Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
1/14

Organization (S): EDF/AMA
Handbook of Validation
V6.05 booklet: Nonlinear statics
Document: V6.05.100
SSNS100 - Nonlinear Comportement of a tablecloth
reinforcements under thermal loading

Summary:

A tablecloth of reinforcements not offset compared to the layer average and embedded on its four sides east
subjected to a thermal loading. The orientations of the reinforcements are confused with the axes (X, Y) of
total reference mark.

The principal interest of this test is to validate the numerical integration of the models of behavior
elastoplastic GRILL_ISOT_LINE, GRILL_CINE_LINE and GRILL_PINTO_MEN of a tablecloth of reinforcements
associated the finite element GRILL (orthotropic plate with offsetting compared to the datum-line), in
general algorithm STAT_NON_LINE.

In order to obtain reference solutions, analytical solutions were established for both
elastoplastic behaviors with linear and kinematic work hardening isotropic linear. The behavior of
Pinto-Menegotto is validated by nonregression of the numerical results obtained with Aster in version 5-3
(cf [§1.3.3]).
Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
2/14

1
Problem of reference

1.1
Geometry of the plate

Y
NO4
NO3
X
X
1m
ref.
NO 1
1 m
NR O2


Z
Y
X
E


Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
3/14

1.2
Characteristics of modelings

This case test is composed of 7 modelings. The table below summarizes their characteristics:

Offsetting = 0 Thickness = 0,01m
Orientation of the reinforcements
longitudinal direction (L): OX
transverse direction (T): OY

Loi modeling of behavior
% braces
% braces
Mode of application of
longitudinal
the temperature
L
transversal T
With
isotropic linear
1
0,1
with the nodes
B
linear kinematics
1
0,1
with the nodes
C
Pinto Menegotto
1
0,1
with the nodes
D
Pinto Menegotto
1
0,1
with the elements
E
Pinto Menegotto
1
0
with the elements
F
isotropic linear
1
0
with the nodes
G
linear kinematics
1
0
with the nodes

1.3
Properties of materials

1.3.1 Properties common to all modelings

Young modulus:
E = 2 1011
.
MPa

Poisson's ratio:
= 0

Elastic limit:
y = 2 108
.
MPa

Thermal dilation coefficient: =
-
10 5 (°C-1)

1.3.2 Behavior
isotropic and kinematic plastic

For the behaviors isotropic (GRILL_ISOT_LINE) and kinematics (GRILL_CINE_LINE)
Slope of work hardening: AND = 2 1010
.
MPa

1.3.3 Behavior of Pinto Menegotto

For behavior PINTO MENEGOTTO (GRILL_PINTO_MEN)

EPSI_ULTM: 3,0.
10­2
SIGM_ULTM: 2,58.
108
EPSP_HARD: 0,0023
R_PM
: 20,0
EP_SUR_E
: 0,01
A1_PM
: 18,5
A2_PM
: 0,15
ELAN
: 4,9
A6_PM
: 620,0
C_PM
: 0,5
A_PM
: 0,008

1.4
Boundary conditions and loading

The plate is entirely embedded.
Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
4/14

The loading is of thermal origin. The change of the temperature according to time is given
for each modeling in the following table. The temperature is applied to the nodes or to
elements, according to modeling.

Moment Evolution
With Evolution B
Evolution C



0 50 50 50
1 ­ 50 ­ 50 ­ 300
2 ­ 250 ­ 250 ­ 100
3 ­ 150 ­ 150
50
4 ­ 250 ­ 250 ­ 150
5 ­ 50 ­ 50 ­ 350
6.350.350 ­ 200
7 50 150

8 ­ 450 ­ 450

9 ­ 110 ­ 250

10.550.650

11 50 450


600
Evol_A
400
Evol_B
Evol_C
200
.
EFF
Tr
0
T
- 200
- 400
- 600
1
2
3
4
5
6
7
8
9
10
11
12


One took for all the tests a temperature of reference of 50°.
Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
5/14

2
Reference solutions

2.1
Isotropic plastic behavior

The reference solution is calculated analytically.
One notes T +
+
, p+
+
, p
, the temperature, plastic deformation, cumulated plastic deformation
and total deflection at the moment of calculation, and T -
-
, p
, p
same quantities at the moment
precedent. Tréf indicates the temperature of reference.

