Code_Aster ®
Version
7.4
Titrate:
Operator POST_ZAC


Date:
31/01/05
Author (S):
S. TAHERI, J. ANGLES, Key Mr. BONNAMY
:
U4.83.21-D Page
: 1/6

Organization (S): EDF-R & D/AMA, AUSY

Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
Document: U4.83.21

Operator POST_ZAC

1 Goal

To determine a state adapted or adapted by the Zarka-Casier method.

This operator gives within the framework of cyclic elastoplasticity with a model of work hardening
linear kinematics the adapted or adapted state of the structure under periodic loading
(presumedly elastic) refines or not refines, with or without calculation of an initial state (for example the first
cycle) elastoplastic. Moreover, it gives estimates of the variables of the amplitude type of constraint
or plastic deformation, or their average values with the absolute limit saturated thanks to the method
simplified Zarka-Casier (ZAC). The method is not validated for the phenomenon of accommodation
in the case of a loading nonclosely connected.

The concept produced by this operator is of mult_elas type comprising one (adaptation) or three
(accommodation) sequence numbers equivalent to the values with the absolute limit (average, amplitude) and
containing the fields of solution displacements of the homogeneous elastic problems with
initial deformations [R7.06.01] as well as the amplitudes of constraints, plastic deformation and
an elementary indicator of adaptation or accommodation.

Product a concept of the mult_elas type.

Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_ZAC


Date:
31/01/05
Author (S):
S. TAHERI, J. ANGLES, Key Mr. BONNAMY
:
U4.83.21-D Page
: 2/6

2 Syntax


[mult_elas] = POST_ZAC



(

MODELE




=
Mo
,
[model]





CHAM_MATER
=
chmater,
[cham_mater]




EXCIT =_F (LOAD

=
chi
,
[char_meca]









FONC_MULT

=
fi
,
[function]









TYPE_CHARGE= “FIXE_CSTE”,
[DEFAUT]








),





EVOL_ELAS
=
evol_elas
,
[evol_elas]






/
NUME_ORDRE =
l_nuor
,
[l_I]






/
LIST_INST
=
l_inst
,
[listr8]






/
INST =
inst,
[l_R]





TEMP_ZAC

=
/
temp,
[R]
/
0.
,
[DEFAUT]





EVOL_NOLI
=
evol_noli
,
[evol_noli]






INST_MAX
=
inst,
[R]




| PRECISION
=
/
prec,
[R]
/
1.0E-3
,
[DEFAUT]





| CRITERE =
/
“RELATIF”
,
[DEFAUT]
/
“ABSOLU”
,




)

Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_ZAC


Date:
31/01/05
Author (S):
S. TAHERI, J. ANGLES, Key Mr. BONNAMY
:
U4.83.21-D Page
: 3/6

3 Operands

3.1 Operands
MODEL/CHAM_MATER

MODELE = Mo

Name of the model whose elements are the subject of calculation.

CHAM_MATER = chmater

Field of affected material to the model Mo. One must find the characteristics material there
used during the elastic designs and elastoplastic preconditions to method ZAC.

3.2 Word
key
EXCIT

Cf [U4.51.03].

Two types of loading are taken into account here:

·
Boundary conditions kinematics of the problem (of imposed displacement type).
·
If the intermediate variable 0 (initial state for method ZAC) is calculated with
to start from an elastoplastic calculation, operator POST_ZAC needs for calculation for
plastic deformation (p T E HT
=
-
-
) and of the field of temperature which was useful for it
calculation.

3.3 Operand
EVOL_ELAS

EVOL_ELAS = evol_elas

Name of a concept result of the evol_elas type.

One indicates here the result of the evol_elas type post-to treat and the moments of elastic design
corresponding to the cycle of loading which one seeks the absolute limit by the simplified method
ZAC. Two moments are enough in the case of a loading refines (mini load and maximum loading).
structure of data must comprise the fields displacements with the nodes and constraints with
points of Gauss.

3.3.1 Operands
NUME_ORDRE/INST/LIST_INST

Cf [U4.71.00].

3.4 Operand
TEMP_ZAC

If the characteristics material depend on the temperature, this operand allows
to indicate the temperature to which one wants that the characteristics material are used in
method ZAC. The values are interpolated in the functions material contained in the field
given by operand CHAM_MATER. the temperature is optional if the constants
material are independent of the temperature (constant temperature).
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_ZAC


Date:
31/01/05
Author (S):
S. TAHERI, J. ANGLES, Key Mr. BONNAMY
:
U4.83.21-D Page
: 4/6

3.5 Operand
EVOL_NOLI

EVOL_NOLI = evol_noli

Name of a concept result of the evol_noli type.

One indicates here the results of the preliminary elastoplastic calculation of which one of the moments will use for
p
to determine the initial state within the meaning of method ZAC:

C
~
~e
0 =
-
+
With
With
With, where ~
is it
With
diverter of the constraints (obtained by elastoplastic calculation) and ~
E the diverter of the constraints
With
for this same calculation carried out in elasticity. The moment of elastic design are equivalent must be present
in the structure of data indicated by key word EVOL_ELAS. The structure of data must
to comprise the fields displacements with the nodes and constraints at the points of Gauss. If this
operand is not indicated, then the initial state within the meaning of method ZAC is null:
0 = 0.

