#### PROP_DAMAGE_GOLDTHORPE

###### Material properties
*PROP_DAMAGE_GOLDTHORPE
"Optional title"
did, erode, noic
$S$, $A$
##### Parameter definition
VariableDescription
did Unique damage identification number
erode Element erosion flag
options:
0 $\rightarrow$ failed element is not eroded
1 $\rightarrow$ failed element is eroded
2 $\rightarrow$ node splitting at failure (crack plane orthogonal to max principal strain)
3 $\rightarrow$ node splitting at failure (crack plane orthogonal max principal stress)
noic Flag to turn off cracking along interface between different materials
options:
0 $\rightarrow$ material interface cracks are allowed
1 $\rightarrow$ material interface cracks are not allowed
$S$ Damage parameter
$A$ Parameter controlling influence of shear strain on damage accumulation
##### Description

This is the Goldthorpe path dependent fracture model. Damage is defined as:

$\displaystyle{D = \frac{1}{S} \cdot \left[0.67 \int_0^{\varepsilon_{eff}^p} exp\left(1.5\sigma_n - 0.04\sigma_n^{-1.5}\right)d\varepsilon_{eff}^p + A\varepsilon_s\right]}$

Parameter $\sigma_n$ is a triaxiality ratio defined based on pressure, $p$, and effective stress, $\sigma_{eff}$, as:

$\displaystyle{\sigma_n = \frac{\mathrm{max}(0,-p)}{\sigma_{eff}}}$

Parameter $\varepsilon_s$ is the maximum shear strain defined based on maximum and minimum principal strains, $\varepsilon_1$ and $\varepsilon_3$, as:

$\displaystyle{\varepsilon_s = \frac{\varepsilon_1 - \varepsilon_3}{2}}$

The material will fail once the damage, $D$, reaches 1.