剪切模量
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剪力模數(shear modulus)是材料力學中的名詞,彈性材料承受剪應力時會產生剪應變,定義為剪應力與剪應變的比值。公式記為
- G=τγdisplaystyle G=frac tau gamma "/>
其中,Gdisplaystyle G, 表示剪力模數,τdisplaystyle tau , 表示剪應力,γdisplaystyle gamma , 表示剪應變。在均質且等向性的材料中:
- G=E2(1+ν)displaystyle G=E over 2(1+nu )
其中,Edisplaystyle E, 是楊氏模數(Young's modulus ),νdisplaystyle nu , 是泊松比(Poisson's ratio)。
参见
- 固體力學
- 流體力學
- 連續介質力學
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换算公式 | ||||||||||
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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+2G3displaystyle lambda +tfrac 2G3 | EG3(3G−E)displaystyle tfrac EG3(3G-E) | λ(1+ν)3νdisplaystyle tfrac lambda (1+nu )3nu | 2G(1+ν)3(1−2ν)displaystyle tfrac 2G(1+nu )3(1-2nu ) | E3(1−2ν)displaystyle tfrac E3(1-2nu ) | M−4G3displaystyle M-tfrac 4G3 | ||||
E=displaystyle E=, | G(3λ+2G)λ+Gdisplaystyle tfrac G(3lambda +2G)lambda +G | 9K(K−λ)3K−λdisplaystyle tfrac 9K(K-lambda )3K-lambda | 9KG3K+Gdisplaystyle tfrac 9KG3K+G | λ(1+ν)(1−2ν)νdisplaystyle tfrac lambda (1+nu )(1-2nu )nu | 2G(1+ν)displaystyle 2G(1+nu ), | 3K(1−2ν)displaystyle 3K(1-2nu ), | G(3M−4G)M−Gdisplaystyle tfrac G(3M-4G)M-G | |||
λ=displaystyle lambda =, | G(E−2G)3G−Edisplaystyle tfrac G(E-2G)3G-E | K−2G3displaystyle K-tfrac 2G3 | 2Gν1−2νdisplaystyle tfrac 2Gnu 1-2nu | Eν(1+ν)(1−2ν)displaystyle tfrac Enu (1+nu )(1-2nu ) | 3Kν1+νdisplaystyle tfrac 3Knu 1+nu | 3K(3K−E)9K−Edisplaystyle tfrac 3K(3K-E)9K-E | M−2Gdisplaystyle M-2G, | |||
G=displaystyle G=, | 3(K−λ)2displaystyle tfrac 3(K-lambda )2 | λ(1−2ν)2νdisplaystyle tfrac lambda (1-2nu )2nu | E2(1+ν)displaystyle tfrac E2(1+nu ) | 3K(1−2ν)2(1+ν)displaystyle tfrac 3K(1-2nu )2(1+nu ) | 3KE9K−Edisplaystyle tfrac 3KE9K-E | |||||
ν=displaystyle nu =, | λ2(λ+G)displaystyle tfrac lambda 2(lambda +G) | E2G−1displaystyle tfrac E2G-1 | λ3K−λdisplaystyle tfrac lambda 3K-lambda | 3K−2G2(3K+G)displaystyle tfrac 3K-2G2(3K+G) | 3K−E6Kdisplaystyle tfrac 3K-E6K | M−2G2M−2Gdisplaystyle tfrac M-2G2M-2G | ||||
M=displaystyle M=, | λ+2Gdisplaystyle lambda +2G, | G(4G−E)3G−Edisplaystyle tfrac G(4G-E)3G-E | 3K−2λdisplaystyle 3K-2lambda , | K+4G3displaystyle K+tfrac 4G3 | λ(1−ν)νdisplaystyle tfrac lambda (1-nu )nu | 2G(1−ν)1−2νdisplaystyle tfrac 2G(1-nu )1-2nu | E(1−ν)(1+ν)(1−2ν)displaystyle tfrac E(1-nu )(1+nu )(1-2nu ) | 3K(1−ν)1+νdisplaystyle tfrac 3K(1-nu )1+nu | 3K(3K+E)9K−Edisplaystyle tfrac 3K(3K+E)9K-E |