Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
Organization (S):
EDF/MMC
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.103
SSNV103 - Tensile test 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.
Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
1
Problem of reference
1.1 Geometry
1
2
3
4
5
6
7
8
Face YZ: (1, 3, 5, 7)
Face XZ: (3, 4, 7, 8)
Face 1YZ: (2, 4, 6, 8)
Face 1XZ: (1, 2, 5, 6)
imposed shearing
y
X
Z
O
imposed pressure
O
function of effort
T
()
O
O
O
Face 1 X Z
Face 1Y Z
Face YZ
1.2
Material properties
isotropic elasticity:
E = 206.400.MPa
= 0.3
plasticity:
(coefficients of the model of
Rousselier)
D = 2.
O
F
= 5.10
4
1
= 490.MPa
The rational traction diagram entered point by point with:
()
(
)
LP
I
O
I
E
R
R
R
p
R
-
-
+
=
with
p: cumulated plastic deformation
and
laughed = 1500 MPa
R
O
= 520.MPa
B = 2.4
Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
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
1.
T (second)
1.4 Conditions
initial
Null stresses 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:
(
)
& &
&
& & exp
& &
& F
&f
-
-
=
-
=
-
-
=
=
E
E
H
E
p D
p
0
0
0
0
1
linear tensor isotropic elasticity
what, in the case of a loading of imposed traction-shearing
()
()
T
T
O
O
O
=
0
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
,
&
,
=
.
409.707
Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
()
&
&
&
&
&
&
&
& &
&
& &
& & exp
&
exp
&
S
F E E
E
F E
p
p
p D
D F E
O
O
E
E
O
O
E
E
O
eq O
E
O
eq O
E
H
O
O
eq O
O
H
µ
µ
+
-
=
+
-
=
-
-
=
-
-
=
-
=
+
+
2
2
1
1
0
2
2
0
0
3
2
0
0
1
3
3
O
eq O
eq O
O
O
H
O
H
R
p p
F E
D
F E
F E
2
1
1
1
1
1
0
&
exp
&
-
+
+
-
-
=
with with T = 0:
()
()
F
,
,
=
=
=
0
0
1
0
0
from where:
()
()
0
0
0
3
0
1
1
eq O
O
O
R
D
F
-
+
=
()
exp
who is solved by a method of NEWTON for
()
0
:
()
()
()
()
()
()
()
µ
0
1
0
0
0
1
2
0
0
0
0
=
=
=
=
=
E
p
O
E
O
E
2.2
Results of reference
One imposes
()
()
T
T
=
+
0
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 =
(
)
,
with the nodes with T = 1.
Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
5/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
2.3
Uncertainty on the solution
Uncertainty related to library NAG.
2.4 References
bibliographical
[1]
User's manual library NAG on CRAY.
Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
6/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D: 1 cubic HEXA8
1
2
7
8
y
X
F
F
F
F
F
F
2F
2F
1 S
102.426 NR
F
Z
5
6
3
4
T
3.2 Functionalities
tested
Order
Key word factor
Simple key word
Argument
DEFI_MATERIAU
ROUSSELIER_FO
STAT_NON_LINE
COMP_INCR
RELATION
“ROUSSELIER”
NEWTON
STAMP
“TANGENT”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
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
11
409.7070 409.7076 1.51 10
4
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
,
.
Code_Aster
®
Version
5.0
Titrate:
SSNV103 - Tensile test shearing models of Rousselier
Date:
03/10/02
Author (S):
R. MASSON
Key
:
V6.04.103-C
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/02/009/A
5
Summary of the results
The values of Code_Aster are in concord with the values of reference.