The solution is calculated in the following way:


+
+
-
E = E [- (T - R
T EFF) - p]
E. AND
R (p) =
p + y
E - AND
if
-
E R (p)
+ = -; p+ = p; + =
p
p
E
if not
if
-
E > R (p)
E - E

+
T
=

+ -
y
E
+
T
-
-
p
(T - reTf) - + [p - p]
E
E
E


p+ = p + + - -
p
p
+ = R (p+)
if not
E - E

+
T
E
=
+

- +
y
T
+
[- -
p + p]
p
(T - reTf) +
E
E
E



p+ = p - +
-
p + p
+
= - R (p+)

This calculation is made in each direction. For the treated case, + = 0 at any moment.
In the longitudinal direction, the constraint memorized in Aster is the real constraint existing
in each grid of this direction.
In the transverse direction, the constraint memorized in Aster is the real constraint existing

in each grid of this direction multiplied by the coefficient T
.
L
Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
6/14

2.2
Kinematic plastic behavior

The reference solution is calculated analytically.
One notes T +
+
+
, X +
, p
the temperature, plastic deformation and the variable of work hardening
kinematics at the moment of calculation, and T -
- X -
, p
same quantities at the previous moment.

The solution is calculated in the following way:


+
+
-
E = E [- (T - R
T EFF) - p]
if - X -
E
y
+ = -; X + = X -; + =
p
p
E
if not
if - X - >
E
y
E - E

+
T
=

+ -
y
+
p
(T - reTf) -
E
E




X + = E
+ -
y
+
T
(T - rTef) -
E


E - E
+
+
+
T
= AND [- (T - rTef)]+
y
E
if not
E - E

+
T
=
+

-
y
+
p
(T - reTf) +
E
E



y
+
X = AND +
- (+
T - Tref) +



E
E -
+
E
= E
T
T [+
- (+
T - Tref)] -

E
y

This calculation is made in each direction. For the treated case, + = 0 at any moment.
In the longitudinal direction, the constraint memorized in Aster is the real constraint existing
in each grid of this direction.
In the transverse direction, the constraint memorized in Aster is the real constraint existing

in each grid of this direction multiplied by the coefficient T
.
L
Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
7/14

2.3
Behavior Pinto Ménégotto

The reference solution is that obtained by a Aster calculation with the same grid on which one
apply cycles of load/discharge, in imposed displacement, allowing to recreate them
deformations resulting from mechanical thermo calculations presented hereafter. The test corresponding is not
thus that a test of nonregression, by comparing the constraints obtained by these two types of
modeling: on the one hand mechanical, and on the other hand thermomechanical.

In the longitudinal direction, the constraint memorized in Aster is the real constraint existing
in each grid of this direction.
In the transverse direction, the constraint memorized in Aster is the real constraint existing

in each grid of this direction multiplied by the coefficient T
.
L

3 Modeling
With

The test-tube is with a grid with two elements `GRILL `with three nodes.

NO3
NO4
NO1
NO2

4 Functionalities
tested

Commands



AFFE_CARA_ELEM ROASTS


DEFI_MATERIAU ECRO_LINE



PINTO_MENEGOTTO
STAT_NON_LINE COMP_INCR
RELATION
“GRILL_ISOT_LINE”
“GRILL_CINE_LINE”
“GRILL_PINTO_MEN”
NEWTON
MATRICE
“TANGENTE”

CALC_ELEM OPTION
SIGM_ELNO_VARI

Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
8/14


5
Results modeling A (linear isotropic work hardening)

5.1
Thermal loading for modeling A

Temperature of reference: 50
History of the loading: Evolution_A (cf [§1.4])
The temperatures re-entered like a field to the nodes.

