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)

σ = C_{0} + (C_{1} \exp ((- C_{3} T + C_{4} T In (\frac{\dot{ε}}{{\dot{ε}}_{0}})))) + C_{5} ε_{p}^{n}

Where,

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

Additional inputs are:

$σ_{\max 0}$: Maximum flow stress
$ε_{\max}$: Plastic strain at rupture

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