#### MAT_CREEP

###### Material properties
*MAT_CREEP
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid
$A$, $B$, $n$, $c_0$, $c_1$, $c_2$, $c_3$
##### Parameter definition
VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus, constant or function of temperature
options: constant, fcn
$\nu$ Poisson's ratio, constant or function of temperature
options: constant, fcn
did Damage property command ID
tid Thermal property command ID
$A$ Initial yield strength, constant or function of temperature
options: constant, fcn
$B$ Hardening parameter, constant or function of temperature
options: constant, fcn
$n$ Hardening exponent, constant or function of temperature
options: constant, fcn
$c_0$ Creep parameter, constant or function of temperature
options: constant, fcn
$c_1$ Creep parameter, constant or function of temperature
options: constant, fcn
$c_2$ Creep parameter, constant or function of temperature
options: constant, fcn
$c_3$ Creep parameter, constant or function of temperature
options: constant, fcn
##### Description

This model combines a plastic yield surface (J2) with a visco-plastic creep law. All inelastic flow follows a simple radial return law. The total strain is assumed additive:

$\varepsilon = \varepsilon^e + \varepsilon^p + \varepsilon^c$

where $e$ stands for elastic, $p$ plastic and $c$ for creep. The effective plastic flow stress is:

$\sigma_y = A(T) + B(T) \left[ \varepsilon_{eff}^p \right]^{n(T)}$

The creep strain rate is:

$\displaystyle{\dot\varepsilon_{eff}^c = \left[ \frac{\sigma_{eff}}{c_1(T) + c_2(T) \varepsilon_{eff}^c + c_3(T) ( \varepsilon_{eff}^c )^2} \right]^{c_0(T)}}$

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 $T_{ref}$ is the reference temperature (see PROP_THERMAL).

##### Example
###### Temperature dependent hardening and creep behavior

Typical (but not real) properties for a generic aluminum alloy. Note the use of both constants and curves (see CURVE or FUNCTION).

*PARAMETER
%n = 0.4
%c0 = 5
*MAT_CREEP
1, 2700.0, 70.0e9, 0.3
fcn(10), fcn(20), [%n], [%c0], fcn(30)
#
# A(T)
*CURVE
10
0.0, 200.0e6
500.0, 20.0e6
#
# B(T)
*CURVE
20
0.0, 100.0e6
500.0, 20.0e6
#
# c1(T)
*CURVE
20
0.0, 1.0e10
300.0, 1.0e10
400.0, 100.0e6
500.0, 40.0e6