@Parser IsotropicMisesCreep;
@Behaviour Norton;
@Author Helfer Thomas;
@Date 23/11/06;
@Description{
This viscoplastic behaviour is fully determined by the evolution
of the equivalent viscoplastic strain "\(p\)" as a function "\(f\)"
of the Von Mises stress "\(\sigmaeq\)":
"\["
"\dot{p}=f\paren{\sigmaeq}=A\,\sigmaeq^{E}"
"\]"
where:
- "\(A\)" is the Norton coefficient.
- "\(E\)" is the Norton exponent.
"\(A\)" and "\(E\)" are declared as material properties.
}
@UMATFiniteStrainStrategies[umat] {None,LogarithmicStrain1D};
//! The Norton coefficient
@MaterialProperty real A;
A.setEntryName("NortonCoefficient");
//! The Norton coefficient
@MaterialProperty real E;
E.setEntryName("NortonExponent");
@FlowRule{
/*!
* The return-mapping algorithm used to integrate this behaviour
* requires the definition of \(f\) and \(\deriv{f}{\sigmaeq}\) (see
* @simo_computational_1998 and @helfer_generateur_2013 for
* details).
*
* We introduce an auxiliary variable called `tmp` to
* limit the number of call to the `pow` function
*/
const real tmp = A*pow(seq,E-1);
f = tmp*seq;
df_dseq = E*tmp;
}