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Organization (S): EDF-R & D/AMA
Handbook of Descriptif Informatique
D4.06 booklet: Structures related to the finite elements
Document: D4.06.14
Structures of data related to contact-friction

Summary:

This document describes the structures of data necessary to the definition (SD “DEFI_CONT”) and for the resolution
(SD “RESO_CONT”) of the problems of contact-friction defined by key word CONTACT of the operator
AFFE_CHAR_MECA. One endeavors to give the detailed instructions of the majority of the tables used in
corresponding routines. Description is purely data-processing, and it is advised to read them before
reference materials [R5.03.50], [R5.03.51], of use [U4.25.01], implementation practical
[U2.04.04] and of maintenance of the contact [D9.05.02].

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1 Philosophy
general

Potential zones of contact are defined in operator AFFE_CHAR_MECA for each
occurrence of key word “CONTACT”. Each zone is defined by an occurrence of the key word. One
zone of contact comprises several surfaces (two in general) which one seeks to prevent
the interpenetration two to two. In the case of methods “NODAL”, “MAIT_ESCL” and
“MAIT_ESCL_SYME”, there are two surfaces whose composition is given under the key words
GROUP_MA_MAIT (or MAILLE_MAIT) and GROUP_MA_ESCL (or MAILLE_ESCL). For the methods
“TERRITOIRE” and “HIERARCHIQUE” (not implemented to date), key word GROUP_MA will be used
(or MAILLE): in this case, each group of meshs (each mesh) of the list will define
a potential surface of contact (there could thus be more than two surfaces per zone).
data relating to the various zones and surfaces of contact are stored in a structure of
given of type “DEFI_CONT” whose name is CHAR (1:8)//“.CONTACT”.

In operators STAT_NON_LINE and DYNA_NON_LINE, one supposes that only one load contains
contact (one checks it in the routine nmdome). During step of time and iterations of
Newton, one fills of the tables of size fixes (dimensioned using the maximum of nodes slaves)
who contain the data necessary to the processing of the contact (structure of data of the type
“RESO_CONT”). They are sometimes under-tables resulting from the tables created in AFFE_CHAR_MECA:
they relate to only the nodes or meshs in the course of processing with the algorithm (zones of contact
effective current). In these tables, information is followed sequentially without concept of
zone or of surface of contact: very coarsely, one stores the couples node slave - mesh (or
node) main and characteristics associated (ddls concerned, coefficients, components of
normal, play running).

Note:

· The system of contact is composed of several zones, themselves consistent in
surfaces, made up of meshs, container of the nodes,
· Surfaces of contact are located by their absolute number I in the list of all
surfaces of contact, all zones confused,
· Only tables CONTMA, CONTNO and SANSNO index the nodes and the meshs by
their absolute number in the code; all the other tables use the index in CONTMA
and CONTNO to indicate a mesh or a node,
· One always takes three components for the normal, in 2D as in 3D. On the other hand,
the table of the degrees of freedom contains of them two per node in 2D, and three in 3D.

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2
Structure of data DEFI_CONT

The structure of data DEFI_CONT contains the tables defining the potential zones of contact (created
in AFFE_CHAR_MECA, except DDLCO and PDDLCO created in STAT_NON_LINE).

2.1
List variables

It is supposed that only one load contains the key word factor “CONTACT”.
All the tables start with CHAR (1:8)//“.CONTACT” (variable DEFICO (1:16)), with the suffix:

