This is the Zerilli-Armstrong constitutive model in its general form. The von Mises flow stress is defined as:

$\displaystyle{\sigma_y = \sigma_a + B \mathrm{e}^{-\beta T} + B_0 \sqrt{\varepsilon_p} \mathrm{e}^{-\alpha T}}$

where $T$ is the current temperature. The athermal part of the flow stress is defined as:

$\displaystyle{ \sigma_a = \sigma_g + \frac{k_h}{\sqrt{l}}+ K \varepsilon_p^n}$

where $k_h / \sqrt{l}$ is the Hall-Petch strengthening limit. The exponents $\alpha$ and $\beta$ are defined as:

$\displaystyle{ \alpha = \alpha_0 - \alpha_1 \mathrm{ln}\frac{\dot{\varepsilon}_p}{\dot{\varepsilon}_0}}$

$\displaystyle{ \beta = \beta_0 - \beta_1 \mathrm{ln}\frac{\dot{\varepsilon}_p}{\dot{\varepsilon}_0}}$

where $\dot{\varepsilon}_p$ is the current effective plastic strain rate. The used parameters depend on the crystal structure of the material. Generally, materials with FCC structure are described as:

$\displaystyle{\sigma_y = \sigma_a + B_0 \sqrt{\varepsilon_p} \mathrm{e}^{-\alpha T}}$

and BCC materials as:

$\displaystyle{\sigma_y = \sigma_a + B \mathrm{e}^{-\beta T}}$