# Norton behaviour description

• file : Norton.mfront
• author : Helfer Thomas
• date : 23 / 11 / 06

This viscoplastic behaviour is fully determined by the evolution of the equivalent viscoplastic strain $$p$$ as a function $$f$$ of the Von Mises stress $${\sigma_{\mathrm{eq}}}$$ : $\dot{p}=f{\left({\sigma_{\mathrm{eq}}}\right)}=A\,{\sigma_{\mathrm{eq}}}^{E}$

where :

• $$A$$ is the Norton coefficient .
• $$E$$ is the Norton exponent .

$$A$$ and $$E$$ are declared as material properties .

## Source code

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  @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[castem] {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; }