5.2 Results

Variable: SIGXX and SIGYY with node NO1

SIGXX
SIGYY
Moment Code_Aster Reference
Variation Code_Aster Reference
Variation (%)
1 2,00000E+08 2,00000E+08 0 2,00000E+07 2,00000E+07 0
2 2,40000E+08 2,40000E+08 0 2,40000E+07 2,40000E+07 0
3 4,00000E+07 4,00000E+07 0 4,00000E+06 4,00000E+06 0
4 2,40000E+08 2,40000E+08 0 2,40000E+07 2,40000E+07 0
5 ­ 1,60000E+08 ­ 1,60000E+08 0 ­ 1,60000E+07 ­ 1,60000E+07
0
6 ­ 3,12000E+08 ­ 3,12000E+08 0 ­ 3,12000E+07 ­ 3,12000E+07
0
7 2,88000E+08 2,88000E+08 0 2,88000E+07 2,88000E+07 0
8 4,09600E+08 4,09600E+08 0 4,09600E+07 4,09600E+07 0
9 ­ 2,70400E+08 ­ 2,70400E+08 0 ­ 2,70400E+07 ­ 2,70400E+07
0
10 ­ 5,27680E+08 ­ 5,27680E+08 0 ­ 5,27680E+07 ­ 5,27680E+07
0
11 4,72320E+08 4,72320E+08 0 4,72320E+07 4,72320E+07 0

Note:

The results presented are given in the reference mark of reference (Xref, Yref) forming an angle of 0°
compared to (X, Y).
Constraints SIGYY are equal to constraints SIGXX multiplied by the report/ratio of
percentages of reinforcement enters the directions transversal and longitudinal.
The case studied test corresponds to the diagrams following in a plan forced deformation:

5,000E+08
4,000E+08
3,000E+08
2,000E+08
1,000E+08
0,000E+00
- 1,000E+08
- 2,000E+08
- 3,000E+08
- 4,000E+08
- 5,000E+08
- 6,000E+08
- 6,00E-03 - 4,00E-03 - 2,00E-03 0,00E+00
2,00E-03
4,00E-03
6,00E-03

Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
9/14


6 Results modeling B (kinematic work hardening
linear)

6.1
Thermal loading for modeling B

Temperature of reference: 50°C
History of the loading: Evolution_B (cf [§1.4)
The temperatures re-entered like a field to the nodes.

6.2 Results

Variable: SIGXX and SIGYY with node NO1

SIGXX
SIGYY
Moment Code_Aster Reference
Variation Reference
Code_Aster Variation
(%)
1 2,00E+08
2,00E+08 0 2,00E+07 2,00E+07
0
2 2,40E+08
2,40E+08 0 2,40E+07 2,40E+07
0
3 4,00E+07
4,00E+07 0 4,00E+06 4,00E+06
0
4 2,40E+08
2,40E+08 0 2,40E+07 2,40E+07
0
5 ­ 1,60E+08
­ 1,60E+08
0 ­ 1,60E+07 ­ 1,60E+07
0
6 ­ 2,40E+08
­ 2,40E+08
0 ­ 2,40E+07 ­ 2,40E+07
0
7 1,60E+08
1,60E+08 0 1,60E+07 1,60E+07
0
8 2,80E+08
2,80E+08 0 2,80E+07 2,80E+07
0
9 ­ 1,20E+08
­ 1,20E+08
0 ­ 1,20E+07 ­ 1,20E+07
0
10 ­ 3,00E+08 ­ 3,00E+08
0 ­ 3,00E+07 ­ 3,00E+07
0
11 1,00E+08 1,00E+08
0 1,00E+07 1,00E+07
0

Note:

The results presented are given in the reference mark of reference (Xref, Yref) forming an angle of 0°
compared to (X, Y).
Constraints SIGYY are equal to constraints SIGXX multiplied by the report/ratio of
percentages of reinforcement enters the directions transversal and longitudinal.
The case studied test corresponds to the following diagram in a plan forced deformation:

3,00E+08
2,00E+08
1,00E+08
0,00E+00
- 1,00E+08
- 2,00E+08
- 3,00E+08
- 6,00E-03 - 4,00E-03 - 2,00E-03 0,00E+00
2,00E-03
4,00E-03
6,00E-03
Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
10/14


7
Results modeling C (model of Pinto Menegotto)

7.1
Thermal loading for modeling C

Temperature of reference: 50°C
History of the loading: Evolution_C (cf [§1.4])
The temperatures re-entered like a field to the nodes.

7.2 Results

Variable: SIGXX and SIGYY with node NO1

SIGXX
SIGYY
Code_Aster moment


Code_Aster

1
2.00000E+08

2.00000E+07

2
2.09416E+08

2.09416E+07

3
­ 1.21555E+08
­ 1.21555E+07

4
­ 1.82862E+08
­ 1.82862E+07

5
1.52164E+08

1.52164E+07

6
2.02506E+08

2.02506E+07

7
­ 7.59307E+07
­ 7.59307E+06


Note:

The results presented are given in the reference mark of reference (Xref, Yref) forming an angle of 0°
compared to (X, Y).
Constraints SIGYY are equal to constraints SIGXX multiplied by the report/ratio of
percentages of reinforcement enters the directions transversal and longitudinal.

