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