Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.133
SSNV133 - uniaxial Traction-compression.
Mixed work hardening
Summary:
The purpose of this test is to validate 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 constraints, 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 constraints: 3D, AXIS, C_PLAN.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
2/8
1
Problem of reference
1.1 Geometry
y
1
2
1 mm
3
4
X
1 mm
1.2
Material properties
Elastoplastic law of behavior to mixed work hardening (isotropic linear and kinematic linear).
C
= 20000
MPa
AND
E
= 200000
y
MPa
= 0 3
.
Y
= 400
MPa
E
1.5C
E
= 40000
MPa
T
1.3
Boundary conditions and loadings
The plate is blocked 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 D along the side [1,2].
y
The way of loading is as follows:
T
U D (mm)
y
1 2.
103
2.4.5d3
3.0.1d3
4 2.
103
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is obtained by an analytical calculation.
D
uy
Displacement imposed U D provides the deformation immediately
=
. Only this
y
yy
1
component (corresponding to the nonnull component of the tensor of the constraints) 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):
With
T (p)
y
3C 2
p = - E
With
C (p)
T
E.E
= F () =
T
y +
p
E - AND
E.E
3
R (p) =
T
y +
- C. p
E - AND 2
2.1.1 T = 1: elastic behavior
Indeed, the behavior is elastic until t=1. For t=1,
=
yy
E yy = 400MPa reaches just it
threshold of plasticity.
2.1.2 T = 2: elastoplastic load
When one reaches the criterion of plasticity (in load or discharge), one a:
3
-
C p = R (p)
2
= E (- p)
T
E.E
E.E
T
T
For the load, it is necessary to solve T = F () = +
p = +
(-
)
y
y
E - E
E - E
E
T
T
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
4/8
y
what gives again: T = + E (-
): one moves on the traction diagram up to the point such
y
T
E
that:
T = (- p
E
With
With
With)
2.1.3 T = 3: discharge elastic
The discharge is elastic up to the A' point:
3
- A' +
p
C
=
With
R (Pa)
2
A' = E (A' - p
With)
2.1.4 T = 4: elastoplastic load in compression
3
C =
p
C
- R (p)
2
2.2
Results of Référence
T
U D (mm)
(MPa)
y
yy
1 2.
103 400
2.4.5d3 500
3.0.1d3 380
4 2.
103 464
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].
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
5/8
3 Modeling
With
3.1
Characteristics of modeling
Modeling AXIS
3.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 QUAD4
3.3 Functionalities
tested
Commands
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
Obstruction memory:
128 Mo
Time CPU To use:
5 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
6/8
5 Modeling
B
5.1
Characteristics of modeling
Z
N07
N05
N08
N06
y
N03
N01
N04
N02
X
5.2
Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 1 HEXA8 + 4 QUAD4 (faces)
5.3 Functionalities
tested
Commands
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
Obstruction memory:
128 Mo
Time CPU To use:
5 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
7/8
7 Modeling
C
7.1
Characteristics of modeling
Modeling C_PLAN
7.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 QUAD4
7.3 Functionalities
tested
Commands
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
Obstruction memory:
128 Mo
Time CPU To use:
6 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.1
Titrate:
SSNV133 - uniaxial Traction-compression. Mixed work hardening
Date:
03/01/00
Author (S):
Key J.M. PROIX
:
V6.04.133-A Page:
8/8
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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Outline document