# 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:(1)
$\sigma ={C}_{0}+\left({C}_{1}\mathrm{exp}\text{ }\text{\hspace{0.17em}}\left(\left(-{C}_{3}\mathrm{T}+{C}_{4}\mathrm{T}\text{ }\text{ }\mathrm{In}\left(\frac{\stackrel{˙}{\epsilon }}{{\stackrel{˙}{\epsilon }}_{0}}\right)\right)\right)\right)+{C}_{5}{\epsilon }_{p}^{n}$
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
$\stackrel{˙}{\epsilon }$
Strain rate, must be 1 s-1 converted into user's time unit
${\stackrel{˙}{\epsilon }}_{0}$
Reference strain rate
${\sigma }_{\mathrm{max}\text{​}0}$
${\epsilon }_{\mathrm{max}}$
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.