Editing Infinitesimal strain theory (section)

=== Equivalent strain ===
A scalar quantity called the '''equivalent strain''', or the [[Richard von Mises|von Mises]] equivalent strain, is often used to describe the state of strain in solids. Several definitions of equivalent strain can be found in the literature. A definition that is commonly used in the literature on [[plasticity (physics)|plasticity]] is
<math display="block">
   \varepsilon_{\mathrm{eq}} = \sqrt{\tfrac{2}{3} \boldsymbol{\varepsilon}^{\mathrm{dev}}:\boldsymbol{\varepsilon}^{\mathrm{dev}}}  = \sqrt{\tfrac{2}{3}\varepsilon_{ij}^{\mathrm{dev}}\varepsilon_{ij}^{\mathrm{dev}}} 
  ~;~~ \boldsymbol{\varepsilon}^{\mathrm{dev}} = \boldsymbol{\varepsilon} - \tfrac{1}{3}\mathrm{tr}(\boldsymbol{\varepsilon})~\boldsymbol{I} 
 </math>
This quantity is work conjugate to the equivalent stress defined as
<math display="block"> \sigma_{\mathrm{eq}} = \sqrt{\tfrac{3}{2} \boldsymbol{\sigma}^{\mathrm{dev}}:\boldsymbol{\sigma}^{\mathrm{dev}}} </math>