Variable suffix
Type
Dimension Subscripted
by
Contents
.NDIMCO NDIMCO I 9+NZOCO
list useful entireties, and numbers effective
nodes slaves for each zone
(the max at the beginning)
.METHCO METHCO I 1+8 * NZOCO
number of
a number of zones and characteristic of
zone of contact
method of pairing for each one
.TOLECO TOLECO R 2 * NZOCO number of
parameters of geometrical tolerance
zone of contact
for pairing
.CONVCO CONVCO I 3 * NZOCO number of
parameters of convergence
zone of contact
.SYMECO SYMECO I NZOCO+1
information on the symmetrical zones
of pairing (MAIT_ESCL_SYME)
.PZONECO PZONE
I
NZOCO+1 number of
number of the last surface of
zone of contact
each zone
.MAILCO CONTMA I
Pointer NMACO PSURMA lists numbers of the meshs of
contact of various surfaces
potential
.PSUMACO PSURMA
I
1+NSUCO number of
index of the last mesh of each
surface
surface in vector CONTMA
.NOEUCO CONTNO I
Pointer NNOCO PSURNO lists numbers of the nodes of
contact of various surfaces
potential
.PSUNOCO PSURNO
I
1+NSUCO number of
index of the last node of each
surface
surface in vector CONTNO
.NOEUQU CONOQU I 3 * NO/2
pointer PNOQUA lists numbers of the nodes of
contact “quadratic” of different
potential surfaces
.PNOEUQU PNOQUA
I
1+NSUCO number of
index of the last node of each
surface
surface in vector CONOQU
.MANOCO MANOCO I
Pointer NMANO PMANO indices of the meshs of CONTMA
containing a given node of CONTNO
.PMANOCO PMANO
I
1+NNOCO index of node
index in MANOCO of the last
in CONTNO
net containing a given node
.NOMACO NOMACO I
Pointer NNOMA PNOMA indices of the nodes of CONTNO
belonging to a mesh given of
CONTMA
.PNOMACO PNOMA
I
1+NMACO index of mesh
index in NOMACO of the last node
in CONTMA
belonging to a given mesh
.MAMACO MAMACO I
Pointer NMAMA PMAMA indices of the meshs of CONTMA
adjacent with a given mesh
.PMAMACO PMAMA
I
1+NMACO index of mesh
index in MAMACO of the last
in CONTMA
adjacent mesh with a given mesh
.SSNOCO SANSNO I
Pointer NNOCO PSANS
absolute numbers of the nodes to be excluded
nodes slaves
.PSSNOCO PSANS
I
1+NZOCO number of
index of the last node to be excluded in
zone of contact
SANSNO
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.JSUPCO JEUSUP R8
NZOCO number of
value of the fictitious play
zone of contact
.NOZOCO NOZOCO I
NNOCO index of node
number of the zone of contact to which
in CONTNO
the node belongs
.CHAMCO CHAMCO I
NZOCO number of
code field to which apply
zone of contact
unilateral conditions
.COEFCO COEFCO R8
NZOCO number of
coefficient of the unilateral relation for
zone of contact
pressure or the temperature
.DDLCO DDLCO I
Pointer NDDL PDDL numbers of the degrees of freedom
potentially implied in the writing
unilateral relations
.PDDLCO PDDL
I
NNOCO index of node
index in DDLCO of the last ddl of one
in CONTNO
node of CONTNO given
.JEUFO1 JJFO1 K8
NZOCO Numéro of
Fictitious play when it is given by one
surface
function of space in
contact
AFFE_CHAR_MECA_F
.JEUFO2 JJFO2 K8
NZOCO Numéro of
Fictitious play when it is given by one
surface
function of space in
contact
AFFE_CHAR_MECA_F
DIRCO JDIR R8
3 * NZOCO
Number of
Direction fixes nodal pairing
surface
data by VECT_Y
contact
RUB IFRO R8 NESMAX
Number of
Coefficient of friction of Coulomb
node slave
PENAL IPENA
R8
2 * NESMAX
Number of
Coefficient of regularization of the contact
node slave
and of friction
COMAFO ICOMA R8 NESMAX
Number of
Value of COEF_MATR_FROT
node slave
TANDEF JTGDEF
R8 3 * NZOCO
Number of
Value of VECT_Y
surface
contact
NORLIS JNORLI I NZOCO+1
Number of
Indicate the presence of smoothing of
surface
normals
contact

This part gathers the objects suitable for method CONTINUE:

.CARACF JCMCF
R 6 * NZOCO+1
number of
integration and coefficients of
zone of contact
regularization
.ECPDON JECPD
I 5 * NZOCO+1
number of
parameters of the loops of
zone of contact
method CONTINUE
.MAESCL JMAESC I 3 * NTMA+1
number of
for each mesh one gives the number
net slave
of its zone numbers points of
contact
.NOESCL JNOESC R 10 * NO
number of node vectors tangent and normal of
of contact
each point.
.TABFIN JTABF
R 16 * NTPC+1
number of point characteristics of pairing.
of contact

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2.2 Table
NDIMCO (addresses JDIM)

ZI (JDIM) =
NDIM
dimension of space (two or three)
ZI (JDIM+1) =
NZOCO
a number of zones of contact
ZI (JDIM+2) =
NSUCO
a number of surfaces of contact
ZI (JDIM+3) =
NMACO
a number of meshs of contact
ZI (JDIM+4) =
NNOCO
a number of nodes of contact
ZI (JDIM+5) =
NMANO
dimension of MANOCO
ZI (JDIM+6) =
NNOMA
dimension of NOMACO
ZI (JDIM+7) =
NMAMA
dimension of MAMACO
ZI (JDIM+8)
= NESMAX
a maximum number of nodes slaves
ZI (JDIM+8+IOC) = an effective number of nodes slaves in zone IOC (a number
maximum at the time of initialization), IOC=1, NZOCO

2.3 Table
METHCO (addresses JMETH)

ZI (JMETH) = NZOCO: a number of zones of contact

For zone N:

ZI (JMETH+8 * (n-1) +1) =
- 1 if APPARIEMENT= “NON”
0 if APPARIEMENT= “NODAL”

1 if APPARIEMENT= “MAIT_ESCL” or “MAIT_ESCL_SYME”

2 if APPARIEMENT= “TERRITOIRE”

3 if APPARIEMENT= “HIERARCHIQUE”

4 if VECT_NORM_2 is defined
ZI (JMETH+8 * (n-1) +2) =
1 VECT_Y is indicated and 0 if not
ZI (JMETH+8 * (n-1) +3) =
not used
ZI (JMETH+8 * (n-1) +4) =
1 if linear projection (rectilinear segment or plane triangle)

2 if quadratic projection
ZI (JMETH+8 * (n-1) +5) =
+1 if RECHERCHE= “NOEUD_BOUCLE”

