# Zerilli-Armstrong Plasticity Model (LAW2)

This law is similar to the Johnson-Cook plasticity model. The same parameters are used to define the work hardening curve.

However, the equation that describes stress during plastic deformation is:

$$\sigma ={C}_{0}+\left({C}_{1}\mathrm{exp}\text{\hspace{0.05em}}\text{\hspace{0.17em}}\left(\left(-{C}_{3}\mathrm{T}+{C}_{4}\mathrm{T}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\mathrm{In}\left(\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{0}}\right)\right)\right)\right)+{C}_{5}{\epsilon}_{p}^{n}$$

Where,

- $\sigma $
- Stress (Elastic + Plastic Components)
- ${\epsilon}_{p}$
- Plastic strain
- $\tau $
- Temperature (computed as in Johnson-Cook plasticity)
- ${C}_{0}$
- Yield stress
- $n$
- Hardening exponent
- $\dot{\epsilon}$
- Strain rate, must be 1 s
^{-1}converted into user's time unit - ${\dot{\epsilon}}_{0}$
- Reference strain rate

Additional inputs are:

- ${\sigma}_{\mathrm{max}\text{}0}$
- Maximum flow stress
- ${\epsilon}_{\mathrm{max}}$
- Plastic strain at rupture

The ${\epsilon}_{\mathrm{max}}$ enables to define element rupture as in the former law. The theoretical aspects related to strain rate computation and filtering are also the same.