Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
1/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.502
SSNP502 - Crushing of a ring in
polyurethane between two indeformable plates
with friction
Summary:
The test consists in simulating crushing in plane stresses of an elastic circular polyurethane ring
by two indeformable symmetrical plates. The objective is to test the functionalities related to the contact. This test
comprise a sticking together on an area of contact important length with the presence of large
elastic strain.
A symmetrical imposed displacement is applied to the two plates; the resulting force as well as the pressure
of contact for various points in contact are compared with the results obtained in the article of
reference.
In three modelings suggested, the ring is modelized with meshs QUAD4 in plane stresses:
·
modeling A, a contact node-meshs (CONTACT) with friction treated with the method
Lagrangian was defined between the plate and the ring,
·
modeling B, a contact node-meshs (CONTACT) with friction treated with the method of
penalization was defined between the plate and the ring,
·
modeling C, a contact node-meshs (CONTACT) with friction treated with the method
continue was defined between the plate and the ring.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
2/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
radius external of the ring
6,35 cm
interior radius of the ring
4,15 cm
imposed displacement
4,45 cm
1.2
Properties of material
Ring: polyurethane, elastic law of behavior.
Young modulus:
E= 407 NR/cm ²
Poisson's ratio:
= 0,48
Coefficient of friction:
µ = 0,4
1.3
Boundary conditions and loadings
The stresses are plane.
An incremental displacement imposed from 0 to 4,45 cm is applied to the nodes of the plates
indeformable.
Notice on the units:
Dimensions and displacements are in centimetres thus, to remain homogeneous, them
pressures must have entered in NR/cm ².
1.4 Conditions
initial
None.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
3/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The solution results from a computer code and an experimental test.
For the reference solution valid for a modeling of the whole plate, it is necessary to divide
normal resultant by two to obtain a reference valid for a half-plate.
2.2
Results of reference
The normal force of reaction is as follows:
Imposed displacement (cm)
Force reaction (NR)
1,1125 8,0083
2,2250 16,0166
3,3375 24,0250
4,4500 32,0333
The normal pressure of contact is bench-mark datum. But, the mesh used is different.
This pressure will be used to define tests of not-regression.
2.3
Uncertainties on the solution
These results are relatively approximate bus directly raised on the curve paper.
2.4 References
bibliographical
[1]
A.F. SALEEB, K. CHEN, and T.Y.P. CHANG: “Year effective two dimensional frictional contact
model for arbitrary curved geometry " - Int. J. Num. Meth. Eng. 37 (1994) p. 1297-1321.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
4/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
A modeling testing the functionalities of contact node (CONTACT) with friction treated with
the Lagrangian method was implemented. Taking into account the symmetry of the problem, it
a quarter of the ring as well as the mesh of an indeformable plate includes/understands.
Boundary condition:
Conditions of symmetry: the nodes of group LAB located in the X=0 plan are locked according to
direction X (DX= 0),
the nodes of group LCD located in the Y=0 plan are locked according to
direction Y (DY= 0),
all the nodes of the group of mesh “Plate” are locked according to
direction X (DX= 0)
To avoid the rigid movements of body, nodes A and P1 have even vertical displacement.
Loadings:
Imposed displacement following Y on all the nodes of the plate: DY varies from 0 to 2,225 cm.
(the value of 4,45 cm is the vertical bringing together of the two symmetrical plates.)
Note:
The mesh was carried out in cm.
3.2
Characteristics of the mesh
A number of nodes: 291
A number of meshs and type: 241 QUAD4 and 51 SEG2
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
5/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
3.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
MODI_MAILLAGE ORIE_PEAU_2D
DEFI_MATERIAU ELAS
AFFE_CHAR_MECA
CONTACT
METHOD = “LAGRANGIAN”
FRICTION = “COULOMB”
STAT_NON_LINE
COMP_ELAS
RELATION = “ELAS”
DEFORMATION = ' GREEN'
4
Results of modeling A
4.1 Values
tested
Identification Displacements
Reference Aster
% difference
force reaction (NR)
1,1125 cm
8,01
8,66
8,13
force reaction (NR)
2,2250 cm
16,02
16,46
2,77
force reaction (NR)
3,3375 cm
24,02
23,98
0,18
force reaction (NR)
4,4500 cm
32,03
31,32
0,88
4.2 Remarks
One can visualize the influence of friction by looking at the shear stress to the nodes in
contact. It is necessary to make the difference between SIXY with friction and SIXY without friction to eliminate them
problems of averages on the nodes of the edge.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
6/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
5 Modeling
B
5.1
Characteristics of modeling
A modeling testing the functionalities of contact node-meshs (CONTACT) with friction
treaty with the method of penalization was implemented. Taking into account the symmetry of the problem,
it includes/understands a quarter of the ring as well as the mesh of an indeformable plate.
