyle G} 上述参数的条件是各向同性材料,并在三维中满足虎克定律。 σ = 2 μ ε + λ t r ( ε ) I {\displaystyle \sigma =2\mu \varepsilon +\lambda \;\mathrm {tr} (\varepsilon )I} 其中σ是应力,ε是体积变形量, I {\displaystyle \scriptstyle I} 是单位矩阵, t r ( ⋅ ) {\displaystyle \scriptstyle \mathrm {tr} (\cdot )} 是迹数函数。 第一参数λ没有物理解释,但其有助于化简胡克定律的刚度矩阵。两个参数构建了均质各向同性介质的弹性模量的参数化形式,并与其他弹性模量形成了联系。 拉梅参数以拉梅(Gabriel Lamé)的名字命名。 Remove ads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) 更多信息 , ... 换算公式 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。 ( λ , G ) {\displaystyle (\lambda ,\,G)} ( E , G ) {\displaystyle (E,\,G)} ( K , λ ) {\displaystyle (K,\,\lambda )} ( K , G ) {\displaystyle (K,\,G)} ( λ , ν ) {\displaystyle (\lambda ,\,\nu )} ( G , ν ) {\displaystyle (G,\,\nu )} ( E , ν ) {\displaystyle (E,\,\nu )} ( K , ν ) {\displaystyle (K,\,\nu )} ( K , E ) {\displaystyle (K,\,E)} ( M , G ) {\displaystyle (M,\,G)} K = {\displaystyle K=\,} λ + 2 G 3 {\displaystyle \lambda +{\tfrac {2G}{3}}} E G 3 ( 3 G − E ) {\displaystyle {\tfrac {EG}{3(3G-E)}}} λ ( 1 + ν ) 3 ν {\displaystyle {\tfrac {\lambda (1+\nu )}{3\nu }}} 2 G ( 1 + ν ) 3 ( 1 − 2 ν ) {\displaystyle {\tfrac {2G(1+\nu )}{3(1-2\nu )}}} E 3 ( 1 − 2 ν ) {\displaystyle {\tfrac {E}{3(1-2\nu )}}} M − 4 G 3 {\displaystyle M-{\tfrac {4G}{3}}} E = {\displaystyle E=\,} G ( 3 λ + 2 G ) λ + G {\displaystyle {\tfrac {G(3\lambda +2G)}{\lambda +G}}} 9 K ( K − λ ) 3 K − λ {\displaystyle {\tfrac {9K(K-\lambda )}{3K-\lambda }}} 9 K G 3 K + G {\displaystyle {\tfrac {9KG}{3K+G}}} λ ( 1 + ν ) ( 1 − 2 ν ) ν {\displaystyle {\tfrac {\lambda (1+\nu )(1-2\nu )}{\nu }}} 2 G ( 1 + ν ) {\displaystyle 2G(1+\nu )\,} 3 K ( 1 − 2 ν ) {\displaystyle 3K(1-2\nu )\,} G ( 3 M − 4 G ) M − G {\displaystyle {\tfrac {G(3M-4G)}{M-G}}} λ = {\displaystyle \lambda =\,} G ( E − 2 G ) 3 G − E {\displaystyle {\tfrac {G(E-2G)}{3G-E}}} K − 2 G 3 {\displaystyle K-{\tfrac {2G}{3}}} 2 G ν 1 − 2 ν {\displaystyle {\tfrac {2G\nu }{1-2\nu }}} E ν ( 1 + ν ) ( 1 − 2 ν ) {\displaystyle {\tfrac {E\nu }{(1+\nu )(1-2\nu )}}} 3 K ν 1 + ν {\displaystyle {\tfrac {3K\nu }{1+\nu }}} 3 K ( 3 K − E ) 9 K − E {\displaystyle {\tfrac {3K(3K-E)}{9K-E}}} M − 2 G {\displaystyle M-2G\,} G = {\displaystyle G=\,} 3 ( K − λ ) 2 {\displaystyle {\tfrac {3(K-\lambda )}{2}}} λ ( 1 − 2 ν ) 2 ν {\displaystyle {\tfrac {\lambda (1-2\nu )}{2\nu }}} E 2 ( 1 + ν ) {\displaystyle {\tfrac {E}{2(1+\nu )}}} 3 K ( 1 − 2 ν ) 2 ( 1 + ν ) {\displaystyle {\tfrac {3K(1-2\nu )}{2(1+\nu )}}} 3 K E 9 K − E {\displaystyle {\tfrac {3KE}{9K-E}}} ν = {\displaystyle \nu =\,} λ 2 ( λ + G ) {\displaystyle {\tfrac {\lambda }{2(\lambda +G)}}} E 2 G − 1 {\displaystyle {\tfrac {E}{2G}}-1} λ 3 K − λ {\displaystyle {\tfrac {\lambda }{3K-\lambda }}} 3 K − 2 G 2 ( 3 K + G ) {\displaystyle {\tfrac {3K-2G}{2(3K+G)}}} 3 K − E 6 K {\displaystyle {\tfrac {3K-E}{6K}}} M − 2 G 2 M − 2 G {\displaystyle {\tfrac {M-2G}{2M-2G}}} M = {\displaystyle M=\,} λ + 2 G {\displaystyle \lambda +2G\,} G ( 4 G − E ) 3 G − E {\displaystyle {\tfrac {G(4G-E)}{3G-E}}} 3 K − 2 λ {\displaystyle 3K-2\lambda \,} K + 4 G 3 {\displaystyle K+{\tfrac {4G}{3}}} λ ( 1 − ν ) ν {\displaystyle {\tfrac {\lambda (1-\nu )}{\nu }}} 2 G ( 1 − ν ) 1 − 2 ν {\displaystyle {\tfrac {2G(1-\nu )}{1-2\nu }}} E ( 1 − ν ) ( 1 + ν ) ( 1 − 2 ν ) {\displaystyle {\tfrac {E(1-\nu )}{(1+\nu )(1-2\nu )}}} 3 K ( 1 − ν ) 1 + ν {\displaystyle {\tfrac {3K(1-\nu )}{1+\nu }}} 3 K ( 3 K + E ) 9 K − E {\displaystyle {\tfrac {3K(3K+E)}{9K-E}}} 关闭 这是一篇物理学小作品。您可以通过编辑或修订扩充其内容。查论编 Remove adsLoading related searches...Wikiwand - on Seamless Wikipedia browsing. On steroids.Remove ads