Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.101
SSNV101 - Essai of tensile 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 constraints.
This test validates the numerical integration of the elastoplastic model of behavior to 2 variables kinematics
of Chaboche.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
2/8
1
Problem of reference
1.1 Geometry
Y, Dy
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
FAC
E 1XZ
O
O
shearing
Face 1Y Z
3
4
X, dx
O pressure
Face YZ
T () function effort
O
7
8
Z, dz
1.2
Material properties
isotropic elasticity
E = 145.200. MPa
= 0.3
Chaboche plasticity
Ro = 87. MPa
A1 = 187.
IH = 151. MPa
A2 = 29.
B = 2.3
C1 = 341.
K = 0.43
C2 = 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.
T (second)
1.
1.4 Conditions
initial
Null constraints and deformations with T = 0.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
In the particular case of traction imposed shearing,
0
0
O
O 0
X
y
I
I
(
T) = (T)
=
-
=
0
I =
O
0
0, X
y
X
I
I
I/2
0
and
1 2
T
,
0
0
0
0
0
- X/2
0 0
I
T
(X I constraint of kinematic work hardening)
one can write the model of Chaboche in the form of a system of 7 differential equations
y = (, X, X, y, y, p
1
2
1
2
)
ordinary in
.
F
(y, T) y = G (y, T)
-
O =
3
p O - (x1 + x2)
R (p)
E
2
-
O = 3 p
(O - (y1+ y2) R (p)
2µ
2
2
O
ix = ic
I
With (p) -
I
X p I
,
1 2
3
E -
=
2
O
I
y
= C
I
I
With (p)
-
- iy
p I =,
1 2
3
2µ
3
3
0
=
(X +
1
x2)
O
(1x x2)
O -
2
-
+
2
R
+
(3 - + - + -
O
(there y
y
y
O
1
2) (
(1 2) p R (p) p
with, with T = 0:
=
2 +
2
3
because threshold F =
O
O
R
O
O
(
)
0
=
O
O O/E
=
O
O O/2µ
x1 = 2 = 1 = 2 =
=
O
X O
y O
y O
Po
0
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, there is O = 0.435
One compares with Aster the values, 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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
4/8
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D:
y
F (Newton)
35.875
F
1
2
25
F
F
T (second)
1 1.435
F
2F
X
F
2F
7
8
F
Z
3.2
Characteristics of the grid
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
MATRICE
“TANGENTE”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
5/8
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
51.0960
51.0847
0.01
1
X
7.9546
7.9574
0.02
2
y
76.6450
76.627
0.01
1
y
11.9320
11.9359
0.01
2
p
0.1922
0.1923
0.04
143.5000
143.4998
0.0001
11
4.2 Parameters
of execution
Version: 4.01.09
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
21 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
6/8
5 Modeling
B
5.1
Characteristics of modeling
Modeling in plane constraints
y
F
F
F (Newton)
35.875
4
3
25
F
2F
T (second)
2F
6
5
1 1.435
2F
1
2
X
3F
F
5.2
Characteristics of the grid
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
MATRICE
“TANGENTE”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
7/8
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
51.0960
51.1011
0.01
1
X
7.9546
7.9599
0.07
2
y
76.6450
76.6150
0.04
1
y
11.9320
11.9345
0.02
2
p
0.1922
0.1923
0.05
143.5000
143.6072
0.07
11
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
Obstruction memory:
8 MW
Time CPU To use:
25 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNV101 Essai of traction-shearing with the model of Chaboche
Date:
01/12/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.101-B Page:
8/8
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).
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/98/040 - Ind A