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SSNP502 - Ecrasement of a polyurethane ring between 2 Date plates
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01/09/05
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S. LAMARCHE, Mr. TORKHANI, NR. TARDIEU
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V6.03.502-B Page:
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Organization (S): EDF-R & D/AMA
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.502
SSNP502 - Ecrasement of a ring in
polyurethane between two indeformable plates
with friction

Summary:

The test consists in simulating crushing in plane constraints 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 a zone 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 modelled with meshs QUAD4 in plane constraints:

·
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.

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A

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SSNP502 - Ecrasement of a polyurethane ring between 2 Date plates
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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 constraints 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.
Handbook of Validation
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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 grids used are 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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A

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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 grid of an indeformable plate includes/understands.



Boundary condition:
Conditions of symmetry: the nodes of group LAB located in the X=0 plan are blocked according to
direction X (DX= 0),

the nodes of group LCD located in the Y=0 plan are blocked according to
direction Y (DY= 0),

all the nodes of the group of mesh “Plaque” are blocked 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 grid was carried out in cm.

3.2
Characteristics of the grid

A number of nodes: 291
A number of meshs and type: 241 QUAD4 and 51 SEG2
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3.3 Functionalities
tested

Commands 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.

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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 grid of an indeformable plate.



Boundary condition:
Conditions of symmetry: the nodes of group LAB located in the X=0 plan are blocked according to
direction X (DX= 0),
the nodes of group LCD located in the Y=0 plan are blocked according to
direction Y (DY= 0),
all the nodes of the group of mesh “Plaque” are blocked 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 grid was carried out in cm.
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HT-66/05/005/A

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5.2
Characteristics of the grid

The grid is in any point identical to the grid used for modeling A.

5.3 Functionalities
tested

Commands 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.

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HT-66/05/005/A

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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 grid of an indeformable plate includes/understands.



Boundary condition:
Conditions of symmetry: the nodes of group LAB located in the X=0 plan are blocked according to
direction X (DX= 0),
the nodes of group LCD located in the Y=0 plan are blocked according to
direction Y (DY= 0),
all the nodes of the group of mesh “Plaque” are blocked 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 grid was carried out in cm.
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V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A

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7.2
Characteristics of the grid

The grid 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 modifications of the grid what implies this
strategy.

7.3 Functionalities
tested

Commands Key word
factor Word-key
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
RELATION = “ELAS”


DEFORMATION = ' GREEN'
SOLVEUR
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.
Handbook of Validation
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HT-66/05/005/A

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9
Summary of the results

Whatever the type of modeling of the zone 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 grid 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 zone
of contact are identical between the two computer codes.

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A

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