Code_Aster
®
Version
7.2
Titrate:
SSNP123 - Plate notched in elastoplasticity
Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX
Key
:
V6.03.123-B
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
V6.03.123 document
SSNP123 - Plate 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 stresses 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.
Code_Aster
®
Version
7.2
Titrate:
SSNP123 - Plate notched in elastoplasticity
Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX
Key
:
V6.03.123-B
Page:
2/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
This calculation is based on the modeling of a notched sample requested by an imposed displacement.
5
5
1
Imposed displacement: DY = 0.1
With
B
D
F G
1.2
Material properties
Elastoplastic behavior with isotropic work hardening:
E = 200 GPa
= 0.4999
y
= 200 MPa
E
T
= 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.
y
E
E
T
Code_Aster
®
Version
7.2
Titrate:
SSNP123 - Plate notched in elastoplasticity
Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX
Key
:
V6.03.123-B
Page:
3/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A
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 mesh
A number of nodes: 527
A number of meshs: 582
SEG2: 102
QUAD4: 480
3.3 Functionalities
tested
Controls
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 stresses in various points of path IJ
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.
I J
Code_Aster
®
Version
7.2
Titrate:
SSNP123 - Plate notched in elastoplasticity
Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX
Key
:
V6.03.123-B
Page:
4/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A
4 Modeling
B
4.1
Characteristics of modeling
One takes again the preceding mesh 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 mesh
A number of nodes: 1533
A number of meshs: 582
SEG3: 102
QUAD8: 480
4.3 Functionalities
tested
Controls
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 stresses 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
Code_Aster
®
Version
7.2
Titrate:
SSNP123 - Plate notched in elastoplasticity
Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX
Key
:
V6.03.123-B
Page:
5/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A
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
conventional elements QUAD4
QUAD8
conventional 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 stresses given by conventional elements QUAD4.
- 50
0
50
100
150
200
250
300
350
0
1
2
3
4
5
6
X-coordinate
yy
[Mpa]
QUAS4
QUAD4
QUAD8
QUAS8
Code_Aster
®
Version
7.2
Titrate:
SSNP123 - Plate notched in elastoplasticity
Date:
06/05/04
Author (S):
NR. TARDIEU, J.M. PROIX
Key
:
V6.03.123-B
Page:
6/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/04/005/A
Intentionally white left page.