Convergence problem with Large Displacement

DEBUT();

#----------------------------------------------------
#parameters R = 1; L=10;
th=0.01;
E=1.e10;
nu=0.3;
P_a=-2e7;
P_b=0.;
presss=P_a-P_b;
tsteps = 100;

#----------------------------------------------------
# (1) Reading of the mesh
#----------------------------------------------------

meshI=LIRE_MAILLAGE(UNITE=20,FORMAT='MED',INFO_MED=1,);

Qmesh=CREA_MAILLAGE(MAILLAGE=meshI,LINE_QUAD=_F(TOUT='OUI',PREF_NOEUD='NNS'),);

mesh=CREA_MAILLAGE(MAILLAGE=Qmesh,
                MODI_MAILLE=(
                            _F(TOUT='OUI',OPTION='QUAD8_9',),
                            #_F(TOUT='OUI',OPTION='TRIA6_7',),
                ),
);

mesh=DEFI_GROUP (
        reuse =mesh,
        MAILLAGE=mesh ,
        CREA_GROUP_MA=_F ( NOM='TOUT' , TOUT='OUI' , ) , 
        CREA_GROUP_NO=_F(TOUT_GROUP_MA='OUI' ,) ,
    );

mesh=MODI_MAILLAGE (
	reuse =mesh ,
	MAILLAGE=mesh ,
	ORIE_NORM_COQUE=(_F (GROUP_MA=('skin',),),), 
	);

#----------------------------------------------------
# (2) Model definition and volume elements
#----------------------------------------------------

ModelI=AFFE_MODELE(MAILLAGE=meshI,
                    AFFE=_F(TOUT='OUI',
                            PHENOMENE='MECANIQUE',
                            MODELISATION='3D',),);
         

Model=AFFE_MODELE(
        MAILLAGE=mesh,
        AFFE=_F(
                TOUT='OUI',
                PHENOMENE='MECANIQUE',
                MODELISATION='COQUE_3D', 
             ),
    );

#----------------------------------------------------
# (3) Allocation of the mesh model
#----------------------------------------------------


CARA=AFFE_CARA_ELEM(MODELE=Model,
                        COQUE=_F(GROUP_MA='skin',
                                 EPAIS=th,                 #thickness of the shell
                                 COQUE_NCOU=1,              #number of nodes on the thickness
                        ),
           );

#----------------------------------------------------
# (4) Definition of material properties
#----------------------------------------------------

#Linear elastic material 

Alu=DEFI_MATERIAU(ELAS=_F(E=E,NU=nu,),);

#----------------------------------------------------
# (5) Allocation of the mesh material
#----------------------------------------------------

Mat=AFFE_MATERIAU(MAILLAGE=mesh,AFFE=_F(TOUT='OUI',MATER=Alu,),);

#----------------------------------------------------
# (6) Definition of boundary conditions (CL) and loads
#----------------------------------------------------

fixZeq=AFFE_CHAR_MECA (MODELE=Model ,
                        DDL_IMPO =(
                                _F( GROUP_MA='equator',DY=0.0, ),
                                _F( GROUP_MA='longi',DX=0.0, ),
                                _F( GROUP_MA='ortho',DZ=0.0, ),
                            )
                        
       );
appP=AFFE_CHAR_MECA (MODELE=Model ,FORCE_COQUE =_F(GROUP_MA='skin',PRES=presss, ) ,);



#----------------------------------------------------
# (7) Resolution
#----------------------------------------------------

ramp=DEFI_FONCTION(
                   NOM_PARA='INST',
                   VALE=(0,0,
                         1,1,
                         ),
                   INTERPOL='LIN',
                   PROL_DROITE='LINEAIRE',);

list_rel=DEFI_LIST_REEL(DEBUT=0,
                        INTERVALLE=(
                               _F(JUSQU_A=1,NOMBRE=10,),
                        ),
);

list_ins=DEFI_LIST_INST(DEFI_LIST=_F(METHODE='AUTO',
                                     LIST_INST=list_rel,
                                     PAS_MINI=1e-4,),);


result=STAT_NON_LINE(MODELE=Model ,
                     CHAM_MATER=Mat, 
                     CARA_ELEM=CARA,
                    EXCIT=(
                            _F(CHARGE=fixZeq,) , 
                            _F( CHARGE=appP,
                                TYPE_CHARGE='SUIV' , 
                                FONC_MULT=ramp , ),
                            ), 
                    COMP_ELAS=_F (
                            RELATION='ELAS' , 
                            DEFORMATION='GROT_GDEP' ,
                            GROUP_MA = ( 'skin' , ) , 
                            ),
                   INCREMENT=_F(LIST_INST=list_ins,),
                   #INCREMENT=_F(LIST_INST=list_rel,),
                   NEWTON=_F(PREDICTION='ELASTIQUE',
                             MATRICE='TANGENTE',
                             REAC_INCR=1,
                             #PAS_MINI_ELAS=1e-4,
                             REAC_ITER=1,),
                   CONVERGENCE=_F (RESI_GLOB_RELA=1e-4,ITER_GLOB_MAXI=30,),
                   SOLVEUR=_F(METHODE='MUMPS',
                              PCENT_PIVOT=70,
                              MATR_DISTRIBUEE='OUI',),
                   ARCHIVAGE=_F(LIST_INST=list_rel,),
INFO=1,
);


