Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
1/8

Organization (S): EDF/MMC

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.103

SSNV103 - Essai of tensile shearing
model of Rousselier

Summary:

It is about a nonlinear quasi-static problem in mechanics of the structures.

One analyzes the response of an element of volume to a loading in traction-shearing, carried out of such
way that that imposes a uniform state of stress-strain.

The case test includes/understands 1 modeling: in 3D.

It validates the numerical integration of the elastoplastic model of behavior with damage of
G. Rousselier.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
2/8

1
Problem of reference

1.1 Geometry

y
Face YZ: (1, 3, 5, 7)
1
2

Face XZ: (3, 4, 7, 8)

Face 1YZ: (2, 4, 6, 8)
5
6


Face 1XZ: (1, 2, 5, 6)
O
Face 1

X Z
3
4


O imposed shearing
O
Face 1

Y Z
X
imposed pressure
O
Face YZ
(T) function of effort
7

8
O
Z


1.2
Material properties

isotropic elasticity:
E = 206.400.MPa
= 0.3

plasticity:
D = 2.

(coefficients of the model of F = 5.10­4
Rousselier)
O
1 = 490.MPa

The rational traction diagram entered point by point with:

R (p) =r + R
R E
-
I
(O I) LP
with
p: cumulated plastic deformation
and
laughed = 1500 MPa
ro = 520.MPa
B = 2.4




Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
3/8

1.3
Boundary conditions and loadings

N04
dx = Dy = 0
Face YZ:
FX = FY = ­ F (T)
N08
dx = Dy = dz = 0
Face XZ:
FX = ­ F (T)
N02, N06
dx = 0
Face 1YZ:
FY = F (T)


Face 1XZ:
FX = F (T)

F (Newton)
409.68
409.707
T (second)
1.


1.4 Conditions
initial

Null constraints and deformations with T = 0.

2
Reference solution

2.1
Method of calculation used for the reference solution

The model 3D of speed is written:

& - & E - &e = 0
(linear tensor isotropic elasticity)




&

- &p D exp H =

0
1



F

& - &e - &p
=

0


&f

= 0





0
O
O



what, in the case of a loading of imposed traction-shearing (T) = (T) O
0

0




0 0


0
conduit to integrate a system of 6 ordinary differential equations in y = (, p
E
E
) of
the form (
With y, T) y & = G (y, T).
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
4/8

& + 2 F E E & - E
O
O
E
&e = 0

& + 2 F E 2µ &
O
O
E - 2 µ &
E = 0


&
O
-
&p - &e




= 0
eq O

3
&
O
-
&p - &e
0

2


=
eq O


(S)


&

- &p D exp
H

= 0


1



1
2


O
R
&
O

+ D F E exp
H
O
O

+ 3 &


-
p&
eq O
3



1


eq O
p









H


+
H

+

-
-
&
eq O
O
F E
D 1 O
F E exp
1 O
F E 1
=



0

1

1




with with T = 0:

F = 0, ()
0
= 1, ()
0
= 0

from where:

()
()
0
0
- R (0
O
eq O
) + D F exp
= 0
1 O

31

who is solved by a method of NEWTON for ()
0:


()
1
0
=
()
0 O = E ()
0

E

()
1
0
=
()
0 O = E ()
0


p ()
0
=
0



2.2
Results of reference

One imposes (T) = ()
0 + T with O = O = 150.MPa.

One obtains ()
0 = 1.73138 and ()
1 = 2.73138.

The system (S) is then solved numerically by a “Backward difference formulated” using
scientific library NAG on CRAY. Result of reference = (,) to the nodes with T = 1.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
5/8

2.3
Uncertainty on the solution

Uncertainty related to library NAG.

2.4 References
bibliographical

[1]
User's manual library NAG on CRAY.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
6/8

3 Modeling
With

3.1
Characteristics of modeling

Modeling 3D: 1 cubic HEXA8

y
F
F
1
102.426 NR
2
F
F
5
F
6
T
1 S
2F
3
X
4
F
2F
7
8
F
Z


3.2 Functionalities
tested

Order
Key word factor
Simple key word
Argument
DEFI_MATERIAU
ROUSSELIER_FO

STAT_NON_LINE
COMP_INCR
RELATION
“ROUSSELIER”

NEWTON
MATRICE
“TANGENTE”

CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”


Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
7/8

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
in all the nodes




0.07830 0.07838 0.111

0.11700 0.11706 0.05
p
0.15260 0.15264 0.024

409.7070 409.7076 1.51 10­4
11

4.2 Remarks

One could expect a better correlation, but it should be stressed that library NAG uses
the function R (p) in algebraic form, whereas Code_Aster uses it in the form of a curve
data point by point.

Moreover, it seems that the integration of the rate of the function threshold poses problems with NAG, whatever
that is to say precision required in addition (the value of the threshold F being appreciably different from 0 in end
of integration). However, one can note the constancy of this correlation throughout integration
(T [
0]
1
,).

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Code_Aster ®
Version
5.0
Titrate:
SSNV103 - Essai of tensile shearing models of Rousselier
Date:
03/10/02
Author (S):
R. Key MASSON
:
V6.04.103-C Page:
8/8

5
Summary of the results

The values of Code_Aster are in concord with the values of reference.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A

Outline document