+/- 2 if RECHERCHE= “NOEUD_VOISIN”/“MAILLE_VOISIN”
+/- 3 if RECHERCHE= “NOEUD_BOITE”/“MAILLE_BOITE”
ZI (JMETH+8 * (n-1) +6) =
- 1 if the method of CONTACT used is “PENALISA”

0 if the method of CONTACT used is “CONTRAIN”

1 if the method of CONTACT used is “LAGRANGI”

2 if the method of FROTTEMENT 2D used is “LAGRANGI”

3 if the method of FROTTEMENT 2D or 3D used is “PENALISA”

4 if the method of FROTTEMENT 3D used is “LAGRANGI”

5 if the method of CONTACT and FROTTEMENT used is
“PENALISA”

6 if the method used is “CONTINUE”
ZI (JMETH+8 * (n-1) +7) =
0 if REAC_GEOM= “SANS”

- 1 if REAC_GEOM= “AUTOMATIQUE”

if not NB_REAC_GEOM (geometrical frequency of reactualization)
ZI (JMETH+8 * (n-1) +8) =
0 if NORMALE= “MAIT”

1 if NORMALE= “MAIT_ESC”
ZI (JMETH+9 * (n-1) +9) =
0 if STOP_SINGULIER= “OUI”
1 if STOP_SINGULIER= “NON”
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2.4 Table
CONVCO (addresses JCONV)

For zone N:

ZI (JCONV+3 * (n-1)) =
0 if STOP_SINGULIER= “OUI”
1 if STOP_SINGULIER= “NON”
ZI (JCONV+3 * (n-1) +1) =
NB_RESOL
ZI (JCONV+3 * (n-1) +2) =
ITER_MULT_MAXI

2.5 Table
TOLECO (addresses JTOLE)

For zone N:

ZI (JTOLE+2 * (n-1)) =
TOLE_PROJ_EXT
ZI (JTOLE+2 * (n-1) +1) =
TOLE_PROJ_INT

2.6 Table
SYMECO (addresses JSYME)

ZI (JSYME): A number of symmetrical zones of contact

For symmetrical zone N:
ZI (JSYME+n) =
Number of the zone principal partner at symmetrical zone N

2.7 Table
CARACF (addresses JCMCF)

ZI (JCMCF) = NZOCO: numbers total zones of contact.
In this table are stored some parameters for methods CONTINUE, LAGRANGIEN and
PENALIZATION. For method CONTINUE, one specifies, inter alia, the diagram of integration with
to use for the terms of contact and friction and the coefficients of increase. Let us recall that
integration with the nodes is taken by defect INTEGRATION=' NOEUD' and that diagrams SIMPSON,
SIMPSON1 and SIMPSON2 are available only in 2D.

For zone N:

CARACF (1+6 * (n-1) +1) =
1 if INTEGRATION=' NOEUD'

2 if INTEGRATION=' GAUSS'

3 if INTEGRATION=' SIMPSON'

4 if INTEGRATION=' SIMPSON1'

5 if INTEGRATION=' SIMPSON2'
CARACF (1+6 * (n-1) +2) =
Coefficient of increase for the contact
COEF_REGU_CONT
CARACF (1+6 * (n-1) +3) =
Coefficient of increase for friction
COEF_REGU_FROT
CARACF (1+6 * (n-1) +4) =
Coefficient of Coulomb for friction.
CARACF (1+6 * (n-1) +5) =
1 if FROTTEMENT=' SANS'

3 if FROTTEMENT=' COULOMB'
CARACF (1+6 * (n-1) +6) =
the value of COEF_MATR_FROT

2.8
System of contact: pointer PZONE (addresses JZONE)

absolute number (I) of the first surface of zone N:
ZI (JZONE+n-1) +1
absolute number (I) of the last surface of zone N:
ZI (JZONE+n)
a number of surfaces of zone N:
ZI (JZONE+n) - ZI (JZONE+n-1)
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2.9 Zone
N: pointers PSURMA, PSURNO and PNOQUA (addresses JSUMA,
JSUNO and JNOQUA)

number of the first
: i1 = ZI (JZONE+n-1) +1
surface
number of the last surface: i2 = ZI (JZONE+n)
a number of meshs of the zone: ZI (JSUMA+i2) - ZI (JSUMA+i1-1)

= ZI (JSUMA+ZI (JZONE+n)) - ZI (JSUMA+ZI (JZONE+n-1))
a number of nodes of the zone: ZI (JSUNO+i2) - ZI (JSUNO+i1-1)

= ZI (JSUNO+ZI (JZONE+n)) - ZI (JSUNO+ZI (JZONE+n-1))
a number of nodes of the zone: ZI (JNOQUA+i2) - ZI (JNOQUA +I1-1)
being node mediums of one
quadratic element

= ZI (JNOQUA +ZI (JZONE+n)) - ZI (JNOQUA +ZI (JZONE+n-1))

2.10 Surface I: tables CONTMA, CONTNO and CONOQU (addresses JMACO,
JNOCO and JNOQU), pointer PSURMA, PSURNO and PNOQUA
(addresses JSUMA, JSUNO and JNOQUA)

The number of meshs of surface I east: nbma = ZI (JSUMA+i) - ZI (JSUMA+i-1)
The index in CONTMA of the first mesh of surface I east: ZI (JSUMA+i-1) +1
The index in CONTMA of the last mesh of surface I east: ZI (JSUMA+i)
The list of the numbers of the meshs of surface I is ZI (JMACO+jdecma+ima-1) for ima=1, nbma,
with jdecma = ZI (JSUMA+i-1).
The imaième mesh of surface I has as an absolute number: ZI (JMACO+jdecma+ima-1); its index
in CONTMA is: posma = jdecma+ima.
Net index posma in CONTMA: its absolute number is ZI (JMACO+posma-1).

