Code_Aster
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Version
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Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
1/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.102
SSNV102 - Tensile test shearing
with the model of S. TAHERI
Summary:
The problem is quasi-static nonlinear in mechanics of the structures.
One analyzes the response of an element of volume to a loading in traction-shearing, carried out in such way
that that imposes a uniform state of stress-strain in the element.
There are 2 modelings: one in voluminal 3D and another in plane stresses 2D.
One validates by this test the numerical integration of the elastoplastic model of behavior of Said Taheri.
Code_Aster
®
Version
4.0
Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
2/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind 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
T
()
O
T
()
O
T
()
O
imposed pressure
T
()
O
function of effort
T
()
Face 1 X Z
Face 1Y Z
Face YZ
1.2
Material properties
isotropic elasticity
E = 200.000 MPa
= 0,3
plasticity Said Taheri
C
inf
= 0.065 MPa
C
1
= - 0.012 Mpa
S = 450
B = 30
m = 0.1
has = 312
= 0.3
R
O
= 72
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 (NR)
88.
1.
T (S)
0.
1.4 Conditions
initial
Null stresses and deformations with T = 0.
Code_Aster
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Version
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Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
3/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
One numerically integrates the following system between T = 0 and T = 1.
(Nonlinear ordinary Differential connection of 6 equations to 6 unknown factors solved using
library NAG by a “Backward difference method”)
(
) (
)
(
)
(
)
(
)
(
)
(
)
µ
-
=
-
=
-
=
-
=
-
+
-
+
-
-
-
+
-
+
+
+
+
+
-
-
-
-
-
p
E
p
p
p F
p
p F
F Kx Cs F
F Ky Cs F
HR
D has
Z
F
F
p
F Qx C
F Qy C
O
O
p
p
N
p
p
N
p
N
p
N
éq 2.1 1
éq 2.1 2
éq 2.1 3
éq 2.1 4
2
0
0
3
2
2
4
3
3
2
2
2
(
)
(
)
(
)
(
)
(
)
(
)
JR
F
F
JR
C
U
C
S
C S
HR
D has
Z
F
F
KX
CS
U
C S
F
C S
p
O
O
p
p
p
N
p
N
p
p
p
N
p
N
p
p
p
N
p
p
N
p
p
p
N
= -
-
+
+
-
+
-
-
+
-
+
-
+
+
-
+
-
-
2
1
3
2
3
2
2
4
3
3 2
3
2
2
2
éq 2.1 5
(
)
p
p
p
N
F
p
-
=
-
0
éq 2.1 6
(
)
(
)
(
)
(
) (
)
with
and
D
me
U
B
S
v
C
C
C
W
D
D
C
C
C E
K
v U
Q
v LP
S
H
W U
J
W LP
S
X
C S
Y
C S
U
X
Y
R
D has Z
R
Z
up
p
up
p
p
p
N
p
p
p
N
p
p
N
p
p
N
= -
=
-
= -
= -
= -
=
=
=
=
=
-
=
-
=
+
=
+
=
-
+
-
-
-
1
1
1
9
4
3
0
4
3
1
2
2
1 2
2
2
/
1 2
/
Code_Aster
®
Version
4.0
Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
4/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
with the initial conditions:
()
()
(
)
()
()
()
()
()
()
()
(
)
()
(
)
µ
0
0
3
0
0
0
0 2
0
0
0
0
1
1
88
88
0
88
0
0
0
0
0
2
2 1 2
=
+
=
=
=
=
=
=
-
=
=
=
R
E
p
R
m R
O
T
O
O
O
O
p
p
N
O
p
/
.
.
.
from where
2.2
Results of reference
Values of
,
,
,
p
p
p
and
p
with the nodes with T = 1 S.
2.3
Uncertainty on the solution
Uncertainty of library NAG.
2.4 References
bibliographical
[1]
User's manual library NAG on CRAY.
[2]
S. ANDRIEUX - P. SCHOENBERGER - S. TAHERI: With three dimensional cyclic constitutive
law for metals with has semi-discrete memory variable - HI-71/8147 (1992)
[3]
P. GEYER - J.M. PROIX - P. SCHOENBERGER - S. TAHERI: Modeling of the phenomena
of progressive deformation - Collection of the notes intern DER 93NB00153
Code_Aster
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Version
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Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
5/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
Intentionally white left page.
Code_Aster
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Version
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Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
6/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D:
Cubic elementary with a grid using a hexahedron with 8 nodes.
1
2
7
8
y
X
F
F
F
F
F
F
2F
2F
T
1s
22 NR
F
Z
5
6
3
4
has
3.2
Characteristics of the mesh
1 mesh HEXA8, width side has = 1.
3.3 Functionalities
tested
Order
Key word factor
Simple key word
Argument
Keys
DEFI_MATERIAU
TAHERI
[U4.23.01]
STAT_NON_LINE
COMP_INCR
RELATION
“TAHERI_FO”
[U4.32.01]
NEWTON
STAMP
“TANGENT”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Code_Aster
®
Version
4.0
Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
7/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
in all nodes
0.01721
0.01722
0.02
0.02573
0.02574
0.01
p
0.01678
0.01677
0.04
p
0.02515
0.02516
0.04
p
0.03356
0.03354
0.06
p
176.00000
175.99999
0.0001
4.2 Remarks
The limitation with 10 of the maximum number of local iterations is very sufficient for a method of
NEWTON exact in this case.
The reduction in the tolerance on total convergence in displacement does not bring gain
significant in precision.
The number of increments of load (8) led to a satisfactory precision of the result.
4.3 Parameters
of execution
Version: 03.02.11
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
18 seconds
Code_Aster
®
Version
4.0
Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
8/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
Modeling in plane stresses 2D
T
1 S
44 NR
F (T)
y
X
F
F
F
2F
N04
N03
N02
N01
5.2
Characteristics of the mesh
Square quadrangle with 4 nodes in plane stresses with:
·
width = 1,
·
thickness = 1.
5.3 Functionalities
tested
Order
Key word factor
Simple key word
Argument
Keys
DEFI_MATERIAU
TAHERI
[U4.23.01]
STAT_NON_LINE
COMP_INCR
RELATION
“TAHERI”
[U4.32.01]
NEWTON
STAMP
“TANGENT”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Code_Aster
®
Version
4.0
Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
9/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
in all nodes
0.01721
0.017224
0.08
0.02573
0.025727
0.008
p
0.01678
0.016784
0.02
p
0.02515
0.025156
0.02
p
0.03356
0.03354
0.06
p
176.
175.9998
0.0001
6.2 Parameters
of execution
Version: 03.02.11
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
16 seconds
Code_Aster
®
Version
4.0
Titrate:
SSNV102 Test tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A
Page:
10/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A
7
Summary of the results
Good precision at the time of the comparison with NAG in spite of some difficulties of convergence with
this mathematical library.