Code_Aster
®
Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
1/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.182
SSNV182 Bloc with interface in rubbing contact
with X-FEM
Summary
The purpose of this test is to validate the taking into account of the contact on the lips of the fissure, while being limited if
the fissure crosses the structure completely. The contact is taken into account by the method continues [bib1]
adapted to the framework of method X-FEM [bib2].
This test brings into play a parallelepipedic block in compression. The interface the beam is represented by one
levet set within the framework of X-FEM. One takes into account several angular positions of the interface: = 0°
(the interface follows the faces of the elements) and = 22.5° (the interface cuts the elements). By taking a coefficient
of friction of sufficiently high Coulomb so that there is adherence, one finds the solution of same
problem without interface.
Code_Aster
®
Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
2/10
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
The structure is a right at square base and healthy parallelepiped. Dimensions of the block
(see [Figure 1.1-a]) are: LX = 5 m, LY = 20 m and LZ = 20 Mr. It does not comprise any fissure.
The interface is introduced by functions of levels (level sets) directly into the file
order using operator DEFI_FISS_XFEM [U4.82.08]. The interface is present in the middle of
the structure by the means of its representation by the level sets. The level set normal (LSN) allows
to define a plane interface forming an angle with the Oxy plan by the following equation:
)
(
LSN
B
aY
Z
+
-
=
éq 1.1-1
where
has
is the slope of the interface, that is to say
2
2
and
)
tan (
LY
has
LZ
B
has
-
=
-
=
.
Appear 1.1-a: Geometry of the bar and positioning of the interface
1.2
Properties of material
Young modulus: E= 100 MPa
Poisson's ratio:
= 0.
1.3
Boundary conditions and loadings
The nodes of the lower face of the bar are embedded and a displacement
UZ
=
- 10
- 6
m is
imposed on those of the higher face which corresponds to a loading in pressure along axis Z.
Displacements along axes X and are locked there for the nodes of the upper surface.
Code_Aster
®
Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
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V6.04 booklet: Nonlinear statics of the voluminal structures
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1.4
Characteristics of the mesh
The structure is modelized by a regular mesh composed of 5x20x20 HEXA8 [Figure 1.4-a].
Appear 1.4-a: Mesh
This mesh is composed of linear finite elements. However, within the framework of the continuous method
[bib1] with X-FEM [bib2], it is necessary to pass to a little special linear elements. These
elements have linear functions of form and a quadratic mesh support. On these elements, them
nodes node carry the unknown factors of displacement, and the nodes medium carry the dependant unknown factors
with the contact. Moreover, when the interface follows the edge of an element, its nodes node carry too
unknown factors of contact.
Code_Aster
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Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
2
Modeling a: interfaces right
In this modeling, one represents a right interface, the angle is worth 0 then. The interface coincides
with the faces of certain finite elements.
2.1 Resolution
analytical
The interface being right, and the state of uniaxial pressing and normal to the interface, it does not have there
possible slip. The solution of the problem is that of the same problem without interface.
The stress in the structure is:
LZ
UZ
E
zz
=
éq 2.1-1
and the value of the contact pressure on the interface is:
zz
=
éq 2.1-2
With the numerical values previously introduced, =
- 5.0 AP.
2.2 Functionalities
tested
Controls
DEFI_FISS_XFEM CONTACT
This case does not require the activation of friction. Under the key word CONTACT of the operator
DEFI_FISS_XFEM, one stipulates FROTTEMENT=' SANS' then.
Moreover, as of the first iteration of the active stresses, one makes the assumption that the points of contact
have a contacting statute. This is possible by specifying CONTACT_INIT=' OUI'.
If not, at the end of the first iteration, the contact not being activated, the higher block re-enters in
lower block but the two blocks did not become deformed. Their state of stresses is thus null, and it
is then necessary to choose a total criterion (RESI_GLOB_MAXI) for the convergence of the algorithm of
Newton-Raphson [bib3], criterion which is likely to be unsuited in the continuation of calculations when the contact
will be activated.
To avoid that, and to have a relative criterion, one needs a state of stresses not no one as of the first
iteration, and thus to activate the contact as of the beginning.
The algorithm of the active stresses thus converges in an iteration.
Code_Aster
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Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
3
Results of modeling A
3.1 Values
tested
One tests the values of the normal pressure of contact after convergence of the iterations of
operator STAT_NON_LINE and of the loop on the active stresses. One tests all the points of
contact, which corresponds to the nodes of the mesh on the interface. It is checked that one finds them well
values determined with [§2.1].
Identification Reference
Aster %
difference
LAGS_C for all the nodes of
the interface
- 5.00
- 5.00
0.00
To test all the nodes in only once, the MIN and the MAX of the column are tested.
3.2 Comments
This modeling shows the possibilities of the continuous method of contact applied to the framework
X-FEM. The advantage is that the procedure of pairing is intrinsic with method X-FEM since
here, there are not really surface Master and slave considering whom one has only one surface.
Code_Aster
®
Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
6/10
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
4
Modeling b: interfaces leaning
In this modeling, one represents a leaning interface. The angle is worth 22.5°, that is to say a slope
has
being worth
- 1/2. The interface does not coincide any more with the faces of the finite elements, and cuts them now
elements. The normal with the interface is noted
N
and the tangent vector is noted
:
-
=
=
5
1
5
2
0
,
5
2
5
1
0
N
éq 4-1
4.1 Resolution
analytical
The interface being leaning, it is likely y to have slip. To avoid that, one forces adherence in
choosing a coefficient of friction of sufficiently high Coulomb. Theoretically, it is enough to
to take:
()
µ
tan
>
éq 4.1-1
Thus, the solution of the problem remains identical to that of the same problem without interface.