The number of nodes of surface I east: nbno = ZI (JSUNO+i) - ZI (JSUNO+i-1)
The index in CONTNO of the first node of surface I east: ZI (JSUNO+i-1) +1
The index in CONTNO of the last node of surface I east: ZI (JSUNO+i)
The list of the numbers of the nodes of surface I is ZI (JNOCO+jdecno+ino-1) for ino=1, nbno,
with jdecno = ZI (JSUNO+i-1).
The inoième node of surface I has as an absolute number: ZI (JNOCO+jdecno+ino-1); its index
in CONTNO is: posno = jdecno+ino.
Node of index posno in CONTNO: its absolute number is ZI (JNOCO+posno-1).

The number of nodes of surface I being node medium of a quadratic mesh is: No =
ZI (JNOQUA+i) - ZI (JNOQUA +i-1)
The index in CONOQU of the first “quadratic” node medium of surface I east: 3 * ZI (JNOQUA
+i-1) +1
The index in CONOQU of the last node “quadratic” medium of surface I east: 3 * ZI (JNOQUA
+i) - 2
The list of the numbers of the nodes medium “
quadratic
” of surface I is ZI (JNOQU
+jdecqu+3 * (inq-1)) for inq=1, No, with jdecqu = 3 * ZI (JNOQUA +i-1) +1.
The list of the numbers of the associated nodes node for surface I is ZI (JNOQU
+jdecqu+3 * (inq-1) +1) and ZI (JNOQU +jdecqu+3 * (inq-1) +2) for inq=1, No, with
jdecqu = 3 * ZI (JNOQUA +i-1) +1.
The inqième “quadratic” node medium of surface I has as an absolute number: ZI (JNOQU
+jdecqu+3 * (inq-1) - 1); its index in CONOQU is: posqu = jdecqu+3 * (inq-1).
“Quadratic” node of index posqu in CONOQU: its absolute number is ZI (JNOQU+posqu-1).
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2.11 Tables MANOCO, NOMACO and MAMACO (addresses JMANO, JNOMA and
JMAMA) pointer PMANO, PNOMA and PMAMA (addresses JPOMA, JPONO and
JPOIN)

For the node of index posno in CONTNO, the index in CONTMA of the meshs of contact of same
surface containing the node is ZI (JMANO+jdec+ima-1) with jdec = ZI (JPOMA+posno-1) and
ima varying of 1 with nbma, for nbma = ZI (JPOMA+posno) - ZI (JPOMA+posno-1), or even
ZI (JMANO+k-1) for K varying of ZI (JPOMA+posno-1) +1 with ZI (JPOMA+posno).

For the mesh of index posma in CONTMA, the index in CONTNO of the nodes of contact of this
mesh is ZI (JNOMA+jdec+ino-1) with jdec = ZI (JPONO+posma-1) and ino varying of 1 with
nbno, for nbno = ZI (JPONO+posma) - ZI (JPONO+posma-1), or even ZI (JNOMA+k-1)
for K varying of ZI (JPONO+posma-1) +1 with ZI (JPONO+posma).

The list of the indices in CONTMA of the meshs close to the mesh of index posma is:
ZI (JMAMA+jdec+ima-1), with jdec = ZI (JPOIN+posma-1) and ima varying of 1 with nbma,
for nbma = ZI (JPOIN+posma) - ZI (JPOIN+posma-1).

2.12 Table
SANSNO and pointer PSANS (addresses JSANS and JPSANS)

For zone N:

a number of nodes to be excluded from the nodes slaves: nsans = ZI (JPSANS+n) - ZI (JPSANS+n-1)
absolute numbers of the nodes to be excluded: ZI (JSANS+jdec+ino-1), for ino = 1, nsans, with
jdec = ZI (JPSANS+n-1).

2.13 Table
JEUSUP (addresses JJSUP)

For zone N: ZR (JJSUP+n-1) = value for the zone of the fictitious play (DIST_1+DIST_2, or
COEF_IMPO) given by the user.

2.14 Tables NOZOCO (addresses JZOCO), CHAMCO (addresses JCHAM) and
COEFCO (addresses JCOEF)

For the node of index posno in CONTNO, the number of the zone of contact to which this one
belongs is:
N = ZI (JZOCO+posno-1).