Boundary condition:
Conditions of symmetry: the nodes of group LAB located in the X=0 plan are locked according to
direction X (DX= 0),
the nodes of group LCD located in the Y=0 plan are locked according to
direction Y (DY= 0),
all the nodes of the group of mesh “Plate” are locked according to
direction X (DX= 0)
To avoid the rigid movements of body, nodes A and P1 have even vertical displacement.
Loadings:
Imposed displacement following Y on all the nodes of the plate: DY varies from 0 to 2,225 cm.
(the value of 4,45 cm is the vertical bringing together of the two symmetrical plates.)
Note:
The mesh was carried out in cm.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
7/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
5.2
Characteristics of the mesh
The mesh is in any point identical to the mesh used for modeling A.
5.3 Functionalities
tested
Controls Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
DEFI_MATERIAU ELAS
AFFE_CHAR_MECA DDL_IMPO
CONTACT
METHOD = “PENALIZATION”
FRICTION = “COULOMB”
E_T = “1.E+06”
STAT_NON_LINE COMP_ELAS
RELATION = “ELAS”
DEFORMATION = ' GREEN'
6
Results of modeling B
6.1 Values
tested
Identification Displacements
Reference Aster
% difference
force reaction (NR)
1,1125 cm
8,01
8,66
8,13
force reaction (NR)
2,2250 cm
16,02
16,46
2,77
force reaction (NR)
3,3375 cm
24,02
23,98
0,18
force reaction (NR)
4,4500 cm
32,03
31,32
0,88
6.2 Notice
The results are very close to those of modeling A.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
8/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
7 Modeling
C
7.1
Characteristics of modeling
A modeling testing the functionalities of contact node-meshs (CONTACT) with friction
treated with the method continues was implemented. Taking into account the symmetry of the problem, it
a quarter of the ring as well as the mesh of an indeformable plate includes/understands.
Boundary condition:
Conditions of symmetry: the nodes of group LAB located in the X=0 plan are locked according to
direction X (DX= 0),
the nodes of group LCD located in the Y=0 plan are locked according to
direction Y (DY= 0),
all the nodes of the group of mesh “Plate” are locked according to
direction X (DX= 0)
To avoid the rigid movements of body, nodes A and P1 have same vertical displacement.
Loadings:
Imposed displacement following Y on all the nodes of the plate: DY varies from 0 to 2,225 cm.
(the value of 4,45 cm is the bringing together vertical of the two symmetrical plates).
Note:
The mesh was carried out in cm.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
9/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
7.2
Characteristics of the mesh
The mesh results from the file “ssnp501b.mail” in which the meshs of ends A and D were
withdrawn from the group of mesh LESC.
Note:
The method continues does not accept the amendments of the mesh what implies this
strategy.
7.3 Functionalities
tested
Controls Key word
factor Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
DEFI_GROUP CREA_GROUP_NO UNION
DEFI_MATERIAU ELAS
AFFE_CHAR_MECA
CONTACT
METHOD = “CONTINUES”
AFFE_CHAR_MECA CONTACT
SEUIL_INIT = 0.1
AFFE_CHAR_MECA DDL_IMPO
STAT_NON_LINE COMP_ELAS
SOLVEUR
RELATION = “ELAS”
DEFORMATION = ' GREEN'
METHOD = “LDLT”
RENUM = “WITHOUT”
8
Results of modeling C
8.1 Values
tested
Identification Displacements
Reference Aster
% difference
force reaction (NR)
1,1125 cm
8,01
8,66
8,13
force reaction (NR)
2,2250 cm
16,02
16,46
2,77
force reaction (NR)
3,3375 cm
24,02
23,98
0,18
force reaction (NR)
4,4500 cm
32,03
32,31
0,88
8.2 Notice
The results are very close to those to modelings A and B.
Code_Aster
®
Version
8.1
Titrate:
SSNP502 - Crushing of a polyurethane ring between 2 plates
Date
:
01/09/05
Author (S):
S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
Key:
V6.03.502-B
Page:
10/10
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
9
Summary of the results
Whatever the type of modeling of the area of contact, the results obtained are satisfactory.
The variations observed on the force of reaction are weak. But the values of reference are very
approximate because they are extracted from a curve paper.
The mesh of the code computer taken in reference and that used by Aster are different. Moreover, it is not
not explained in the reference how is extracted the normal pressure from contact. Thus, it does not have
summer carried out of tests of reference on this pressure. However tests of not-regression are
carried out on the contact pressure (SIYY to the node in contact). Pace of this pressure and the area
of contact are identical between the two computer codes.