#### MAT_JC_FIELD

###### Material properties
*MAT_JC_FIELD
"Optional title"
mid, $\rho$, $E$, $\nu$
$A$, $B$, $n$, $C$, $m$, $T_0$, $T_m$, $\dot{\varepsilon}_0$
$C_p$, $k$, $W_{c0}$, $c_1$, $c_2$, erode
##### Parameter definition
VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus
$\nu$ Poisson's ratio
$A$ Initial yield strength
$B$ Hardening parameter
$n$ Hardening parameter
$C$ Strain rate hardening parameter
$m$ Thermal softening parameter
$T_0$ Ambient temperature
$T_m$ Melting temperature
$\dot{\varepsilon}_0$ Strain rate parameter
default: 1
$C_p$ Specific heat capacity
$k$ Plastic work to heat conversion factor
default: 0.9
$W_{c0}$ Cockcroft-Latham damage parameter
default: damage not active
$c_1$ Extended rate dependency parameter to the Cockcroft-Latham damage criterion
default: not active
$c_2$ Extended rate dependency parameter to the Cockcroft-Latham damage criterion
default: not active
erode Element erosion flag
options:
0 $\rightarrow$ failed elements keep the bulk stiffness
1 $\rightarrow$ failed elements are eroded
2 $\rightarrow$ node splitting
##### Description

Field version of Johnson-Cook's constitutive model. All parameters (including density) can be functions or parameters. A function can be defined to depend on the initial integration point location $(x,y,z)$. A function is referenced by typing fcn(id), where id is the function ID.

The von Mises flow stress is defined as:

$\displaystyle{\sigma_y = \left( A + B(\varepsilon_{eff}^p)^n \right) \cdot \left( 1 + C \cdot \mathrm{ln}\left( \frac{\dot\varepsilon_{eff}^p}{\dot{\varepsilon}_0} \right) \right) \cdot \left(1 - \left( \frac{\mathrm{T}-\mathrm{T}_0}{\mathrm{T}_m - \mathrm{T}_0} \right)^m \right)}$

$T$ is the current temperature. The hydrostatic pressure $p$ is defined as:

$p = -K \varepsilon_v + 3K \alpha_T (T-T_{ref})$

where $K$ is the bulk modulus, $\varepsilon_v$ is the volumetric strain. $\alpha_T$ is the thermal expansion coefficient and $T_{ref}f$ is the reference temperature (see PROP_THERMAL).

Failure modeling is currently limited to a Cockcroft-Latham criterion that has been extended to account for rate effects. Failure occurs once the damage parameter, D, has evolved from 0 to 1.

$D = \displaystyle{\int_0^{\varepsilon_{eff}^p} \frac{\mathrm{max}(0,\sigma_1)} {W_{c0} \cdot (1 + c_1 \dot\varepsilon_{eff}^p)^{c_2}}} \mathrm{d}\varepsilon_{eff}^p$
##### Example
###### JC Field with function

A plate where the yield stress (A) and damage parameter (Wc) are functions. The functions depend on the distance from the upper surface of the plate (see built in function dist_surf).

*PARAMETER
%A0 = 1.0e9
%B = 2.0e8
%n = 0.3
%Wc0 = 4.0e8
*MAT_JC_FIELD
1, 7800.0, 210.0e9, 0.3
fcn(10), [%B], [%n]
0, 0, fcn(20), 2
*FUNCTION
10
%A0*crv(11,dist_surf(0, 0, 1))
*FUNCTION
20
%Wc0*crv(21,dist_surf(0, 0, 1))
#
# Yield stress scale factor as function of distance from plate surface
*CURVE
11
0.0, 1.0
5.0e-3, 1.0
8.0e-3, 0.5
1.0, 0.5
#
# Wc scale factor as function of distance from plate surface
*CURVE
21
0.0, 0.25
5.0e-3, 0.25
8.0e-3, 1.0
1.0, 1.0