For zone N:

Code field to which applies the unilateral relation: icode = ZI (JCHAM+n-1)
icode = +1: relation on displacements (with pairing: “deformable” contact)
icode = - 1: relation on displacements (without pairing: “rigid” contact)
icode = - 2: relation on the pressure (without pairing: only for one modeling
“THM”)
icode = - 3: relation on the temperature (without pairing “: only for one modeling
“THM”)
icode = - 4: relation on pressure 1 (without pairing “: only for one modeling
“THM”)
icode = - 5: relation on pressure 2 (without pairing “: only for one modeling
“THM”)

Multiplying coefficient of the unilateral relation: ZR (JCOEF+n-1)
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2.15 Table
DDLCO and pointer PDDLCO (addresses JDDL and JPDDL)

These two tables are in the structure of data DEFI_CONT but are defined in the routine
crsdco called by STAT_NON_LINE.

For the node of index posno in CONTNO, the degrees of freedom are ZI (JDDL+jdecdl+iddl-1)
for iddl varying of 1 with nbddl with nbddl = ZI (JPDDL+posno) - ZI (JPDDL+posno-1) and
jdecdl = ZI (JPDDL+posno-1).

One gathered in the continuation the structures of data suitable for method CONTINUE.

2.16 Table
ECPDON (addresses JECPD)

This table gives some parameters total necessary for the algorithmic one used by
method CONTINUE. Let us note that parameters ITER_CONT_MAX, ITER_FROT_MAX and
ITER_GEOM_MAX fix the maximum number of the loops of contact, threshold of friction and of
geometry. These numbers can not be reached if the test of stop of each ball is satisfied. It
test, to see routine mmmcri.f, relates to the value of the relative increment of displacement:

U
U
with 10
= - 2.

NR being the number of the zone of contact.

ECPDON (1+5 * (N-1) +1) =
1 if MODL_AXIS=' OUI'

0 if MODL_AXIS=' NON'
ECPDON (1+5 * (N-1) +2) =
The value of ITER_CONT_MAX
ECPDON (1+5 * (N-1) +3) =
The value of ITER_FROT_MAX
ECPDON (1+5 * (N-1) +4) =
The value of ITER_GEOM_MAX
ECPDON (1+5 * (N-1) +5) =
The initial threshold value SEUIL_INIT

MAESCL (1): numbers total zones of contact.

2.17 Table
MAESCL (addresses JMAESC)

NR being the number of the mesh slave.

MAESCL (1+3 * (N-1) +1) =
index of the mesh NR in table CONTMA
MAESCL (1+3 * (N-1) +2) =
number of the zone of contact of NR
MAESCL (1+3 * (N-1) +3) =
numbers points of contact in NR

MAESCL (1): numbers total meshs slave.

2.18 Table
NOESCL (addresses JNOESC)

NR is the number of node of contact. The whole parameter I varies from 1 to 3.

NOESCL (1+3 * (N-1) +1) =
0 if NR is slave 1 if not.
NOESCL (1+3 * (N-1) +1+I) =
components of the first tangent vector
NOESCL (1+3 * (N-1) +4+I) =
components of the first tangent vector
NOESCL (1+3 * (N-1) +7+I) =
components of the first tangent vector
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NOESCL (1): numbers total nodes of contact. Let us recall that in 2D the 3rd component of
vectors tangent or normal is taken equalizes to zero.

This table is used for the smoothing (routine “lissag”) which makes it possible to smooth the normals on the surfaces
of contact intervening in the calculation of the matrix of contact. Let us recall that smoothing is made in
two stage. The first consists in carrying out an average of the normals to the meshs which contain
the node of contact. The second consists in interpolating, with the functions of form associated with
the element, a field of normals in any point of the element.

2.19 Table
TABFIN (addresses JTABF)

In this table is classified all information necessary for the resolution concretes
problem of the rubbing contact. This information is described in the routine mappar. Let us recall that
pairing is made in an exact way using a method of Newton for the resolution of one
problem of optimization with constraints (cf routine mprojp) and which allows us, at the same time
to recover the values of the tangent vectors.

NR being the number of the point of contact. TABFIN (1): numbers total points of contact.
whole parameter I varies from 1 to 3.

TABFIN (1+16 * (N-1) +1) =
absolute number of the mesh Master
TABFIN (1+16 * (N-1) +2) =
absolute number of the mesh slave
TABFIN (1+16 * (N-1) +3) =
first barycentric parameter of the point NR
TABFIN (1+16 * (N-1) +4) =
first barycentric parameter of the point in screw-with
live
TABFIN (1+16 * (N-1) +5) =
second barycentric parameter of the point in opposite
TABFIN (1+16 * (N-1) +5+I) =
3 components of the 1st tangent vector
TABFIN (1+16 * (N-1) +8+I) =
3 components of the 2nd tangent vector
TABFIN (1+16 * (N-1) +12) =
second barycentric parameter of the point NR
TABFIN (1+16 * (N-1) +13) =
statute of contact
TABFIN (1+16 * (N-1) +14) =
initial value of contact pressure
TABFIN (1+16 * (N-1) +15) =
number of the zone of contact of the point NR
TABFIN (1+16 * (N-1) +16) =
weight of the point of contact

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3
Structure of data RESO_CONT

The structure of data RESO_CONT contains the tables defining the effective couples of contact (created
in STAT_NON_LINE or DYNA_NON_LINE) and the variables used in the method of resolution by
methods CONTRAINTES, LAGRANGIEN and PENALIZATION.

