Shear modulus

In <a href="/facts/Materials_science/N5HrXRYW">materials science</a>, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the <a href="/facts/Elasticity_(physics)/wcJoIFg1">elastic</a> shear stiffness of a material and is defined as the ratio of <a href="/facts/Shear_stress/aWWnzIhE">shear stress</a> to the <a href="/facts/Shear_strain/xK7R59oI">shear strain</a>:

G
         
        
          
            
              
                =
              
              
                
                  d
                  e
                  f
                
              
            
          
        
         
        
          
            
              τ
              
                x
                y
              
            
            
              γ
              
                x
                y
              
            
          
        
        =
        
          
            
              F
              
                /
              
              A
            
            
              Δ
              x
              
                /
              
              l
            
          
        
        =
        
          
            
              F
              l
            
            
              A
              Δ
              x
            
          
        
      
    
    {\displaystyle G\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\tau _{xy}}{\gamma _{xy}}}={\frac {F/A}{\Delta x/l}}={\frac {Fl}{A\Delta x}}}

where

τ
          
            x
            y
          
        
        =
        F
        
          /
        
        A
        
      
    
    {\displaystyle \tau _{xy}=F/A\,}
  
 = shear stress

F
      
    
    {\displaystyle F}
  
 is the force which acts

A
      
    
    {\displaystyle A}
  
 is the area on which the force acts

γ
          
            x
            y
          
        
      
    
    {\displaystyle \gamma _{xy}}
  
 = shear strain. In engineering 
  
    
      
        :=
        Δ
        x
        
          /
        
        l
        =
        tan
        ⁡
        θ
      
    
    {\displaystyle :=\Delta x/l=\tan \theta }
  
, elsewhere 
  
    
      
        :=
        θ
      
    
    {\displaystyle :=\theta }

Δ
        x
      
    
    {\displaystyle \Delta x}
  
 is the transverse displacement

l
 
 
 {\displaystyle l}
 
 is the initial length of the area.
The derived <a href="/facts/SI/S7YLglNz">SI</a> unit of shear modulus is the <a href="/facts/Pascal_(unit)/Am1To2Qm">pascal</a> (Pa), although it is usually expressed in <a href="/facts/Pascal_(unit)/Am1To2Qm">gigapascals</a> (GPa) or in thousand <a href="/facts/Pounds_per_square_inch/RMdeTlB0">pounds per square inch</a> (ksi). Its <a href="/facts/Dimensional_analysis/t6UskoCD">dimensional form</a> is M1L−1T−2, replacing force by mass times acceleration.

Shear modulus open-in-new

Shear modulus