test

\[\varepsilon_{xx} = \varepsilon_{yy} = \frac{a_0-a}{a} \]

\[\sigma_{xx} = \sigma_{yy} =T, \sigma_{zz}=0\\ \sigma_{xz} = \sigma_{yz} = \sigma_{xy} = 0\\ \varepsilon_{xx} = \varepsilon_{yy} = (s_{11} + s_{12} )T\\ \varepsilon_{zz} = 2s_{12}T\\ \varepsilon_{zz} = \frac{2s_{12}}{s_{11} + s_{12}}\varepsilon_{xx} \]

\[\varepsilon= \begin{pmatrix} \varepsilon_{xx} & 0 &0\\ 0&\varepsilon_{xx}&0\\ 0&0&\varepsilon_{zz} \end{pmatrix} \]

[110] uniaxial stress

\[\sigma_{xx} = \sigma_{yy} = \sigma_{xy} = T/2\\ \sigma_{zz} = \sigma_{xz} = \sigma_{yz} = 0\\ e_{xx} = e_{yy} = \frac{s_{11} + s_{12}}{2}T\\ e_{xy} = \frac{s_{44}}{2}T\\ e_{zz} = s_{12}T \]

\[\varepsilon= \begin{pmatrix} e_{xx} & e_{xy}/2 &0\\ e_{xy}/2&e_{xx}&0\\ 0&0&e_{zz} \end{pmatrix} \]

\[G^{(1)}=\begin{bmatrix} G_{11} \end{bmatrix} \]

\[G^{(2)}=\begin{bmatrix} G_{11} & G_{12} \\ G_{21} & G_{22} \end{bmatrix} \]

\[G^{(3)}=\begin{bmatrix} G_{11} & G_{12} & G_{13} \\ G_{21} & G_{22} & G_{23} \\ G_{31} & G_{32} & G_{33} \end{bmatrix} \]

\[G^{(4)}=\begin{bmatrix} G_{11} & G_{12} & G_{13} & G_{14}\\ G_{21} & G_{22} & G_{23} & G_{24}\\ G_{31} & G_{32} & G_{33} & G_{34} \\ G_{41} & G_{42} & G_{43} & G_{44} \end{bmatrix} \]

\[G^{(n)}=\begin{bmatrix} G_{11} & G_{12} & \cdots & G_{1n} \\ G_{21} & G_{22} & \cdots & \cdots \\ \vdots & \vdots & \vdots & \vdots \\ G_{n1} & \cdots & \cdots & G_{nn} \end{bmatrix} \]

\[G^{(n)}=\begin{bmatrix} G_{11} & G_{12} & G_{13} & G_{14} & \cdots & G_{1n} \\ G_{21} & G_{22} & G_{23} & G_{24} &\cdots & \cdots \\ G_{31} & G_{32} & G_{33} & G_{34} &\cdots & \cdots \\ G_{41} & G_{42} & G_{43} & G_{44} &\cdots & \cdots \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ G_{n1} & \cdots & \cdots & \cdots & \cdots & G_{nn} \end{bmatrix} \]