泊松比 导航菜单编编
固体力学无量纲比率
材料力學弹性力学無因次量等向性剪切模數楊氏模數
泊松式比（英语：Poisson's ratio），又译泊松比，是材料力學和弹性力学中的名詞，定義為材料受拉伸或壓縮力時，材料會發生變形，而其橫向應變與縱向應變的比值，是一無因次量的物理量。
当材料在一个方向被压缩，它会在与该方向垂直的另外两个方向伸长，这就是泊松现象，泊松比是用来反映泊松现象的无量纲的物理量。
在均匀等向性材料中，剪切模數G、楊氏模數E 和泊松比ν{displaystyle nu }三个量中只有两个是独立的，它们之间存在以下关系：
G=E2(1+ν){displaystyle G={frac {E}{2(1+nu )}}}
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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+2G3{displaystyle lambda +{tfrac {2G}{3}}} | EG3(3G−E){displaystyle {tfrac {EG}{3(3G-E)}}} | λ(1+ν)3ν{displaystyle {tfrac {lambda (1+nu )}{3nu }}} | 2G(1+ν)3(1−2ν){displaystyle {tfrac {2G(1+nu )}{3(1-2nu )}}} | E3(1−2ν){displaystyle {tfrac {E}{3(1-2nu )}}} | M−4G3{displaystyle M-{tfrac {4G}{3}}} | ||||
E={displaystyle E=,} | G(3λ+2G)λ+G{displaystyle {tfrac {G(3lambda +2G)}{lambda +G}}} | 9K(K−λ)3K−λ{displaystyle {tfrac {9K(K-lambda )}{3K-lambda }}} | 9KG3K+G{displaystyle {tfrac {9KG}{3K+G}}} | λ(1+ν)(1−2ν)ν{displaystyle {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−G{displaystyle {tfrac {G(3M-4G)}{M-G}}} | |||
λ={displaystyle lambda =,} | G(E−2G)3G−E{displaystyle {tfrac {G(E-2G)}{3G-E}}} | K−2G3{displaystyle K-{tfrac {2G}{3}}} | 2Gν1−2ν{displaystyle {tfrac {2Gnu }{1-2nu }}} | Eν(1+ν)(1−2ν){displaystyle {tfrac {Enu }{(1+nu )(1-2nu )}}} | 3Kν1+ν{displaystyle {tfrac {3Knu }{1+nu }}} | 3K(3K−E)9K−E{displaystyle {tfrac {3K(3K-E)}{9K-E}}} | M−2G{displaystyle M-2G,} | |||
G={displaystyle G=,} | 3(K−λ)2{displaystyle {tfrac {3(K-lambda )}{2}}} | λ(1−2ν)2ν{displaystyle {tfrac {lambda (1-2nu )}{2nu }}} | E2(1+ν){displaystyle {tfrac {E}{2(1+nu )}}} | 3K(1−2ν)2(1+ν){displaystyle {tfrac {3K(1-2nu )}{2(1+nu )}}} | 3KE9K−E{displaystyle {tfrac {3KE}{9K-E}}} | |||||
ν={displaystyle nu =,} | λ2(λ+G){displaystyle {tfrac {lambda }{2(lambda +G)}}} | E2G−1{displaystyle {tfrac {E}{2G}}-1} | λ3K−λ{displaystyle {tfrac {lambda }{3K-lambda }}} | 3K−2G2(3K+G){displaystyle {tfrac {3K-2G}{2(3K+G)}}} | 3K−E6K{displaystyle {tfrac {3K-E}{6K}}} | M−2G2M−2G{displaystyle {tfrac {M-2G}{2M-2G}}} | ||||
M={displaystyle M=,} | λ+2G{displaystyle lambda +2G,} | G(4G−E)3G−E{displaystyle {tfrac {G(4G-E)}{3G-E}}} | 3K−2λ{displaystyle 3K-2lambda ,} | K+4G3{displaystyle K+{tfrac {4G}{3}}} | λ(1−ν)ν{displaystyle {tfrac {lambda (1-nu )}{nu }}} | 2G(1−ν)1−2ν{displaystyle {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+ν{displaystyle {tfrac {3K(1-nu )}{1+nu }}} | 3K(3K+E)9K−E{displaystyle {tfrac {3K(3K+E)}{9K-E}}} | |
