Code_Aster ®
Version
8.1
Titrate:
SSNP118 - Validation of the element of joint


Date:
29/06/05
Author (S):
J. LAVERNE Key
:
V6.03.118-B Page:
1/4

Organization (S): EDF-R & D/AMA

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.118

SSNP118 - Validation of the element of joint in 2D
plan

Summary:

Validation of the element of joint plane 2D with a cohesive law of behavior: CZM_EXP_REG and a control
of elastic prediction type. Comparison between the results and the analytical solution.

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

Code_Aster ®
Version
8.1
Titrate:
SSNP118 - Validation of the element of joint


Date:
29/06/05
Author (S):
J. LAVERNE Key
:
V6.03.118-B Page:
2/4

1
Problem of reference

1.1 Geometry

cubic on L=1mm side
element of joint

U = (2.167302, 1.251293)

T
y

N

= 30°

X

1.2
Properties of material

Cubic: rubber band
E = 0.5 MPa,
= 0

Element of joint: cohesive law of behavior: CZM_EXP_REG with:



tenacity:
Gc = 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 joint.
Displacements imposed on the right face of the cube.

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

Code_Aster ®
Version
8.1
Titrate:
SSNP118 - Validation of the element of joint


Date:
29/06/05
Author (S):
J. LAVERNE Key
:
V6.03.118-B Page:
3/4

2
Reference solution

2.1
Method of calculation

The cohesive law of behavior: CZM_EXP_REG gives the relations between the normal constraint and
tangential in the element of joint and the jump in the element:

[U] [loc
U
loc
] N
the jump in the element is noted:

=

[loc
U
] T




[loc
U
] - C [locu]
N
G


C
C
E
loc


[loc
U
]


loc
N
the constraint in the element:



=
=


loc

T
[loc
U
] - C [locu]

T
C
G

E
C [loc
U
]





loc
U

[loc
U
]
[loc
U
] = [loc
U
]
[loc
U
]
a normal loading is carried out: N

thus
= 0
>
T
and
N (if
0
N
)
0


- C [loc
U]

N
loc
G

From where:
=
C
it




0


loc
U N = [loc
U
]
And like
+
N
L elast

One has
U loc
N
= - (Gc/c) ln (loc
N/c)
loc
+
L/E
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:

U loc = RtU
loc

= Rt R
cos - sin
with R =

and = 30°
sin
cos

One checks that for a loading U = (2.
,
167302 1.251293) there is a constraint
= 0.075
XX

loc
01. 0
knowing that
loc
U
= (2.
,
502585 0) and
=

check [éq 2.1-1].
0 0
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNP118 - Validation of the element of joint


Date:
29/06/05
Author (S):
J. LAVERNE Key
:
V6.03.118-B Page:
4/4

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 joint.

The cube is a QUAD4.
The element of joint is a degenerated QUAD4 (confused nodes).

3.2
Characteristics of the grid

A number of nodes: 6
Numbers and type of meshs: 2 QUAD4.

3.3 Functionalities
tested

Commands



STAT_NON_LINE COMP_INCR
RELATION
CZM_EXP_REG
PILOTAGE
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 (%)
in the element
7.5E-02
7.49999794404E-02
2.74E-05
XX

4.2 Remarks

·
The law of behavior of the element of joint 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.
·
Control 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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/05/005/A

Outline document