查看“︁剪切模量”︁的源代码

{{Infobox Physical quantity
| bgcolour =
| name = 剪力模數
| image = 
| caption = 数学
| unit = [[帕斯卡]]
| symbols = {{mvar|G}}, {{mvar|S}}
| derivations = {{math|1=''G'' = [[剪应力|τ]] / [[剪应变|γ]]}}
}}
[[File:Shear scherung.svg|thumb|right|剪應變]]
'''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
:<math>
G = \frac {\tau } {\gamma}
</math>

其中，<math> G\, </math> 表示剪力模數，<math>\tau\, </math> 表示剪應力，<math>\gamma\, </math> 表示剪應變。在均質且等向性的材料中：
:<math>G = {E \over {2(1 + \nu)}}</math>
其中，''<math>E\,</math>'' 是[[楊氏模數]](Young's modulus )，''<math>\nu\,</math>'' 是[[泊松比]](Poisson's ratio)。
==波==
在均匀各向同性固体中，有两种波:[[P波]]和[[S波]]。剪切波的速度，<math>(v_s)</math>由剪切模量控制， 
:<math>v_s = \sqrt{\frac {G} {\rho} }</math>
其中
:G是剪切模量
:<math>\rho</math>是固体的[[密度]].
== 金属的剪切模量 ==
[[File:CuShearMTS.svg|300px|thumb|Shear modulus of copper as a function of temperature. The experimental data<ref name=Overton55>{{cite journal|last1=Overton|first1=W.|last2=Gaffney|first2=John|title=Temperature Variation of the Elastic Constants of Cubic Elements. I. Copper|url=https://archive.org/details/sim_physical-review_1955-05-15_98_4/page/n121|journal=Physical Review|volume=98|pages=969|year=1955|doi=10.1103/PhysRev.98.969|issue=4|bibcode = 1955PhRv...98..969O }}</ref><ref name=Nadal03/> are shown with colored symbols.]]
金属的剪切模量通常随温度的升高而降低。在高压下，剪切模量也随外加压力的增大而增大。在许多金属中，熔点温度、空位形成能和剪切模量之间的关系已经被观察到。<ref name=March>March, N. H., (1996), [https://books.google.com/books?id=PaphaJhfAloC&pg=PA363 ''Electron Correlation in Molecules and Condensed Phases''] {{Wayback|url=https://books.google.com/books?id=PaphaJhfAloC&pg=PA363 |date=20201209145126 }}, Springer, {{ISBN|0-306-44844-0}} p. 363</ref>

有几种模型试图预测金属的剪切模量(可能还有合金的剪切模量)。在塑性流动计算中使用的剪切模量模型包括:

# MTS剪切模量模型由机械阈值应力(MTS)塑性流动应力模型开发并与之结合使用。<ref name=Varshni70>{{cite journal|last1=Varshni|first1=Y.|title=Temperature Dependence of the Elastic Constants|journal=Physical Review B|volume=2|pages=3952–3958|year=1970|doi=10.1103/PhysRevB.2.3952|issue=10|bibcode = 1970PhRvB...2.3952V }}</ref><ref name=Chen96>{{cite journal|last1=Chen|first1=Shuh Rong|last2=Gray|first2=George T.|title=Constitutive behavior of tantalum and tantalum-tungsten alloys|journal=Metallurgical and Materials Transactions A|volume=27|pages=2994|year=1996|doi=10.1007/BF02663849|issue=10|bibcode=1996MMTA...27.2994C|url=https://zenodo.org/record/1232556/files/article.pdf|access-date=2019-11-22|archive-date=2020-10-01|archive-url=https://web.archive.org/web/20201001172340/https://zenodo.org/record/1232556/files/article.pdf|dead-url=no}}</ref><ref name=Goto00>{{cite journal|doi=10.1007/s11661-000-0226-8|title=The mechanical threshold stress constitutive-strength model description of HY-100 steel|year=2000|last1=Goto|first1=D. M.|last2=Garrett|first2=R. K.|last3=Bingert|first3=J. F.|last4=Chen|first4=S. R.|last5=Gray|first5=G. T.|journal=Metallurgical and Materials Transactions A|volume=31|issue=8|pages=1985–1996|url=http://www.dtic.mil/get-tr-doc/pdf?AD=ADA372816|access-date=2019-11-22|archive-date=2017-09-25|archive-url=https://web.archive.org/web/20170925012725/http://www.dtic.mil/get-tr-doc/pdf?AD=ADA372816|dead-url=no}}</ref>
#由SCGL流动应力模型开发并与之结合使用的SCGL剪切模量模型。<ref name=Guinan74>{{cite journal|last1=Guinan|first1=M|last2=Steinberg|first2=D|title=Pressure and temperature derivatives of the isotropic polycrystalline shear modulus for 65 elements|journal=Journal of Physics and Chemistry of Solids|volume=35|pages=1501|year=1974|doi=10.1016/S0022-3697(74)80278-7|bibcode=1974JPCS...35.1501G|issue=11}}</ref>
# 纳达尔和LePoac (NP)剪切模量模型，利用Lindemann理论确定剪切模量对温度的依赖关系，利用SCG模型确定剪切模量对压力的依赖关系。<ref name=Nadal03>{{cite journal|last1=Nadal|first1=Marie-Hélène|last2=Le Poac|first2=Philippe|title=Continuous model for the shear modulus as a function of pressure and temperature up to the melting point: Analysis and ultrasonic validation|journal=Journal of Applied Physics|volume=93|pages=2472|year=2003|doi=10.1063/1.1539913|issue=5|bibcode = 2003JAP....93.2472N }}</ref>
=== MTS剪切模型 ===
MTS剪切模量模型为:

:<math> 
 \mu(T) = \mu_0 - \frac{D}{\exp(T_0/T) - 1}
 </math>

其中<math> \mu_0 </math>为<math> T=0K </math>处的剪切模量，<math>D</math>和<math> T_0 </math>为材料常数。

=== SCG剪切模型 ===
=== NP剪切模型 ===
== 剪切松弛模量 ==

== 参见 ==
*[[固體力學]]
*[[流體力學]]
*[[連續介質力學]]

{{连续介质力学}}
{{弹性模量}}
[[Category:固体力学|J]]
[[Category:物理量|J]]