Code_Aster ®
Version
7.2
Titrate:
SSNP123 - Plaque notched in elastoplasticity


Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX Key
:
V6.03.123-B Page:
1/6

Organization (S): EDF-R & D/AMA
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
V6.03.123 document

SSNP123 - Plaque notched in elastoplasticity (test
elements QUAD4 under integrated)

Summary:

This test 2D in plane deformations quasi-static makes it possible to illustrate the questions relating to the incompressibility
during the use of an elastoplastic law of behavior: when the rate of plasticity becomes important, of
nonphysical oscillations of constraints can appear. It is shown that the use of elements QUAD4
under integrated can allow to mitigate this problem.

It is about a notched rectangular plate made up of an elastoplastic material with isotropic work hardening
who is subjected to a traction at his ends. One is interested in the elastoplastic solution in load.

Modeling A corresponds to the use of elements QUAD4 under integrated stabilized by the method
“assumed strain”.

Modeling B corresponds to the use of the incompressible elements QUAD8 which make it possible to obtain one
reference solution.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP123 - Plaque notched in elastoplasticity


Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX Key
:
V6.03.123-B Page:
2/6

1
Problem of reference

1.1 Geometry

This calculation is based on the modeling of a notched sample requested by an imposed displacement.

Imposed displacement: DY = 0.1
F G
5
With
1
D
B
5

1.2
Material properties

Elastoplastic behavior with isotropic work hardening:

E
E = 200 GPa
T
= 0.4999

y
y = 200 MPa
E
AND = 1000 MPa

1.3
Boundary conditions and loadings

On data base: DY=0.
On DF: DX=0.
On FG: DY=0.1

2
Reference solution

The reference solution is given by the modeling B carried out with elements
quasi-incompressible.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP123 - Plaque notched in elastoplasticity


Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX Key
:
V6.03.123-B Page:
3/6

3 Modeling
With

3.1
Characteristics of modeling

Modeling C_PLAN with elements QUAD4 under integrated stabilized by the method assumed
strain.

3.2
Characteristics of the grid

A number of nodes: 527

A number of meshs: 582
SEG2: 102
QUAD4: 480



3.3 Functionalities
tested

Commands



AFFE_MODELE MODELING “D_PLAN_SI”
STAT_NON_LINE COMP_INCR
“VMIS_ISOT_LINE”


3.4
Sizes tested and results

One tests co-ordinate SIYY of the tensor of the constraints in various points of path IJ

I J


ABS. Curv.
Reference
Code_Aster
Difference (%)
0.0 234.174
234.930
0.323
1.54051 257.417 257.208 - 0.081
3.26795 300.333 298.685 - 0.549
3.83403 263.212 261.746 - 0.557
4.37942 175.829 173.440 - 1.359

One carries out also a test of nonregression on the values above.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP123 - Plaque notched in elastoplasticity


Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX Key
:
V6.03.123-B Page:
4/6

4 Modeling
B

4.1
Characteristics of modeling

One takes again the preceding grid which one passes in quadratic elements with an aim of using
modeling D_PLAN_INCO (elements adapted to the incompressible problems).

4.2
Characteristics of the grid

A number of nodes: 1533

A number of meshs: 582
SEG3: 102
QUAD8: 480

4.3 Functionalities
tested

Commands


AFFE_MODELE MODELING “D_PLAN_INCO”

STAT_NON_LINE COMP_INCR
“VMIS_ISOT_LINE”


4.4
Sizes tested and results

One tests co-ordinate SIYY of the tensor of the constraints in various points of path IJ in not
regression.

ABS. Curv.
Reference
Code_Aster
Difference (%)
0.0 234.174
234.174
1.30E-04
1.54051 257.417 257.417
1.14E-04
3.26795 300.333 300.333
1.60E-04
3.83403 263.212 263.212
2.31E-05
4.37942 175.829 175.829
9.19E-05

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP123 - Plaque notched in elastoplasticity


Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX Key
:
V6.03.123-B Page:
5/6

5
Summary of the results

The result obtained using elements QUAD4 under integrated stabilized by the method assumed
strain is very close to that provided by the incompressible quadratic elements, as it can
to note on the graph below. This graph gathers the results for various elements:

QUAS4 elements QUAD4 under integrated
QUAD4 traditional elements QUAD4
QUAD8 traditional elements QUAD8
QUAS8 quasi incompressible elements QUAD8

One thus notes the good quality of the solution given by elements QUAD4 under integrated and
disappearance of the oscillations of constraints given by traditional elements QUAD4.

350
300
250
200
150
[Mpa]
yy 100
50
0
- 50
0
1
2
3
4
5
6
X-coordinate
QUAS4
QUAD4
QUAD8
QUAS8


Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP123 - Plaque notched in elastoplasticity


Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX Key
:
V6.03.123-B Page:
6/6

Intentionally white left page.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A

Outline document