Brittle Damage: Johnson-Cook
Plasticity Model (LAW27)

Johnson-Cook plasticity model is presented in Johnson-Cook Plasticity Model (LAW2). For
shell applications, a simple damage model can be associated to this law to take into account
the brittle failure. The crack propagation occurs in the plan of shell in the case of
mono-layer property and through the thickness if a multi-layer property is defined (Figure 1).

The elastic-plastic behavior of the material is defined by Johnson-Cook model. However, the
stress-strain curve for the material incorporates a last part related to damage phase as
shown in Figure 2. The damage parameters are:

${\epsilon}_{t1}$

Tensile rupture strain in direction 1

${\epsilon}_{m1}$

Maximum strain in direction 1

d_{max1}

Maximum damage in direction 1

${\epsilon}_{f1}$

Maximum strain for element deletion in direction 1

The element is removed if one layer of element reaches the failure tensile strain, ${\epsilon}_{f1}$. The nominal and effective stresses developed in an element
are related by:

$${\sigma}_{n}={\sigma}_{eff}\left(1-d\right)$$

Where,

$\text{0d1}$

Damage factor

The strains and the stresses in each direction are given by:

The mathematical approach described here can be applied to the modeling of rivets. Predit
law in Radioss allows achievement of this end by a simple model
where for the elastic-plastic behavior a Johnson-Cook model or a tabulated law (LAW36) may
be used.