Alternative stress measures

<p>In <a href="/facts/Continuum_mechanics/vI7LpFDk">continuum mechanics</a>, the most commonly used measure of <a href="/facts/Stress_(mechanics)/ErAXDbbd">stress</a> is the <a href="/facts/Cauchy_stress_tensor/5MsXPQVH">Cauchy stress tensor</a>, often called simply <i>the</i> stress tensor or "true stress".  However, several alternative measures of stress can be defined:
</p>
<ol><li>The Kirchhoff stress (
  
    
      
        
          τ
        
      
    
    {\displaystyle {\boldsymbol {\tau }}}
  
).</li>
<li>The nominal stress (
  
    
      
        
          N
        
      
    
    {\displaystyle {\boldsymbol {N}}}
  
).</li>
<li>The <a href="/facts/Piola%E2%80%93Kirchhoff_stress_tensor/ErAXDbbd">Piola–Kirchhoff stress tensors</a>
<ol><li>The first Piola–Kirchhoff stress (
  
    
      
        
          P
        
      
    
    {\displaystyle {\boldsymbol {P}}}
  
).  This stress tensor is the transpose of the nominal stress (
  
    
      
        
          P
        
        =
        
          
            N
          
          
            T
          
        
      
    
    {\displaystyle {\boldsymbol {P}}={\boldsymbol {N}}^{T}}
  
).</li>
<li>The second Piola–Kirchhoff stress or PK2 stress (
  
    
      
        
          S
        
      
    
    {\displaystyle {\boldsymbol {S}}}
  
).</li></ol></li>
<li>The Biot stress (
  
    
      
        
          T
        
      
    
    {\displaystyle {\boldsymbol {T}}}
  
)</li></ol>

Alternative stress measures open-in-new

Alternative stress measures