Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
1/10
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.102
SSNV102 - Essai of tensile 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 constraints 2D.
One validates by this test the numerical integration of the elastoplastic model of behavior of Said Taheri.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
2/10
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)
(T) O
Face 1

X Z
3
4
(T) imposed shearing
(

T)
O
O
Face 1

Y Z
X
(T) imposed pressure
O
Face YZ
(T)
function of effort
7
8
Z
1.2
Material properties
isotropic elasticity
E = 200.000 MPa
= 0,3
plasticity Said Taheri
Cinf = 0.065 MPa
C1 = - 0.012 Mpa
S = 450
B = 30
m = 0.1
has = 312
= 0.3
Ro = 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.
T (S)
0.
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-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
3/10
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”)


-

p = O
-
éq 2.1 1

E


-

p = O


-
éq 2.1 2

F
p -
p = 0
-
éq 2.1 3

F
p -
p

= 0
-
éq 2.1 4
3 F
F
F
F

-
-
Kx
Cs
2
Ky
Cs
HR
D has
Z
2
2 (
+
) - (+
)
(
)
-
-





N
F
4
N
F
3 F
N
F
N


(


p - p)



+ (p - p)

2
JR
3
p 2 (Qx

C p)
(Qy

C p)

+
+
+
+
+
p




F
F
= -

-

2
-
O
O



éq 2.1 5

C
3
3

1+


JR +
C
2

2


(S
N
N
N
N
- +
-


p
p
p)
C
p
(S p p p)
U
p
p
2








(- 2)
4

N
F
N
F
- HR + has D Z


(- + -
p
p)
(p p)
KX
3
+




CS 3

N
F
+ 3
C



(S - + (
N
F
-

0
-
p
p
p)
p
p
p)
2C S
p
éq 2.1 6
U
2
2






=
with
and



p
U
= b1-



S

X = C (S
N
-
p
p
p)

C - C

v
=
N

C
Y
= C

(S -
p
p
p)


1 - D
1/2

-

9 2
2
up W =
D = 1 - me

D
U

=
X + 3 Y



4


-
C = C - C E up

1


R

=

(Da Z +r) 0
LP
K = v U
Q = v

1/2
S


2
4
2
Z =

(N
N
-
+ -
p
p)
(p p)

LP



3


H = W U
J = W


S
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
4/10
with the initial conditions:

R
()
()
0
0
=
/

(2
1 2
O + 3 2
O)



()
0
= ()
0
O
88
. 88. 0

E



from where (T =)

1
=
88.
0
0
O



()
0
= ()
0



0
0
0



(
p)
0
= ()
0
N
p
= p = 0

R ()
0
= (1 -)
m ro = (O)

p
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
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
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Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
5/10
Intentionally white left page.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
6/10
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D:
Cubic elementary with a grid using a hexahedron with 8 nodes.
F
y
22 NR
F
1
2
F
T
F
1s
5
F
6
2F
3
has
X
4
F
2F
7
8
F
Z
3.2
Characteristics of the grid
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
MATRICE
“TANGENTE”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
7/10
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

0.01678
0.01677
­ 0.04
p

0.02515
0.02516
0.04
p
p
0.03356
0.03354
­ 0.06

176.00000
175.99999
­ 0.0001
p
4.2 Remarks
The limitation with 10 of the maximum number of local iterations is very sufficient for a method of
Exact NEWTON 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
Obstruction memory:
8 MW
Time CPU To use:
18 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
8/10
5 Modeling
B
5.1
Characteristics of modeling
Modeling in plane constraints 2D
y
F
N04
N03
F
F (T)
44 NR
X
2F
N01
N02
F
T
1 S
5.2
Characteristics of the grid
Square quadrangle with 4 nodes in plane constraints 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
MATRICE
“TANGENTE”
CONVERGENCE
TYPE_MATR_COMP
“TANG_VIT”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
9/10
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

0.01678
0.016784
0.02
p

0.02515
0.025156
0.02
p
p
0.03356
0.03354
­ 0.06

176.
175.9998
­ 0.0001
p
6.2 Parameters
of execution
Version: 03.02.11
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
16 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSNV102 Essai of tensile shearing with the method of S. TAHERI
Date:
04/02/98
Author (S):
P. SCHOENBERGER
Key:
V6.04.102-A Page:
10/10
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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/96/044 - Ind A