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Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/IMA/MN













Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.133



SSNV133 - Uniaxial traction and compression.
Mixed work hardening




Summary:

The purpose of this test is to validate the elastoplastic behaviors
VMIS_ECMI_TRAC
and
VMIS_ECMI_LINE
, which
combine an isotropic work hardening (linear or given by a traction diagram) and a work hardening
linear kinematics.

The geometrical and mechanical data make it possible to be in uniaxial situation (uniform stresses, one
only nonnull component). The reference solution is simple, analytical. This test allows simply
to check that the integration of the model of behavior is correct.

3 modelings make it possible to check the uniaxiality of the stresses: 3D, AXIS, C_PLAN.
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Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
y
X
1
2
3
4
1 mm
1 mm

1.2
Material properties
Elastoplastic law of behavior to mixed work hardening (isotropic linear and kinematic linear).
1.5C
y
E
E
T
C
E
E
Y
T
=
=
=
=
=
20000
200000
0 3
400
40000
MPa
MPa
MPa
MPa

.

1.3
Boundary conditions and loadings
The plate is locked according to
OY
along the side [3,4], following
OX
along the side [1,3] while being
subjected to a displacement imposed in y:
U
y
D
along the side [1,2].
The way of loading is as follows:
T
U
y
D
(mm)
1 2.
10
­ 3
2.4.5d3
3.0.1d3
4 ­ 2.
10
­ 3
background image
Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is obtained by an analytical calculation.
Imposed displacement
U
y
D
provides the deformation immediately
yy
y
D
U
= 1
. Only this
component (corresponding to the nonnull component of the tensor of the stresses) interests us here.
In addition, to calculate the behavior, it is necessary to extract from the data the function of work hardening
isotropic R (p):
3 2
C
()
T
p
p
E
= -
()
C
p
With
With
y
()
()
T
y
T
T
y
T
T
F
E E
E E p
R p
E E
E E
C p
=
=
+
-
=
+
-
-




.
.
.
3
2

2.1.1 T = 1: elastic behavior
Indeed, the behavior is elastic until t=1. For t=1,
yy
yy
E
MPa
=
= 400
reached it just
threshold of plasticity.
2.1.2 T = 2: elastoplastic load
When one reaches the criterion of plasticity (in load or discharge), one a:
(
)
-
=
=
-
3
2 C
R p
E
p
p
()
For the load, it is necessary to solve
()
T
y
T
T
y
T
T
T
F
E E
E E p
E E
E E
E
=
=
+
-
=
+
-
-
.
.
(
)
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Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
what gives again:
T
y
T
y
E
E
=
+
-
(
)
: one moves on the traction diagram up to the point such
that:
(
)
With
T
With
With
p
E
=
-
2.1.3 T = 3: discharge elastic
The discharge is elastic up to the A' point:
(
)
-
+
=
=
-
With
With p
With
With
With
With p
C
R p
E
'
'
'
(
)
3
2
2.1.4 T = 4: elastoplastic load in compression
()
C
p
C
R p
=
-
3
2

2.2
Results of Reference
T
U
y
D
(mm)
yy
(MPa)
1 2.
10
­ 3
400
2.4.5d3 500
3.0.1d3 ­ 380
4 ­ 2.
10
­ 3
­ 464



2.3
Uncertainty on the solution
Analytical solution.

2.4 References
bibiographic
[1]
Relation of behavior to linear and isotropic work hardening kinematic nonlinear. Note
[R5.03.16].
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Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
5/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling
AXIS

3.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 1 QUAD4

3.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU TRACTION
SIGM
[U4.23.01]
PRAGER
C
STAT_NON_LINE COMP_INCR RELATION
VMIS_ECMI_TRAC
[U4.32.01]


4
Results of modeling A
4.1 Values
tested

Identification Moments Reference
Aster %
difference
yy
1
400.400 0
yy
2
500.500 0
yy
3
­ 380 ­ 380 0
yy
4
­ 464 ­ 464 0

4.2 Parameters
of execution
Version: 5.1
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
128 Mo
Time CPU To use:
5 seconds
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Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
6/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
Z
X
y
N07
N05
N06
N08
N03
N01
N02
N04
5.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and types: 1 HEXA8 + 4 QUAD4 (faces)
5.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU ECRO_LINE D_SIGM_EPSI
[U4.23.01]
SY
PRAGER
C
STAT_NON_LINE COMP_INCR RELATION
VMIS_ECMI_LINE
[U4.32.01]

6
Results of modeling B
6.1 Values
tested
Identification Moments
Reference
Aster %
difference
yy
1
400.400 0
yy
2
500.500 0
yy
3
­ 380 ­ 380 0
yy
4
­ 464 ­ 464 0
6.2 Parameters
of execution
Version: 5.1
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
128 Mo
Time CPU To use:
5 seconds
background image
Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling
Modeling
C_PLAN

7.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 1 QUAD4

7.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU TRACTION
SIGM
[U4.23.01]
PRAGER
C
STAT_NON_LINE COMP_INCR RELATION
VMIS_ECMI_TRAC
[U4.32.01]


8
Results of modeling C
8.1 Values
tested

Identification Moments Reference
Aster %
difference
yy
1
400.400 0
yy
2
500.500 0
yy
3
­ 380 ­ 380 0
yy
4
­ 464 ­ 464 0

8.2 Parameters
of execution
Version: 5.1
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
128 Mo
Time CPU To use:
6 seconds
background image
Code_Aster
®
Version
5.1
Titrate:
SSNV133 - Uniaxial traction and compression. Mixed work hardening
Date:
03/01/00
Author (S):
J.M. PROIX
Key
:
V6.04.133-A
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
9
Summary of the results
The results provided by Code_Aster coincide with the values of reference, because the test is
uniaxial, and the stress and strain state is homogeneous.