Code_Aster ®
Version
4.0
Titrate:
SSLP102 Taux of restitution of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
Document: V3.02.102
SSLP102 - Taux of restitution 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 Lagrangienne 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.
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLP102 Taux of restitution of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A Page:
2/6
1
Problem of reference
1.1 Geometry
It is about a rectangular plate with side fissure (one represents only half of the structure).
y
I
B
D
H
With
O
C
X
has
Height plates: H = 200.
Width plates: I = 100.
Length fissures: has = 50.
1.2
Material properties
Young modulus:
E= 2.104 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))
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLP102 Taux of restitution of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A Page:
3/6
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 6/° C
T (X) = 2 To X/L
To =
°
100 C
E = 20.000MPa, = 0 3
.
One thus imposes
=
=
= 1 =
xx
yy zz F
2 To X/L
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 Use off J-Integrals in thermal stress ace problems - International Journal 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
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLP102 Taux of restitution of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
Y
0
With
X
F (X)
5.10-4
X
50.
The initial deformations are such as:
3.2
Characteristics of the grid
A number of nodes: 853
A number of meshs and types: 359 TRIA6 and 27 QUAD8
3.3 Functionalities
tested
Commands
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]
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLP102 Taux of restitution of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A Page:
5/6
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. Les results of J resulting from
WILSON and YU are close to the Aster result (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
Obstruction memory:
8 megawords
Time CPU To use:
22 seconds
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSLP102 Taux of restitution of energy with initial deformations
Date:
19/01/98
Author (S):
G. DEBRUYNE
Key:
V3.02.102-A Page:
6/6
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 Aster calculation.
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 grid corresponds to this case test is also appreciably finer than that used for
results of reference.
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HI-75/96/016 - Ind A