Code_Aster
®
Version
8.1
Titrate:
SSNP118 - Validation of the element of gasket
Date:
29/06/05
Author (S):
J. LAVERNE
Key
:
V6.03.118-B
Page:
1/4
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: V6.03.118
SSNP118 - Validation of the element of gasket in 2D
plan
Summary:
Validation of the element of gasket plane 2D with a cohesive law of behavior: CZM_EXP_REG and a piloting
of elastic prediction type. Comparison between the results and the analytical solution.
Code_Aster
®
Version
8.1
Titrate:
SSNP118 - Validation of the element of gasket
Date:
29/06/05
Author (S):
J. LAVERNE
Key
:
V6.03.118-B
Page:
2/4
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
1.2
Properties of material
Cubic: rubber band
E = 0.5 MPa,
= 0
Element of gasket: cohesive law of behavior: CZM_EXP_REG with:
tenacity:
C
G
= 1 NR/mm
(key word: GC)
critical stress:
C
=1 MPa
(key word: SIGM_C)
penalization of adherence PENA_ADHERENCE = 10
- 3
mm
(key word: PENA_ADHERENCE)
(small parameter of regularization of energy in 0, to see [R7.02.11])
penalization of the contact
PENA_CONTACT = 1 (default value) (key word: PENA_CONTACT)
1.3
Boundary conditions and loadings
Null displacements imposed on the left face of the element of gasket.
Displacements imposed on the right face of the cube.
= 30°
T
N
U
= (2.167302, 1.251293)
y
X
cubic on L=1mm side
element of gasket
Code_Aster
®
Version
8.1
Titrate:
SSNP118 - Validation of the element of gasket
Date:
29/06/05
Author (S):
J. LAVERNE
Key
:
V6.03.118-B
Page:
3/4
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
The cohesive law of behavior: CZM_EXP_REG gives the relations between the normal stress and
tangential in the element of gasket and the jump in the element:
the jump in the element is noted:
[] []
[]
=
T
loc
N
loc
loc
U
U
U
the stress in the element:
[]
[]
[]
[]
[]
[]
=
=
-
-
loc
C
C
loc
C
C
U
G
loc
T
loc
C
U
G
loc
N
loc
C
loc
T
loc
N
loc
E
U
U
E
U
U
a normal loading is carried out:
0
loc
N
U
thus
[]
0
=
T
loc
U
and
[] []
N
loc
loc
U
U
=
(if
[]
0
>
N
loc
U
)
From where:
[]
=
-
0
N
loc
C
C
U
G
C
loc
E
And like
[]
elast
N
loc
loc
N
L
U
U
+
=
One has
(
)
(
)
E
L
ln
G
U
loc
N
C
loc
N
C
C
loc
N
/
/
/
+
-
=
éq
2.1-1
This last relation is used to compare the analytical values with the numerical results.
2.2
Sizes and results of reference
In the local reference mark of the element one a:
R
R
U
R
U
T
loc
T
loc
=
=
with
-
=
cos
sin
sin
cos
R
and
= 30°
One checks that for a loading
(
)
251293
.
1
,
167302
.
2
=
U
there is a stress
0.075
XX
=
knowing that
(
)
0
,
502585
.
2
=
loc
U
and
=
0
0
0
1
0.
loc
check [éq 2.1-1].
Code_Aster
®
Version
8.1
Titrate:
SSNP118 - Validation of the element of gasket
Date:
29/06/05
Author (S):
J. LAVERNE
Key
:
V6.03.118-B
Page:
4/4
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
Modeling in plane deformations for the cube on side 1.
Modeling plan fissures (key word PLAN_JOINT) for the element of gasket.
The cube is a QUAD4.
The element of gasket is a degenerated QUAD4 (confused nodes).
3.2
Characteristics of the mesh
A number of nodes: 6
Numbers and type of meshs: 2 QUAD4.
3.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR
RELATION
CZM_EXP_REG
PILOTING
PRED_ELAS
AFFE_MODELE MODELING PLAN_JOINT
DEFI_MATERIAU RUPT_FRAG
SIGM_C
PENA_ADHERENCE
4
Results of modeling A
4.1
Sizes tested and results
Size tested
Theory
Code_Aster
Difference (%)
XX
in the element
7.5E-02
7.49999794404E-02
2.74E-05
4.2 Remarks
·
The law of behavior of the element of gasket is given locally (reference mark (N, T)), calculations
system are carried out in the total reference mark (X, y). The basic change was taken in
count in calculations. The case test was developed with a rotation of 30° with an aim of
to validate this basic change.
·
Piloting was tested, one arrives has to follow the unstable branch of the total curve (force,
imposed displacement).
5
Summary of the results
The numerical results are in agreement with the theory.