The case studied test corresponds to the following diagram in a plan forced deformation:

2,50E+08
2,00E+08
1,50E+08
1,00E+08
5,00E+07
0,00E+00
- 5,00E+07
- 1,00E+08
- 1,50E+08
- 2,00E+08
0,0E+00 5,0E-04 1,0E-03 1,5E-03 2,0E-03 2,5E-03 3,0E-03 3,5E-03 4,0E-03

Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
11/14


8
Results modeling D (model of Pinto-Menegotto)

Modeling D is the same one as modeling C, with the difference which the temperatures are
defined by a card.
The results are identical.

9
Results modeling E (model of Pinto-Menegotto)

Modeling E approaches modeling D, with the difference that it there not of reinforcement
transversal (T = 0).

9.1 Results


Variable: SIGXX and SIGYY with node NO1

SIGXX SIGYY
Moment
Code_Aster


Code_Aster

1
2.00000E+08

0,0

2
2.09416E+08

0,0

3
­ 1.21555E+08

0,0

4
­ 1.82862E+08

0,0

5
1.52164E+08

0,0

6
2.02506E+08

0,0

7
­ 7.59307E+07

0,0


Note:

The results presented are given in the reference mark of reference (Xref, Yref) forming an angle of 0°
compared to (X, Y).
Constraints SIGYY are null, since there are not any more transverse reinforcements.

Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
12/14

10 Results modeling F (linear isotropic work hardening)

Modeling F approaches modeling A, with the difference that it there not of reinforcement
transversal (T = 0).

10.1 Results

Variable: SIGXX and SIGYY with node NO1

SIGXX SIGYY
Moment
Code_Aster


Code_Aster

1
2.00000E+08

0,0

2
2.40000E+08

0,0

3
4.00000E+07

0,0

4
2.40000E+08

0,0

5
­ 1.60000E+08

0,0

6
­ 3.12000E+08

0,0

7
2.88000E+08

0,0

8
4.09600E+08

0,0

9
­ 2.70400E+08

0,0

10
­ 5.27680E+08

0,0

11
4.72320E+08

0,0


Note:

The results presented are given in the reference mark of reference (Xref, Yref) forming an angle of 0°
compared to (X, Y).
Constraints SIGYY are null, since there are not any more transverse reinforcements.

10.2 Parameters
of execution

Version: 5.03.13

Machine: SGI ORIGIN 2000 - R 12000

Obstruction memory: 32 Mo
Time CPU To use: 6, 43 S

Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
13/14

11 Results modeling G (linear kinematic model)

Modeling F approaches modeling B, with the difference that it there not of reinforcement
transversal (T = 0).

11.1 Results

Variable: SIGXX and SIGYY with node NO1

SIGXX
SIGYY
Moment
Code_Aster


Code_Aster

1
2,00E+08
0,0
2
2,40E+08
0,0
3
4,00E+07
0,0
4
2,40E+08
0,0
5
­ 1,60E+08
0,0
6
­ 2,40E+08
0,0
7
1,60E+08
0,0
8
2,80E+08
0,0
9
­ 1,20E+08
0,0
10
­ 3,00E+08

0,0

11
1,00E+08

0,0


Note:

The results presented are given in the reference mark of reference (Xref, Yref) forming an angle of 0°
compared to (X, Y).
Constraints SIGYY are null, since there are not any more transverse reinforcements.

11.2 Parameters
of execution

Version: 5.03.13

Machine: SGI ORIGIN 2000 - R 12000

Obstruction memory: 32 Mo
Time CPU To use: 7, 52 S
Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Code_Aster ®
Version 5.0
Titrate:
Nonlinear SSNS100 Comportement of a tablecloth of reinforcements
Date:
05/02/02
Author (S):
C. CHAVANT Key
:
V6.05.100-A Page:
14/14

12 Summary of the results

For elastoplastic behaviors with linear work hardening, the analytical solution is
perfectly found.

The behavior of Pinto-Menegotto is validated by nonregression.

Handbook of Validation
V6.05 booklet: Nonlinear statics
HT-66/02/001/A

Outline document