Code_Aster
®
Version
4.0
Titrate:
SSLP102 Rate of refund of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A
Page:
1/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
Document: V3.02.102
SSLP102 - Rate of refund of energy with
initial deformations (Lagrangian propagation)
Summary
This test makes it possible to calculate the rate of refund of energy G for a static problem of mechanics in
plane deformations with initial deformations by a Lagrangian method of propagation of fissure and of
to check the stability of the calculation of G with initial deformations on 4 different crowns of integration.
This test contains a modeling in plane deformations.
Code_Aster
®
Version
4.0
Titrate:
SSLP102 Rate of refund of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A
Page:
2/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
1
Problem of reference
1.1 Geometry
It is about a rectangular plate with side fissure (one represents only half of the structure).
H
I
With
has
C
O
B
D
X
y
Height plates: H = 200.
Width plates: I = 100.
Length fissures: has = 50.
1.2
Material properties
Young modulus:
E= 2.10
4
MPa
Poisson's ratio:
= 0.3
We place ourselves on the assumption of the plane deformations.
1.3
Boundary conditions and loadings
·
Displacements for A < X < I: y = 0. : v = 0.
0 < X < I: y = H.: v = 0.
·
Not fix b: U = v = 0.
·
Initial deformations:
(
)
xx
yy
zz
F X
=
=
=
()
Code_Aster
®
Version
4.0
Titrate:
SSLP102 Rate of refund of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A
Page:
3/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The results of reference result from a test WILSON and YU [bib1] or from a calculation of J (integral from
Rice) in thermo elasticity in the cards of the ECA [bib2] whose characteristics are as follows:
()
=
°
=
=
°
=
=
-
5 10
2
100
20 000
0 3
6
/
/
,
.
C
T X
To X L
To
C
E
MPa
One thus imposes
xx
yy
zz
F
To X L
=
=
=
=
1
2
/
2.2
Results of references
The result for J in card ECA (Code CASTEM 2000) is J = 0.390 kgf/mm (not of indication on
contours).
The results resulting from WILSON and YU vary for five different contours:
1
0.392
2
0.362
3
0.369
4
0.361
5
0.371
2.3 References
bibliographical
[1]
The Uses off J-Integrals in thermal stress ace problems - International Newspaper off Fracture
(1979) WILSON and YU.
[2]
Breaking process, methods numerical for engineer IPSI November 18-20, 1986,
card-index validation CASTEM p 47-48
Code_Aster
®
Version
4.0
Titrate:
SSLP102 Rate of refund of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A
Page:
4/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Y
X
With
0
The initial deformations are such as:
5.10
- 4
F (X)
X
50.
3.2
Characteristics of the mesh
A number of nodes: 853
A number of meshs and types: 359
TRIA6
and 27
QUAD8
3.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
EPSI_INIT
[U4.25.01]
CALC_MATR_ELEM
RIGI_MECA_LAGR
[U4.41.01]
CALC_VECT_ELEM
[U4.41.02]
CALC_G_THETA
OPTION
CALC_G_LAGR
[U4.63.03]
Code_Aster
®
Version
4.0
Titrate:
SSLP102 Rate of refund of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A
Page:
5/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
4
Results of modeling A
4.1 Values
tested
J Reference
G
Identification
J: CASTEM
WILSON and YU
Aster
% difference
contour 1
0.195 *
0.196
0.180
9%
contour 2
0.181
0.180
0.5%
contour 3
0.184
0.180
2%
contour 4
0.180
0.180
0%
* not of indication on contour corresponding to this value.
4.2 Remarks
It is necessary to multiply by 2 the rough results since one accounted for 1 half-structure (in one
half-crown).
The method of calculation used for this result (ECA) is the integral J. the results of J resulting from
WILSON and YU are close to the result
Aster
(less than 2%) except for crown 1 (or contour 1
in the case of J).
The classification of contours or the crowns corresponds to an order ascending of the radius of these
the last
4.3 Parameters
of execution
Version: 3.06
Machine: CRAY C90
System: UNICOS
8.0
Overall dimension memory:
8 megawords
Time CPU To use:
22 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLP102 Rate of refund of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A
Page:
6/6
Manual of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
5
Summary of the results
The variation of the results of G with the values of 5 data in WILSON and YU is less than 2%
except for smallest contour where the variation reaches 9%. No indication of contour is mentioned for
the single value indicated in card CASTEM, this value is very close to that of WILSON and YU
for smallest contour. The invariance of G following the crown is excellent for calculation
Aster
.
Let us note the difference in modeling between this test where deformations directly are imposed
initial and results of reference where these deformations are induced by an imposed temperature.
The mesh corresponds to this case test is also appreciably finer than that used for
results of reference.