3.1
List variables

All the tables start with RESOCO (1:14) (“&&RESOCO”), followed suffix:

Variable suffix Standard Dimension
Subscripted
by
Contents
.APREAC APREAC
I
4 * NZOCO number of
indicator of reactualization for
zone of contact pairing, fixed meter of pairing,
type of projection and reactualization of
normals, number of surface slave
.APPARI APPARI
I 1+3 * NESMAX
number of
a number of nodes slaves, and for each one

node slave
: index of the node slave, index of the mesh
Master paired, indicating of reactualization
.APMEMO APMEMO
I
4 * NNOCO index of the node
data relating to pairing of the last
in CONTNO
blow where this node was slave
.APPOIN APPOIN
I
1+NESMAX number of
pointer of navigation in APCOEF,
node slave
APCOFR and APDDL
.APCOEF APCOEF R8 30 * pointer NESMAX APPOIN multiplying coefficients of the ddls (1 by
ddl) for imposition of nonthe penetration
(+1 for the node slave, and the opposite of
value of the function of form for each
main node)
.APCOFR APCOFR R8 60 * pointer NESMAX APPOIN multiplying coefficients of the ddls (1 by
ddl) for imposition friction (+1 for
node slave, and opposite of the value of
function of form for each main node)
.APDDL APDDL
I 30 * NESMAX
pointer APPOIN numbers of the degrees of freedom of the node
slave and of the nodes of the mesh Master
paired
.NORINI NORINI R8
3 * NNOCO index of the node
direction of evaluation of the normal play on
in CONTNO
the whole of the potential nodes of contact
.NORMCO NORMCO R8
3 * NESMAX number of
direction of evaluation of the normal play on
node slave
connection of contact
.TANGCO TANGCO R8
6 * NESMAX number of
direction of evaluation of the tangent play on
node slave
connection of contact
.APJEU APJEU R8
NESMAX number of
value of the normal play running between the node
node slave
slave and the mesh Master paired
.APJEFX APJEFX R8
NESMAX
number of
value of the tangent play in direction 1
node slave
between the node slave and the mesh Master
paired
.APJEFY APJEFY R8
NESMAX
number of
value of the tangent play in direction 2
node slave
between the node slave and the mesh Master
paired
.JEUINI JEUINI R8
NESMAX
number of
value of the initial play when
node slave
REAC_GEOM=' SANS'
.COCO COCO
I
8

to remember the state of preceding contact
.LIAC LIAC
I
3 * NESMAX+1
number of
absolute numbers of the active connections of
node slave
contact-friction
.CONVEC CONVEC K8 3 * NESMAX+1
number of
Type of active connections
: contact or
node slave
adherent friction
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.LIOT LIOT
I
4 * NESMAX+4
number of
removed connections of contact-friction
node slave
.MU DRIVEN R8
6 * NESMAX
number of
multipliers of Lagrange related to
node slave
contact-friction
.COEFMU COEFMU R8
NESMAX
number of
coefficient by which it is necessary to multiply it
node slave
multiplier of Lagrange of the front contact
to test its sign
.ATMU ATMU R8
NEQ number of ddl
nodal forces of contact
.AFMU AFMU R8
NEQ number of ddl
nodal forces of friction
.DEL0 DELT0 R8
NEQ number of ddl
vector used in the algorithm of resolution
.DELT DELTA R8
NEQ number of ddl
vector used in the algorithm of resolution
.CM1A CM1A



second members used in the algorithm
of resolution of the contact
.CM2 A CM2 A



second members used in the algorithm
of resolution of friction
.CM3 A CM3 A



second members used in the algorithm
of resolution of friction
.MATR MATR



SD of the type MATR_ASSE [D4.06.10]: stamp
used in the algorithm of resolution
.SLCS STOC



SD of the type STOC_LCIEL [D4.06.07]:
description of the storage of matrix MATR

For the link of the variables described with the resolution of the problem of contact by the method of the constraints
active, one will refer to the document [R5.03.50] and for the resolution of the problem of contact-friction to
document [R5.03.51].

3.2 Table
APREAC (addresses JREAC)

For zone N:
ZI (JREAC+4 * (n-1)) : reactualization of pairing

0:
not
- 1:
no pairing but initial passage in rechno
1:
by double loop on the nodes (“NOEUD_BOUCLE”)
+/­ 2: by vicinity of “last” (“NOEUD_VOISIN”/“MAILLE_VOISIN”)
+/­ 3: by boxes of position (“NOEUD_BOITE”/“MAILLE_BOITE”)
ZI (JREAC+4 * (n-1) +1): a number of times where pairing was kept fixed
ZI (JREAC+4 * (n-1) +2): type of projection and normal reactualization geometry/
+/­ 1: linear projection
+/­ 2: quadratic projection
> 0
so normal and recomputed co-ordinates
< 0
if not

