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Update README.md
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haidi-ustc authored Sep 28, 2023
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Expand Up @@ -35,7 +35,9 @@ pip install .

Please refer to [mech2d](https://doi.org/10.3390/molecules28114337)
The polar plot of Young's modulus and Poisson's ratio is obtained by following equation:
$$ \begin{align*}

$$
\begin{align*}
v_{zz} & = \frac{C_{12}}{C_{22}} \\
d_1 & = \frac{C_{11}}{C_{22}} + 1 - \frac{C_{11} C_{22} - C_{12}^2}{C_{22} C_{66}} \\
d_2 & = -\left(2 \frac{C_{12}}{C_{22}} - \frac{C_{11} C_{22} - C_{12}^2}{C_{22} C_{66}}\right) \\
Expand All @@ -44,7 +46,8 @@ Y_{zz} & = \frac{C_{11} C_{22} - C_{12}^2}{C_{22}} \\
\theta & \in [0, 2\pi] \text{ with 360 points} \\
E(\theta) & = \frac{Y_{zz}}{\cos(\theta)^4 + d_2 \cos(\theta)^2 \sin(\theta)^2 + d_3 \sin(\theta)^4} \\
V(\theta) & = \frac{v_{zz} \cos(\theta)^4 - d_1 \cos(\theta)^2 \sin(\theta)^2 + v_{zz} \sin(\theta)^4}{\cos(\theta)^4 + d_2 \cos(\theta)^2 \sin(\theta)^2 + d_3 \sin(\theta)^4}
\end{align*} $$
\end{align*}
$$

## Usage

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