在線性彈性力學中,拉梅常數包括以下兩個常數: 拉梅常數λ,又稱拉梅第一常數 剪切模數μ,又稱拉梅第二常數,也可記為 G {\displaystyle G} 上述常數的條件是等向性材料,並在三維中滿足虎克定律。 σ = 2 μ ε + λ t r ( ε ) I {\displaystyle \sigma =2\mu \varepsilon +\lambda \;\mathrm {tr} (\varepsilon )I} 其中σ是應力,ε是體積變形量, I {\displaystyle \scriptstyle I} 是單位矩陣, t r ( ⋅ ) {\displaystyle \scriptstyle \mathrm {tr} (\cdot )} 是跡數函數。 第一常數λ沒有物理解釋,但其有助於化簡胡克定律的剛度矩陣。兩個常數構建了均質等向性介質的彈性模數的常數化形式,並與其他彈性模數形成了聯繫。 拉梅常數以拉梅(Gabriel Lamé)的名字命名。 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) More information , ... 換算公式 均質等向性線彈性材料具有獨特的彈性性質,因此知道彈性模數中的任意兩種,就可由下列換算公式求出其他所有的彈性模數。 ( 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}}} Close 這是一篇物理學小作品。您可以透過編輯或修訂擴充其內容。閱論編 Wikiwand in your browser!Seamless Wikipedia browsing. On steroids.Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.Wikiwand for ChromeWikiwand for EdgeWikiwand for Firefox
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