ZI (JREAC+4 * (n-1) +3): not used

3.3 Table
APPARI (addresses JAPPAR)

ZI (JAPPAR) = NESCL: numbers effective nodes slaves

For the iesclième node slave
ZI (JAPPAR+3 * (iescl-1) +1): index in CONTNO of the node slave
ZI (JAPPAR+3 * (iescl-1) +2): index in main CONTMA of the paired mesh
(negative if nodal pairing: opposed index in CONTNO of the paired main node)
(0 if not of pairing)
ZI (JAPPAR+3 * (iescl-1) +3): indicator of reactualization
0
: no the reactualization of projection
+1
: reactualized linear projection + normal
+2
: reactualized quadratic projection + normal
­ 1
: reactualized linear projection, not normals (not used)
­ 2
: reactualized quadratic projection, not normals (not used)
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3.4 Table
APMEMO (addresses JAPMEM)

For the posnoième node of CONTNO (slave or not)

ZI (JAPMEM+4 * (posno-1)) : 1 if the node is slave
0 if the node is a Master
- 1 if the node is excluded (belongs to SNAS_GROUP_NO)
- 2 if the node is excluded (null pivot during symmetrical pairing)
ZI (JAPMEM+4 * (posno-1) +1): index in CONTNO of the main node nearest the last time that
this node was slave
ZI (JAPMEM+4 * (posno-1) +2): index in main CONTMA of the paired mesh the last time that it
node was slave
ZI (JAPMEM+4 * (posno-1) +3): number of the box of current position

3.5 Pointer
APPOIN and tables APCOEF, APCOFR and APDDL (addresses
JAPPTR, JAPCOE, JAPCOF and JAPDDL)

Tables APCOEF and APDDL have same dimension (a coefficient by ddl implied). They are subscripted by
even pointer APPOIN.

For the iesclième node slave:

ZI (JAPPTR+iescl-1) + 1: beginning of the arrangement in APCOEF and APDDL
ZI (JAPPTR+iescl)
: end of the arrangement in APCOEF and APDDL

ZI (JAPPTR+iescl) - ZI (JAPPTR+iescl-1) = nbddl1 + nap of the nbddl2 of the main nodes
nbddl1 = a number of ddls of the node slave of index posno1 in CONTNO:
NBDDL1 = ZI (JPDDL+posno1) - ZI (JPDDL+posno1-1),
with posno1 = ZI (JAPPAR+3 * (iescl-1) +1)
nbddl2 = a number of ddls of each main node of index posno2 in CONTNO:
NBDDL2 = ZI (JPDDL+posno2) - ZI (JPDDL+posno2-1)

jdec1 = ZI (JAPPTR+iescl-1)
ZI (JAPDDL+jdec1+k-1), k=1, nbddl1:
number of the kth ddl of the node slave
ZR (JAPCOE+jdec1+k-1), k=1, nbddl1:
coefficient associated with the kth ddl with the node slave

jdec2 = ZI (JAPPTR+iescl-1) + nbddl1
for m = 1, nmaitr (nmaitr main nodes with each one nbddl2 ddls) and K = 1, nbddl2
ZI (JAPDDL+jdec2+ (M-1) * nbddl2+k-1): number of the kth ddl of the main mièmenoeud
ZR (JAPCOE+jdec2+ (M-1) * nbddl2+k-1): coefficient associated with the kth ddl with the main mièmenoeud

Tables APCOFR and APDDL, subscripted by same pointer APPOIN, are used in the case of presence of
friction. The arrangement is exactly the same one as in what precedes with the details close following:

· APCOFR connects the ddl nodes Master and slave concerning displacements in
tangent plan on the surface of contact
· APCOFR contains 60 * NESMAX terms is twice as much as APCOEF. Indeed, from 1 to 30 * NESMAX
the relations in a direction of the tangent plan are stored, of 30 * NESMAX+1 with 60 * NESMAX are
stored relations in the orthogonal direction with the preceding one in the tangent plan (useful
only in 3D).

NB:

In the case of the contact between two surfaces, the coefficients of the ddls are then multiplied by
components of the entering normal of the mesh Master paired. In the case of the rigid contact, them
coefficients are then multiplied by the components of the normal outgoing slave.
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3.6 Table
NORINI (addresses JNRINI)
Components of the current normal to the posnoième node: ZI (JNRINI+3 * (posno-1) +k-1),
k=1,3

3.7 Table
NORMCO (addresses JNORMO)
For the iesclième node slave

ZI (JNORMO+3 * (iescl-1) +k-1), k=1,3: components of the direction (normalized) of evaluation of the play
normal.

3.8 Table
TANGCO (addresses JTANGO)
For the iesclième node slave

ZI (JTANGO+6 * (iescl-1) +k-1), k=1,3: components of the first direction (normalized)
of evaluation of the tangent play.
ZI (JTANGO+6 * (iescl-1) +k-1), k=4,6: components of the second direction (normalized)
of evaluation of the tangent play.

3.9 Table
APJEU (addresses JAPJEU)

For the iesclième node slave

ZI (JAPJEU+iescl-1):
play enters the node slave and the mesh (or the node) main








or: specified value of the second member (case without pairing)

3.10 Table
COCO (addresses JCOCO)

It contains the memories of the state of preceding contact.