3.5.1 Operand
INST_MAX

INST_MAX = inst
[R]

One indicates here the moment tmax (maximum loading before discharge) of elastoplastic calculation (word
key EVOL_NOLI) which will use to determine the initial state. This moment must also be present in
the list of moments provided with key word EVOL_ELAS.

3.6 Operands
PRECISION/CRITERION

Cf [U4.71.00]. These operands are to be used with operand INST_MAX and make it possible to refine
the extraction of a field by a real variable of access. By defect PRECISION = 1.D-3 and
CRITERION = “RELATIVE”.

4
Results provided in the produced concept

The produced concept is of mult_elas type and comprises is a sequence number (situation
of adaptation), that is to say three sequence numbers (situation of accommodation).

Those are referred by the variable of access NOM_CAS. This variable of access is worth is:
“VALEUR MOYENNE”, either “AMPLITUDE I”, or “AMPLITUDE S”.

The following fields are stored:

|
“DEPL”

Displacements obtained by the resolution of the homogeneous elastic problems provided with
initial deformation (or
,).
lim
moy
I
S

|
“SIEF_ELGA”

Stress field at the points of Gauss calculated starting from preceding displacements. It
represent the state of residual stresses estimated by method ZAC.

|
“ALPH0_ELGA_EPSP”

Initial State ()
0 calculated at the points of Gauss starting from the data of elastoplastic calculation,
p
p
cf [§3.5], (
~
~


C

E)
0 =
-
+
With
With
With if this one is indicated if not the initial state is null
(=)
0
0.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_ZAC


Date:
31/01/05
Author (S):
S. TAHERI, J. ANGLES, Key Mr. BONNAMY
:
U4.83.21-D Page
: 5/6

|
“ALPHP_ELGA_ALPHP”

Fields (or
,) calculated at the points of Gauss starting from the projection of
lim
moy
I
S
the initial state ()
el
0 on the intersection of convex of center ~
I and of radius y, y threshold of
plasticity and I index of loading.

|
“SIGM_ELNO_ZAC”

Average constraints and two amplitudes of constraints to the nodes with the absolute limit:
lim (residual stress) for the sequence number 1 in a case of adaptation,
moy, for the sequence numbers 1,2 and 3 in a case of accommodation.
I
S

|
“EPSP_ELNO_ZAC”

Average plastic deformations and amplitudes of deformations to the nodes with the absolute limit:
p for the sequence number 1 in a case of adaptation,
lim
p, p, p for the sequence numbers 1,2 and 3 in a case of accommodation.
moy
I
S

|
“VARI_ELGA_ZAC”

Elementary indicator on the nature of the phenomenon to the absolute limit. Value 1 indicates one
situation of accommodation and the value a 0 situation of adaptation on the element considered.
This field is stored on the sequence number 1 only.

Caution:

·
The file result comprises a message specifying the situation with the absolute limit
(ADAPTATION or ACCOMMODATION).
·
A situation of accommodation in the case of a loading nonclosely connected causes one
and emission program stop of a message in file RESULTAT: method
is then not applicable.

Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_ZAC


Date:
31/01/05
Author (S):
S. TAHERI, J. ANGLES, Key Mr. BONNAMY
:
U4.83.21-D Page
: 6/6

5 Examples

5.1
Calculation without initial state

solsta = MECA_STATIQUE (
MODELE = Mo,
LIST_INST = listel,
CHAM_MATER = chmat,
EXCIT = _F (CHARGE = chme),
OPTION = (“SIEF_ELGA_DEPL”, “EPSI_ELGA_DEPL”)
)

chzac1 = POST_ZAC (MODELE = Mo, CHAM_MATER = chmat,






EXCIT = _F (CHARGE = chme),






EVOL_ELAS = solsta, LIST_INST = listel)





)

5.2
Calculation with initial state

solpl = STAT_NON_LINE (
MODELE = Mo,
CHAM_MATER = chmat,
EXCIT = _F (CHARGE = chpres, FONC_MULT = varpress),
EXCIT = _F (CHARGE = chcl),
COMP_INCR = _F (RELATION = “VMIS_CINE_LINE”),
INCREMENT = _F (LIST_INST = listpl, NUME_INST_FIN = 20),
NEWTON = _F (MATRIX = “TANGENT”),
CONVERGENCE = _F (RESI_GLOB_RELA= 0.001,
ITER_GLOB_MAXI= 100)
)

solsta = MECA_STATIQUE = (
MODELE = Mo,
LIST_INST = listel,
CHAM_MATER = chmat,
EXCIT = _F (CHARGE = chme),
OPTION = (“SIEF_ELGA_DEPL”, “EPSI_ELGA_DEPL”)
)

chzac2 = POST_ZAC (MODELE = Mo, CHAM_MATER = chmat,
EXCIT

=
_F (
CHARGE
=
chme
),







EVOL_ELAS = solsta, LIST_INST = listel







EVOL_NOLI = solpl, INST_MAX = 3.






)

Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

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