Org source:
---
For isotropic materials:
\begin{equation}
\begin{bmatrix}
\epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ 2\epsilon_{23} \\ 2\epsilon_{13} \\ 2\epsilon_{12}
\end{bmatrix} =
\frac{1}{E}
\begin{bmatrix}
1 & -\nu & -\nu & 0 & 0 & 0 \\
-\nu & 1 & -\nu & 0 & 0 & 0 \\
-\nu & -\nu & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 2+2\nu & 0 & 0 \\
0 & 0 & 0 & 0 & 2+2\nu & 0 \\
0 & 0 & 0 & 0 & 0 & 2+2\nu
\end{bmatrix}
\begin{bmatrix}
\sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12}
\end{bmatrix}
\end{equation}
\begin{equation}
\begin{bmatrix}
\sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12}
\end{bmatrix} =
\frac{E}{\left(1+\nu\right)\left(1-2\nu\right)}
\begin{bmatrix}
1-\nu & \nu & \nu & 0 & 0 & 0 \\
\nu & 1-\nu & \nu & 0 & 0 & 0 \\
\nu & \nu & 1-\nu & 0 & 0 & 0 \\
0 & 0 & 0 & \frac{1-2\nu}{2} & 0 & 0 \\
0 & 0 & 0 & 0 & \frac{1-2\nu}{2} & 0 \\
0 & 0 & 0 & 0 & 0 & \frac{1-2\nu}{2}
\end{bmatrix}
\begin{bmatrix}
\epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ 2\epsilon_{23} \\ 2\epsilon_{13} \\ 2\epsilon_{12}
\end{bmatrix}
\end{equation}
\begin{equation}
\begin{bmatrix}
\sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12}
\end{bmatrix} =
\begin{bmatrix}
2\mu+\lambda & \lambda & \lambda & 0 & 0 & 0 \\
\lambda & 2\mu+\lambda & \lambda & 0 & 0 & 0 \\
\lambda & \lambda & 2\mu+\lambda & 0 & 0 & 0 \\
0 & 0 & 0 & \mu & 0 & 0 \\
0 & 0 & 0 & 0 & \mu & 0 \\
0 & 0 & 0 & 0 & 0 & \mu
\end{bmatrix}
\begin{bmatrix}
\epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ 2\epsilon_{23} \\ 2\epsilon_{13} \\ 2\epsilon_{12}
\end{bmatrix}
\end{equation}
\begin{equation}
E=2\mu(1+\nu)
\end{equation}
\begin{equation}
G=2\mu
\end{equation}
--
Ihor Radchenko // yantar92,
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