ZI (JCOCO)
= NDIM: dimension of space (2 or 3)
ZI (JCOCO+1) = INDIC: 0 if initialization
+1 if one added a connection
­ 1 if a connection were removed
ZI (JCOCO+2) = NBLIAC: a number of active connections in the preceding state
ZI (JCOCO+3) = AJLIAI: index in the list of the active connections of the last connection having been
calculated for vector CM1A
ZI (JCOCO+4) = SPLIAI: index in the list of the active connections of the last correct line of
calculation of the matrix
1
T
A.C .A
ZI (JCOCO+5) = LLF: a number of connections of adherent friction in the preceding state
ZI (JCOCO+6) = LLF1: a number of connections of adherent friction following the first direction
in the preceding state
ZI (JCOCO+7) = LLF: a number of connections of adherent friction following the second direction
in the preceding state

3.11 Table
LIAC (addresses JLIAC)

It contains the absolute numbers of the active connections of contact and adherent friction.
The list is not ordered

3.12 Table
CONVEC (addresses JVECC)
It is fixed on table LIAC. It contains the type of the connection:
C0 if it is about a connection in contact
F0 if it is about a connection in adherent friction following the two directions of slips
F1 if it is about a connection in adherent friction following the first direction of slips
F2 if it is about a connection in adherent friction following the second direction of slips
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3.13 Table
LIOT (addresses JLIOT)

It contains the absolute numbers of the connections of contact-friction causing the appearance of a null pivot
at the time of the resolution. This connection will thus be removed system.

ZI (JLIOT) = Nombre of connections of contact to null pivot
ZI (JLIOT+1) with ZI (JLIOT+NBLIAC)
= Connections of contact to null pivot
ZI (JLIOT+NBLIAI+1) = Nombre of connections of friction to null pivot in
directions 1 and 2
ZI (JLIOT+NBLIAI+2) with
= Connections of friction to null pivot in
ZI (JLIOT+2 * NBLIAC+1)
directions 1 and 2
ZI (JLIOT+2 * NBLIAI+2) = Nombre of connections of friction to null pivot in
direction 1
ZI (JLIOT+2 * NBLIAI+3) with
= Connections of friction to null pivot in the direction
ZI (JLIOT+3 * NBLIAC+2)
1
ZI (JLIOT+3 * NBLIAI+3) = Nombre of connections of friction to null pivot in
direction 2
ZI (JLIOT+3 * NBLIAI+4) with
= Connections of friction to null pivot in the direction
ZI (JLIOT+4 * NBLIAC+3)
2

Caution:

Each under-vector of LIOT is length NBLIAI, this is why one stores at the beginning of these
the last their working length.

3.14 Table
DRIVEN (addresses JMU)

It contains the multipliers of Lagrange associated with contact-friction. Its maximum length is
6 * NESMAX, but its effective length with a given iteration is based on the number of connections
active NBLIAC. It is organized as follows:

ZR (JMU) with ZR (JMU+NBLIAC-1)
= Lagrange of the contact
ZR (JMU+NBLIAC) with ZR (JMU+2 * NBLIAC-1)
= Lagrange of the adherent connections in the direction
1
ZR (JMU+2 * NBLIAC) with ZR (JMU+3 * NBLIAC-1) = Lagrange of the adherent connections in the direction
2
ZR (JMU+3 * NBLIAC) with ZR (JMU+4 * NBLIAC-1) = Lagrange of the sliding joints
ZR (JMU+6 * NBLIAC-1) = useful Grandeur for the resolution

3.15 Table
COEFMU (addresses JCMU)

It contains the coefficient by which it is necessary to multiply the multiplier of Lagrange DRIVEN in the routine
algoco before testing its sign. This coefficient is worth +1 in the case of a unilateral relation on
displacement, - 1 in the case of a unilateral relation on the pressure or the temperature of the elements
THM (this in order to be coherent with the fact that the hydraulic equation and the thermal equation of
problem coupled THM are multiplied by - 1).

3.16 Table
ATMU (addresses JATMU)

It contains the nodal reactions of contact, i.e. DRIVEN AT
.
, where A is the matrix of contact. Its
dimension is the total number of degrees of freedom of the problem, that is to say NEQ.

3.17 Tables
DELT0 and DELTA (addresses JDELT0 and JDELTA)

They are auxiliary vectors, dimensioned with the total number of degrees of freedom NEQ, used in
the algorithm of active constraints.
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3.18 Variables
CM1A, MATR and STOC

CM1A is a collection of NBLIAI objects length NEQ: each one of these objects contains one
column of the matrix
1
T
C .A, where C is the matrix of tangent rigidity (including/understanding the terms of
Lagrange) and À la stamp contact. These vectors are used in the calculation of the matrix
1
T
A.C
-
.A, stored in matrix MATR, with a line storage of sky describes by the variable
STOC. In these vectors and matrices, matrix A is reduced to the only active connections.

3.19 Variables
CM2 A and CM3 A

CM2 A and CM3 A are collections of NBLIAI objects length NEQ: each one of these objects contains
a column of the tangent matrices of friction. For more precise details, to refer to the document
[R5.03.51].

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