#----------------------------------------------------
# (8) Printing
#----------------------------------------------------
Tdisp=POST_RELEVE_T(
		ACTION=(_F (
			GROUP_NO='top' ,
			INTITULE='displ_top' ,
			RESULTAT=result,
			NOM_CHAM='DEPL' ,
			NOM_CMP=('DX' , 'DY' , 'DZ' , ) ,
			TOUT_ORDRE='OUI' , #all time steps
			OPERATION='EXTRACTION' ,
		 ),
		),
TITRE='displacement' ,
);

IMPR_TABLE ( TABLE=Tdisp , );

D=RECU_FONCTION(TABLE=Tdisp,
                 PARA_X='INST',
                 PARA_Y='DY',
);


IMPR_FONCTION(
              FORMAT='TABLEAU',
              UNITE=81,
              COURBE=_F(FONC_X=D,FONC_Y=D,),
              COMMENTAIRE = '%',
              COMM_PARA = '%',
);

resultI=PROJ_CHAMP(RESULTAT=result,
                    MODELE_1=Model,    # project fields of this model to
                    MODELE_2=ModelI,); # field of model_2

IMPR_RESU(FORMAT='MED',UNITE=80,RESU=_F(MAILLAGE=meshI,RESULTAT=resultI,NOM_CHAM=('DEPL'),),);

L_prof=POST_RELEVE_T(
		ACTION=(_F (
			GROUP_NO='longi' ,
			INTITULE='displ_top' ,
			RESULTAT=result,
			NOM_CHAM='DEPL' ,
			NOM_CMP=('DX' , 'DY' , 'DZ' , ) ,
			TOUT_ORDRE='OUI' , #all time steps
			OPERATION='EXTRACTION' ,
		 ),
		),
TITRE='displacement' ,
);
IMPR_TABLE (FORMAT='TABLEAU',
              COMMENTAIRE = '%',
              COMM_PARA = '%',
            UNITE=82,
            TABLE=L_prof ,);


O_prof=POST_RELEVE_T(
		ACTION=(_F (
			GROUP_NO='ortho' ,
			INTITULE='displ_top' ,
			RESULTAT=result,
			NOM_CHAM='DEPL' ,
			NOM_CMP=('DX' , 'DY' , 'DZ' , ) ,
			TOUT_ORDRE='OUI' , #all time steps
			OPERATION='EXTRACTION' ,
		 ),
		),
TITRE='displacement' ,
);
IMPR_TABLE (FORMAT='TABLEAU',
              COMMENTAIRE = '%',
              COMM_PARA = '%',
            UNITE=83,
            TABLE=O_prof ,);


FIN();

cl1 = 0.25;
R = 1;
L=10;

Point(1) = {0,0,-L/2,cl1};
Point(2) = {R,0,-L/2,cl1};
Point(3) = {0,R,-L/2,cl1};
Point(4) = {-R,0,-L/2,cl1};
Point(5) = {0,-R,-L/2,cl1};

Circle(1) = {2,1,3};
Circle(2) = {3,1,4};
Circle(3) = {4,1,5};
Circle(4) = {5,1,2};

Line(5) = {5, 1};
Line(6) = {2, 1};
Line(7) = {3, 1};
Line(8) = {4, 1};

Line Loop(12) = {6, -5, 4};
Plane Surface(12) = {12};
Line Loop(14) = -{6, -7, -1};
Plane Surface(14) = {14};
Line Loop(16) = {2, 8, -7};
Plane Surface(16) = {16};
Line Loop(18) = {3, 5, -8};
Plane Surface(18) = {18};

Extrude {0,0,L/2} {
  Surface{12,14,16,18};
}

Extrude {0,0,L/2} {
  Surface{35,52,69,86};
}

Coherence ;


Transfinite Surface "*";
Recombine Surface "*";
Transfinite Volume "*";


Physical Point("top")={18};
Physical Line("longi")={29,97};//{29,97,46,114};
Physical Line("ortho")={38,54};//{38,54,71,22};
Physical Line("front")={106,122,90,139};
Physical Line("back")={1,2,3,4};
Physical Line("equator")={24,59,92,127};
Physical Surface("skin")={47,60,128,115,145,102,77,34};