Editing Infinitesimal strain theory (section)

=== Strain invariants ===
Certain operations on the strain tensor give the same result without regard to which orthonormal coordinate system is used to represent the components of strain. The results of these operations are called '''strain invariants'''. The most commonly used strain invariants are
<math display="block"> \begin{align}
   I_1 & = \mathrm{tr}(\boldsymbol{\varepsilon}) \\
   I_2 & = \tfrac{1}{2}\{[\mathrm{tr}(\boldsymbol{\varepsilon})]^2 - \mathrm{tr}(\boldsymbol{\varepsilon}^2)\} \\
   I_3 & = \det(\boldsymbol{\varepsilon})
\end{align} </math>
In terms of components
<math display="block"> \begin{align}
   I_1 & = \varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33} \\
   I_2 & = \varepsilon_{11}\varepsilon_{22} + \varepsilon_{22}\varepsilon_{33} + \varepsilon_{33}\varepsilon_{11} - \varepsilon_{12}^2 - \varepsilon_{23}^2 - \varepsilon_{31}^2 \\
   I_3 & = \varepsilon_{11}(\varepsilon_{22}\varepsilon_{33} - \varepsilon_{23}^2) - \varepsilon_{12}(\varepsilon_{21}\varepsilon_{33}-\varepsilon_{23}\varepsilon_{31}) + \varepsilon_{13}(\varepsilon_{21}\varepsilon_{32}-\varepsilon_{22}\varepsilon_{31})
\end{align} </math>