#1 2019-10-14 10:52:39

Alessia Bez

Member

Registered: 2019-10-14

Posts: 10

How to add a nonlinear behaviour in STAT_NON_LINE analysis

Hello all,

I'm trying to model a material with non-linear elastic behavior with increasing stiffness for a static non linear analysis. I've tried several things but none of them work:
- DEFI_MATERIAU - TRACTION but since the stiffness increasing the software gives an error;
- I've defined a function with Young's modulus-EPSI trend, I've inserted it in ELAS_FO but it gives an interpolation error;
- I interpolated the constitutive law into a polynomial as a function of the deformations and defined it in FORMULE but the independent variable is not recognized

I would like to know if there is a possibility to insert a non-linear behavior with increasing stiffness.

Thank you in advance for sharing your knowledge

Alessia

AsterO'dactyle

Administrator

Registered: 2007-11-29

Posts: 413

Re: How to add a nonlinear behaviour in STAT_NON_LINE analysis

Hello,

Elastic non-linear with increasing stiffness is ELAS_HYPER (hyperelastic material as Mooney-Rivlin, neo-hookean or Signorini model)
You cannot use TRACTION. It's only for (visco)-plastic material (generalized standard materials) with strain hardening

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Alessia Bez

Member

Registered: 2019-10-14

Posts: 10

Re: How to add a nonlinear behaviour in STAT_NON_LINE analysis

Thank you so much for your answer. You confirmed what I imagined, but is this the only way to consider non-linear elastic behavior? I would like to insert a constitutive law obtained from laboratory tests to describe the behavior of a particular material, do you think it is possible?

nirmaljoshi

Member

From: Japan

Registered: 2018-10-12

Posts: 190

Re: How to add a nonlinear behaviour in STAT_NON_LINE analysis

Thank you so much for your answer. You confirmed what I imagined, but is this the only way to consider non-linear elastic behavior? I would like to insert a constitutive law obtained from laboratory tests to describe the behavior of a particular material, do you think it is possible?

For that case, you can define function for the material properties (copied from book by jean)
e.g.

s235elpl=DEFI_FONCTION(
NOM_PARA=’EPSI’ ,NOM_RESU=’SIGMA’ ,
VALE=(
#there should not be a point at 0.0, 0.0
#0.0000, 0.0
0 . 0 0 1 1 4 , 2 4 0 . 0 ,
0 . 0 0 1 2 , 2 4 1 . 0 ,
0 . 0 0 2 0 , 2 4 1 . 6 ,
0 . 0 0 5 0 , 2 4 4 . 0 ,
0 . 0 1 0 0 , 2 4 8 . 0 ,
0 . 0 1 5 0 , 2 5 2 . 0 ,
0 . 0 5 0 0 , 2 8 0 . 0 ,
0 . 1 0 0 0 , 3 2 0 . 0 ,
0 . 1 5 0 0 , 3 6 0 . 0 ,
0 . 2 0 0 0 , 3 8 0 . 0 ,
0 . 4 0 0 0 , 4 2 0 . 0 ,
) ,
INTERPOL=’LIN’ ,
PROL_DROITE=’LINEAIRE’ ,
PROL_GAUCHE=’CONSTANT’ ,
) ;

and define the material and apply it

steel=DEFI_MATERIAU(
ELAS=_F(E=210000 ,NU = 0 . 3 , ) ,
TRACTION=_F(SIGM=s235elpl , ) ,
) ;
mate=AFFE_MATERIAU(
MAILLAGE=mesh1 ,
AFFE=_F(TOUT=’OUI’ ,MATER=steel , ) ,
) ;

and perform analysis

resunl=STAT_NON_LINE(
MODELE=mod1 ,
CHAM_MATER=mate ,
EXCIT=(
_F(CHARGE=fix1 , ) ,
_F(CHARGE=load , TYPE_CHARGE=’FIXE_CSTE’ ,FONC_MULT=load_m , ) ,
) ,
COMPORTEMENT=_F(
RELATION=’VMIS_ISOT_TRAC’ , #U4.51.11 para 4.3.1.3
DEFORMATION=’SIMO_MIEHE’ , #U4.51.11 para 4.5.3
) ,
INCREMENT=_F(LIST_INST=linst , ) ,
NEWTON=_F(
PREDICTION=’TANGENTE’ ,
MATRICE=’TANGENTE’ ,
REAC_ITER=1 ,
) ,
CONVERGENCE=_F(RESI_GLOB_RELA=1e?4,ITER_GLOB_MAXI=3 0 0 , ) ,
) ;

Alessia Bez

Member

Registered: 2019-10-14

Posts: 10

Re: How to add a nonlinear behaviour in STAT_NON_LINE analysis

I'm sorry because my answer was incomplete. The behavior of the material in question is infinitely elastic nonlinear, with Young's modulus increasing, so unfortunately using TRACTION the software signals an error. Thanks for your advice.
Alessia

Last edited by Alessia Bez (2019-10-16 07:30:01)

Pisolino

Member

From: Italy

Registered: 2009-04-06

Posts: 64

Re: How to add a nonlinear behaviour in STAT_NON_LINE analysis

Hello,

Elastic non-linear with increasing stiffness is ELAS_HYPER (hyperelastic material as Mooney-Rivlin, neo-hookean or Signorini model)
You cannot use TRACTION. It's only for (visco)-plastic material (generalized standard materials) with strain hardening

Dear Aster'O'dactyle i have a question about it:
is it really ELAS_HYPER non-linear in terms of stiffness?  As written in u4.43.01.

"Le matériau est élastique incompressible en petites déformations si on prend C10 et C01 tels que 6*( C01+ C10)= E , où E est le module de Young."

So E doesn't change according to epsilon, the same goes for K parameter. Am i wrong or basically the material is treated with a constant E modulus across all the strains ?

I'm asking this since i have problems with strong compression of a rubber and the material doesn't reach the stiffness it should have.

Thank you in advance

Andrea

thomas.helfer

Member

Registered: 2013-09-26

Posts: 122

Re: How to add a nonlinear behaviour in STAT_NON_LINE analysis

Hi @Alessia Bez,
Another option is to use MFront. For an example, you can search "Ramberg-Osgood MFront" in google.
Regards,
Thomas