剪切模量

Multi tool use
Multi tool use

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP




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,定義為剪應力剪應變的比值。公式記為


G=τγdisplaystyle G=frac tau gamma <br/>G = "/>

其中,Gdisplaystyle G, G, 表示剪力模數,τdisplaystyle tau ,tau, 表示剪應力,γdisplaystyle gamma ,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 )G = E over 2(1 + nu)

其中,Edisplaystyle E,E, 是楊氏模數(Young's modulus ),νdisplaystyle nu ,nu , 是泊松比(Poisson's ratio)。



参见


  • 固體力學

  • 流體力學

  • 連續介質力學


















































































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)(lambda ,,G)

(E,G)displaystyle (E,,G)(E,,G)

(K,λ)displaystyle (K,,lambda )(K,,lambda )

(K,G)displaystyle (K,,G)(K,,G)

(λ,ν)displaystyle (lambda ,,nu )(lambda ,,nu )

(G,ν)displaystyle (G,,nu )(G,,nu )

(E,ν)displaystyle (E,,nu )(E,,nu )

(K,ν)displaystyle (K,,nu )(K,,nu )

(K,E)displaystyle (K,,E)(K,,E)

(M,G)displaystyle (M,,G)(M,,G)

K=displaystyle K=,K=,

λ+2G3displaystyle lambda +tfrac 2G3lambda +tfrac 2G3

EG3(3G−E)displaystyle tfrac EG3(3G-E)tfrac EG3(3G-E)



λ(1+ν)3νdisplaystyle tfrac lambda (1+nu )3nu tfrac lambda (1+nu )3nu

2G(1+ν)3(1−2ν)displaystyle tfrac 2G(1+nu )3(1-2nu )tfrac 2G(1+nu )3(1-2nu )

E3(1−2ν)displaystyle tfrac E3(1-2nu )tfrac E3(1-2nu )



M−4G3displaystyle M-tfrac 4G3M-tfrac 4G3

E=displaystyle E=,E=,

G(3λ+2G)λ+Gdisplaystyle tfrac G(3lambda +2G)lambda +Gtfrac G(3lambda +2G)lambda +G


9K(K−λ)3K−λdisplaystyle tfrac 9K(K-lambda )3K-lambda tfrac 9K(K-lambda )3K-lambda

9KG3K+Gdisplaystyle tfrac 9KG3K+Gtfrac 9KG3K+G

λ(1+ν)(1−2ν)νdisplaystyle tfrac lambda (1+nu )(1-2nu )nu tfrac lambda (1+nu )(1-2nu )nu

2G(1+ν)displaystyle 2G(1+nu ),2G(1+nu ),


3K(1−2ν)displaystyle 3K(1-2nu ),3K(1-2nu ),


G(3M−4G)M−Gdisplaystyle tfrac G(3M-4G)M-Gtfrac G(3M-4G)M-G

λ=displaystyle lambda =,lambda =,


G(E−2G)3G−Edisplaystyle tfrac G(E-2G)3G-Etfrac G(E-2G)3G-E


K−2G3displaystyle K-tfrac 2G3K-tfrac 2G3


2Gν1−2νdisplaystyle tfrac 2Gnu 1-2nu tfrac 2Gnu 1-2nu

Eν(1+ν)(1−2ν)displaystyle tfrac Enu (1+nu )(1-2nu )tfrac Enu (1+nu )(1-2nu )

3Kν1+νdisplaystyle tfrac 3Knu 1+nu tfrac 3Knu 1+nu

3K(3K−E)9K−Edisplaystyle tfrac 3K(3K-E)9K-Etfrac 3K(3K-E)9K-E

M−2Gdisplaystyle M-2G,M-2G,

G=displaystyle G=,G=,



3(K−λ)2displaystyle tfrac 3(K-lambda )2tfrac 3(K-lambda )2


λ(1−2ν)2νdisplaystyle tfrac lambda (1-2nu )2nu tfrac lambda (1-2nu )2nu


E2(1+ν)displaystyle tfrac E2(1+nu )tfrac E2(1+nu )

3K(1−2ν)2(1+ν)displaystyle tfrac 3K(1-2nu )2(1+nu )tfrac 3K(1-2nu )2(1+nu )

3KE9K−Edisplaystyle tfrac 3KE9K-Etfrac 3KE9K-E


ν=displaystyle nu =,nu =,

λ2(λ+G)displaystyle tfrac lambda 2(lambda +G)tfrac lambda 2(lambda +G)

E2G−1displaystyle tfrac E2G-1tfrac E2G-1

λ3K−λdisplaystyle tfrac lambda 3K-lambda tfrac lambda 3K-lambda

3K−2G2(3K+G)displaystyle tfrac 3K-2G2(3K+G)tfrac 3K-2G2(3K+G)





3K−E6Kdisplaystyle tfrac 3K-E6Ktfrac 3K-E6K

M−2G2M−2Gdisplaystyle tfrac M-2G2M-2Gtfrac M-2G2M-2G

M=displaystyle M=,M=,

λ+2Gdisplaystyle lambda +2G,lambda +2G,

G(4G−E)3G−Edisplaystyle tfrac G(4G-E)3G-Etfrac G(4G-E)3G-E

3K−2λdisplaystyle 3K-2lambda ,3K-2lambda ,

K+4G3displaystyle K+tfrac 4G3K+tfrac 4G3

λ(1−ν)νdisplaystyle tfrac lambda (1-nu )nu tfrac lambda (1-nu )nu

2G(1−ν)1−2νdisplaystyle tfrac 2G(1-nu )1-2nu tfrac 2G(1-nu )1-2nu

E(1−ν)(1+ν)(1−2ν)displaystyle tfrac E(1-nu )(1+nu )(1-2nu )tfrac E(1-nu )(1+nu )(1-2nu )

3K(1−ν)1+νdisplaystyle tfrac 3K(1-nu )1+nu tfrac 3K(1-nu )1+nu

3K(3K+E)9K−Edisplaystyle tfrac 3K(3K+E)9K-Etfrac 3K(3K+E)9K-E

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