来不及了，就这个吧
弹性状态：

$$ f(\sigma_{ij})\begin{cases} <\ C弹性状态\\ =\ C塑形状态\\ >\ C不存在 \end{cases} $$

Tresca准则

$$ \tau_{max}=\left| \frac{\sigma_{max}-\sigma_{min}}{2}\right| =C $$

$$ \tau_{max}=\frac{\sigma_s}{2} $$

Mises准则

$$ C=\frac{1}{3}\sigma_s^2 $$

$$ (\sigma_x - \sigma_y)^2 + (\sigma_y - \sigma_z)^2 + (\sigma_z - \sigma_x)^2 + 6 \left( \tau_{xy}^2 + \tau_{yz}^2 + \tau_{zx}^2 \right) = 2\sigma_s^2 $$

或

$$ (\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2 = 2\sigma_s^2 $$