Editing Infinitesimal strain theory (section)

===Strain deviator tensor===
The infinitesimal strain tensor <math>\varepsilon_{ij}</math>, similarly to the [[Cauchy stress tensor]], can be expressed as the sum of two other tensors: 
# a '''mean strain tensor''' or '''volumetric strain tensor''' or '''spherical strain tensor''', <math>\varepsilon_M\delta_{ij}</math>, related to dilation or volume change; and
# a deviatoric component called the '''strain deviator tensor''', <math>\varepsilon'_{ij}</math>, related to distortion.

<math display="block">\varepsilon_{ij}= \varepsilon'_{ij} + \varepsilon_M\delta_{ij}</math>
where <math>\varepsilon_M</math> is the mean strain given by
<math display="block">\varepsilon_M = \frac{\varepsilon_{kk}}{3} = \frac{\varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33}}{3} = \tfrac{1}{3}I^e_1</math>

The deviatoric strain tensor can be obtained by subtracting the mean strain tensor from the infinitesimal strain tensor:
<math display="block">\begin{align}
\ \varepsilon'_{ij} &= \varepsilon_{ij} - \frac{\varepsilon_{kk}}{3}\delta_{ij} \\
\begin{bmatrix}
   \varepsilon'_{11} & \varepsilon'_{12} & \varepsilon'_{13} \\
   \varepsilon'_{21} & \varepsilon'_{22} & \varepsilon'_{23} \\
   \varepsilon'_{31} & \varepsilon'_{32} & \varepsilon'_{33} \\
  \end{bmatrix}
&=\begin{bmatrix}
   \varepsilon_{11} & \varepsilon_{12} & \varepsilon_{13} \\
   \varepsilon_{21} & \varepsilon_{22} & \varepsilon_{23} \\
   \varepsilon_{31} & \varepsilon_{32} & \varepsilon_{33} \\
  \end{bmatrix}
- \begin{bmatrix}
   \varepsilon_M & 0 & 0 \\
   0 & \varepsilon_M & 0 \\
   0 & 0 & \varepsilon_M \\
  \end{bmatrix} \\
&=\begin{bmatrix}
   \varepsilon_{11}-\varepsilon_M & \varepsilon_{12} & \varepsilon_{13} \\
   \varepsilon_{21} & \varepsilon_{22}-\varepsilon_M & \varepsilon_{23} \\
   \varepsilon_{31} & \varepsilon_{32} & \varepsilon_{33}-\varepsilon_M \\
  \end{bmatrix} \\
\end{align}</math>