The stress in the structure is always that of [éq 2.1-1], and the value of the contact pressure
on the interface is a function of the normal
N
with the interface:
Z
zz
Z
N
N
=
=
N
N
éq
4.1-2
where
Z
N
is the component according to
Z
of
N
.
The semi-multiplier of friction
is defined by:
R
µ
=
éq 4.1-3
With the density of tangential stress being written as follows:
(
)
N
R
=
éq 4.1-4
From where:
N
N
N
=
=
Z
Z
N
µ
µ
1
1
éq
4.1-5
One takes
µ
= 1.
With the numerical values previously introduced,
5
.
0
and
AP
0
.
4
-
=
-
=
.
4.2 Functionalities
tested
Controls
DEFI_FISS_XFEM CONTACT
This case requires the activation of friction. Under the key word CONTACT of the operator
DEFI_FISS_XFEM, one stipulates FROTTEMENT=' COULOMB' then.
Code_Aster
®
Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
5
Results of modeling B
5.1 Values
tested
One tests the values of the normal pressure of contact and the semi-multiplier of friction afterwards
convergence of the iterations of operator STAT_NON_LINE, the loop on the active stresses and
loop on the thresholds of friction. All the points of contact are tested. It is reminded the meeting that these
points of contact can be of two kinds: either of the nodes node, or of the nodes medium,
according to whether the interface cuts or not the elements.
It is checked that one finds well the values determined with [§4.1]. LAGS_F1 corresponds to
semi-multiplier of friction in direction OX (it is thus null), whereas LAGS_F2 corresponds
with the semi-multiplier of following friction
.
Identification Reference
Aster %
difference
LAGS_C for all the points of contact
- 4.00
- 4.00
0.00
LAGS_F1 for all the points of contact
0.00
2.10
- 14
0.00
LAGS_F2 for all the points of contact
- 0.50
- 0.50
0.00
To test all the points of contact in only once, the MIN and the MAX of the column are tested.
5.2 Comments
Let us specify that in this study, the key word CONTACT_INIT = “YES” makes it possible to begin the loop
on the active stresses with an assumption of statute contacting for all the points of contact.
That authorizes to take a relative criterion (“RESI_RELA_MAX”) for the convergence of the iterations of
Newton. Indeed, if one selected CONTACT_INIT = “NOT”, at the time of the phase of prediction of Newton, it
contact not being activated, the higher structure moves without becoming deformed, and that lower
remain motionless. The stresses are then null and a relative criterion is not usable, only a criterion
total is, whose value is left with the choice of the user. The problem is that this value can
to reveal calculation (active contact thereafter….) inadequate with the loadings and the stresses then in
play. Thus, it is to better provide to take a single relative criterion as of the beginning.
Moreover, the initial value of the threshold of friction was taken with
- 10
11
in order to be sure that one has
adherence as of the 1
era
iteration on the thresholds of friction.
Code_Aster
®
Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
8/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
6
Modeling C: interface right and under-integration
This modeling is exactly the same one as modeling A, except that the diagram of integration
numerical the terms of contact changed.
In modeling A, one uses a diagram of Gauss at 12 points by triangular breakages of
contact. In modeling C, one only uses a diagram reduced to 4 points.
Indeed, the diagram must allow the exact integration of a constant field of pressure. The intégrande
on the breakage is then a students'rag procession in
3
with
+ J
I
y
X
I
I
.
According to [bib4], a diagram at 4 points of Gauss is enough.
6.1 Functionalities
tested
Controls
DEFI_FISS_XFEM CONTACT
INTEGRATION=' FPG4'
7
Results of modeling C
7.1 Values
tested
One tests the same values as for modeling A.
Identification Reference
Aster %
difference
LAGS_C for all the points of contact
- 5.00
- 5.00
0.00
LAGS_F1 for all the points of contact
0.00
0.00
0.00
LAGS_F2 for all the points of contact
0.00
0.00
0.00
To test all the nodes of the interface in only once, one tests the values min and max.
7.2 Comments
This modeling shows that a diagram of integration reduced to 4 points makes it possible to pass the patch test
where the solution in pressure is constant.
Code_Aster
®
Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
9/10
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
8
Summaries of the results
The objectives of this test are achieved:
·
It is a question of showing the feasibility of the taking into account of the contact rubbing on the lips of
fissure with the method continues adapted to framework X-FEM. Only the case of a fissure
crossing the structure completely was considered (interface).
·
The cases where the interface follows the border of the elements (= 0°) and where the interface cut them
elements (= 22.5°) were validated.
9 Bibliography
[1]
MASSIN P., BEN DHIA H., ZARROUG Mr.: Elements of contacts derived from a formulation
continuous hybrid, Manual of reference of Code_Aster, [R5.03.52]
[2]
MASSIN P., GENIAUT S.: Method X-FEM, Manual of reference of Code_Aster, [R7.02.12]
[3]
TARDIEU NR., VAUTIER I., LORENTZ E.: Quasi-static nonlinear algorithm, Manual of
Reference of Code_Aster, [R5.03.01]
[4]
DHATT G., TOUZOT G.: A presentation of the finite element method, Maloine ED.,
PARIS
Code_Aster
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Version
8.2
Titrate:
SSNV182 Bloc in contact with X-FEM
Date:
25/11/05
Author (S):
S. GENIAUT, P. MASSIN
Key
:
V6.04.182-B
Page:
10/10
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
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