Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.101
SSNV101 - Tensile test shearing
with the model of Chaboche
Summary:
Problem of quasi static evolution nonlinear of mechanics of the structures.
Analyze response of an element of volume to a loading of traction-shearing which imposes a state of
uniform stress-strain.
There are 2 modelings: one in 3D and one in plane stresses.
This test validates the numerical integration of the elastoplastic model of behavior to 2 variables kinematics
of Chaboche.
Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
1
2
3
4
5
6
7
8
O
O
O
Face YZ: (1, 3, 5, 7)
Face XZ: (3, 4, 7, 8)
Face 1YZ: (2, 4, 6, 8)
Face 1XZ: (1, 2, 5, 6)
O
shearing
O
pressure
T
()
function effort
Face 1XZ
Face 1Y Z
Face YZ
X, dx
Z, dz
Y, Dy
1.2
Material properties
isotropic elasticity
E = 145.200. MPa
= 0.3
Chaboche plasticity
R
O
= 87. MPa
With
1
= 187.
R
I
= 151. MPa
With
2
= 29.
B = 2.3
C
1
= 341.
K = 0.43
C
2
= 17.184.
W = 6.09
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)
100.
1.
T (second)
1.4 Conditions
initial
Null stresses and deformations with T = 0.
Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
In the particular case of traction imposed shearing,
()
()
T
T
O
O
O
=
0
0
0
0
0
0
,
X
X
y
y
X
X
I
I
I
I
I
I
=
-
-
0
2
0
0
0
2
/
/
and
=
=
0
0
0
0
1 2
T
T
I
,
,
(
X
I
kinematic stress of work hardening)
one can write the model of Chaboche in the form of a system of 7 differential equations
ordinary in
(
)
()
()
y
X
X
y
y
p
F y T y
G y T
=
=
,
,
,
,
,
,
,
1
2
1
2
.
(
)
()
(
)
(
)
()
()
()
,
,
µ
µ
-
=
-
+
-
=
-
+
=
-
-
=
=
-
-
=
=
-
O
O
O
O
I
I
I
O
I
I
I
I
O
I
O
E
p
X
X
R p
p
y
y
R p
X
C
With
p
E
X p
I
y
C
With
p
y p
I
3
2
2
3
2
2
3
1 2
2
3
2
1 2
0
1
2
1
2
(
)
(
)
(
)
(
)
(
)
(
)
()
3
2
3
2
3
1
2
1
2
1
2
1
2
X
X
X
X
y
y
y
y
p R p
R
p
O
O
O
+
-
+
+
-
+
-
+
-
with, with T = 0:
(
)
µ
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
R
E
X
X
y
y
p
=
+
=
=
=
=
=
=
=
=
2
2
1
2
1
2
3
0
2
0
because threshold
F
/
/
and one imposes
()
T
T
O
=
+
.
This system is solved numerically by a “Backward difference formulated” using the library
scientist NAG on CRAY.
2.2
Results of reference
With the imposed loading, one has
O
= 0.435
One compares with
Aster
values of
,
,
,
,
,
X X
y
y
p
1
2
1
2
who must be identical in all them
nodes at the moment T = 1.435 dryness.
2.3
Uncertainty on the solution
Uncertainty of NAG: the resolution is carried out with 218 increments of calculated times
automatically.
Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D:
1
2
7
8
y
X
F
F
F
F
F
F
2F
2F
T (second)
1.435
1
25
35.875
F (Newton)
Z
3.2
Characteristics of the mesh
1 HEXA8.
3.3 Functionalities
tested
Order
Key word factor
Simple key word
Argument
Keys
DEFI_MATERIAU
CHABOCHE_FO
[U4.23.01]
STAT_NON_LINE
COMP_INCR
RELATION
“CHABOCHE”
[U4.32.01]
NEWTON
STAMP
“TANGENT”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
5/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
in all nodes with T = 1.435
0.0970
0.0971
0.05
0.1454
0.1455
0.07
X
1
51.0960
51.0847
0.01
X
2
7.9546
7.9574
0.02
y
1
76.6450
76.627
0.01
y
2
11.9320
11.9359
0.01
p
0.1922
0.1923
0.04
11
143.5000
143.4998
0.0001
4.2 Parameters
of execution
Version: 4.01.09
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
21 seconds
Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
6/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
Modeling in plane stresses
T (second)
1.435
1
25
35.875
F (Newton)
y
X
F
F
F
F
2F
2F
2F
3F
4
3
6
5
1
2
5.2
Characteristics of the mesh
2 meshs QUAD4.
5.3 Functionalities
tested
Order
Key word factor
Simple key word
Argument
Keys
DEFI_MATERIAU
CHABOCHE
[U4.23.01]
STAT_NON_LINE
COMP_INCR
RELATION
“CHABOCHE”
[U4.32.01]
NEWTON
STAMP
“TANGENT”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
0.0970
0.0971
0.05
0.1454
0.1455
0.05
X
1
51.0960
51.1011
0.01
X
2
7.9546
7.9599
0.07
y
1
76.6450
76.6150
0.04
y
2
11.9320
11.9345
0.02
p
0.1922
0.1923
0.05
11
143.5000
143.6072
0.07
6.2 Remarks
The values of shearings are multiplied by
2
in the display of the results of the variables
interns.
6.3 Parameters
of execution
Version: 4.00.12
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
25 seconds
Code_Aster
®
Version
4.0
Titrate:
SSNV101 Test of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
7
Summary of the results
Good precision at the time of the comparison of the results, in spite of the number of very different increments
for NAG (218) and
Aster
(12).