Code_Aster
®
Version
7.2
Titrate:
SSNP113 - Rotation of the main stresses (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
V6.03.113-B
Page:
1/6
Manual of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA, DeltaCAD
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.113
SSNP113 - Rotation of the main stresses
(law of MAZARS)
Summary:
This case test of mechanics is inspired by work of Willam [bib1] and was used in the benchmark
EDF/Division R & D “Model three-dimensional of non-linear behaviors of the material concrete in
cracking “[bib2] to evaluate the models of behavior dedicated to the concrete. It is characterized by a way
of specific loading which creates a continuous rotation of the main stresses. It is used here to test
establishment of the model of Mazars in its local version (modeling
3D
) and in its delocalized version
(modeling
3d_GRAD_EPSI
). The validation is carried out by comparison with the results obtained with
code CASTEM 2000 with the LGCNSN (Central School of Nantes).
Code_Aster
®
Version
7.2
Titrate:
SSNP113 - Rotation of the main stresses (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
V6.03.113-B
Page:
2/6
Manual of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A
1
Problem of reference
1.1
Geometry and boundary conditions
length of the edges: has = 0.56 m, thickness 0.1 m
Appear 1.1-a: Geometry and boundary conditions
The loading is such as one obtains a homogeneous state of plane forced stress and type
even if modeling in Aster were carried out in 3D. The loading is imposed in the form of
displacements imposed in two stages:
1) direction
(
xx
,
yy
,
xy
) = (1, -
, 0)
until the maximum stress
(initiation of the lenitive phase)
2) direction
(
xx
,
yy
,
xy
) = (1, 1.5, 1) until
xx
= 0.0015
-
xx
: displacement on the side delimited by the side
3
2
P
P
-
in direction OX
-
yy
: displacement on the side delimited by the side
4
3
P
P
-
in direction OY
-
xy
: displacement on the side delimited by the side
3
2
P
P
-
in direction OY
That is to say P5P6P7P8 the plan of the cube in z=0.1.
Practically, the following conditions are imposed
· during all the loading: P1P4P8P5: dx = 0
P1: Dy = dz = 0
P5: Dy = 0
· during phase 1:
P2, P6: Dy = 0
P2P3P7P6: dx = 1
P3P4P8P7: Dy = - 0.2
· during phase 2:
P2P3P7P6: dx = 1
P4, P8: Dy = 1.5
P3, P7: Dy = 3.5
P2, P6: Dy = 2.
1.2
Properties of material
For the model of Mazars, the following parameters were used:
Elastic behavior:
2
.
0
,
000
32
=
=
MPa
E
Damaging behavior:
06
.
1
;
000
10
;
3
.
1391
;
8
.
0
;
15
.
1
;
10
.
375
.
9
4
0
=
=
=
=
=
=
-
LT
Bc
At
Ac
D
P1
P4
P3
P2
y
X
Code_Aster
®
Version
7.2
Titrate:
SSNP113 - Rotation of the main stresses (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
V6.03.113-B
Page:
3/6
Manual of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A
2
Reference solution
It is about a comparison code-code. The reference used is the code Castem2000 (version 2001).
The results were obtained by the LGCNSN (Central School of Nantes) with the same parameters
materials and same discretization in time. Contrary to the calculation carried out with Code_Aster, it
Castem calculation was carried out in 2D under the assumption of plane stresses.
The delocalized version of the model of Mazars was tested with a null length characteristic of
way to check that one finds the same results as with the local version.
3 References
bibliographical
[1]
Willam K., Pramono E. and Sture S. - Fundamental exits off smeared ace models, Proc. off
the Int. Conf. one fractures and concrete and rock'n'roll, Huston Texas, 1987, p 17-19
[2]
CR-99-232, concrete tests Evaluation one models off non-linear behavior off cracking using
three dimensional modelling, Benchmark EDF/Division R & D S. Ghavamian
Code_Aster
®
Version
7.2
Titrate:
SSNP113 - Rotation of the main stresses (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
V6.03.113-B
Page:
4/6
Manual of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A
4 Modeling
With
4.1
Characteristics of modeling
Modeling 3D
Element MECA_HEXA8
4.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and type: 1 HEXA8
4.3 Functionalities
tested
The law of behavior MAZARS local version in 3D.
5
Results of modeling A
One compares with 3 pitches times different (at the end from stage 1, during the phase of growth of
the damage and at the end of the loading) strains, stresses as well as the value of
the damage.
Identification Reference
Aster %
difference
N°10
xx
9.375 10
5
9.375 10
5
5.8
10
14
xx
3.00 10
6
3.00 10
6
4.7
10
14
yy
1.875 10
5
1.875 10
5
9.0
10
14
yy
0.
2.83 10
10
2.83 10
10
xy
0. 0.
-
xy
0.
0. -
D
0. 2.22
10
16
2.22
10
16
Identification Reference
Aster %
difference
N°25
xx
1.64 10
4
1.64 10
4
0.065
xx
2.04 10
6
2.04 10
6
- 0.048
yy
8.67 10
5
8.68 10
5
0.099
yy
1.35 10
6
1.35 10
6
- 0.016
xy
7.03 10
5
7.04 10
5
0.081
xy
6.34 10
5
6.33 10
5
- 0.016
D
0.66211 0.66238
0.040
Identification Reference
Aster
%
difference
N°310
xx
1.50 10
3
1.50 10
3
0.06
xx
3.69 10
5
3.69 10
5
- 0.002
yy
2.09 10
3
2.09 10
3
0.064
yy
4.59 10
5
4.59 10
5
5.22 10
4
xy
1.41 10
3
1.41 10
3
0.063
xy
2.16 10
5
2.16 10
5
6.85 10
4
D
0.99423 0.99424 8.07
10
4
Code_Aster
®
Version
7.2
Titrate:
SSNP113 - Rotation of the main stresses (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
V6.03.113-B
Page:
5/6
Manual of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A
6 Modeling
B
6.1
Characteristics of modeling
The use of the delocalized version of the model of Mazars passes by the use of modeling
3d_GRAD_EPSI and implies the use of quadratic elements.
The test is carried out with a null characteristic length.
Modeling: 3d_GRAD_EPSI
Element: MGCA_HEXA20
6.2
Characteristics of the mesh
A number of nodes:20
A number of meshs and type: 1 HEXA20
6.3 Functionalities
tested
The law of behavior of Mazars in delocalized.
7
Results of modeling B
One compares with 3 pitches times different (at the end from stage 1, during the phase of growth of
the damage and at the end of the loading) strains, stresses as well as the value of
the damage.
Identification Reference
Aster %
difference
N°10
xx
9.375 10
5
9.375 10
5
2.02
10
13
xx
3.00 10
6
3.00 10
6
- 2.33
10
13
yy
1.875 10
5
1.875 10
5
5.42
10
14
yy
0.
5.98 10
10
5.98 10
10
xy
0. 6.88
10
21
6.88 10
21
xy
0.
0. -
D
0. 3.88
10
15
3.88
10
15
Identification Reference
Aster %
difference
N°25
xx
1.64 10
4
1.64 10
4
0.038
xx
2.04 10
6
2.04 10
6
- 1.89
10
4
yy
8.67 10
5
8.67 10
5
0.022
yy
1.35 10
6
1.35 10
6
- 3.39 10
4
xy
7.03 10
5
7.03 10
5
0.018
xy
6.34 10
5
6.34 10
5
1.4 10
5
D
0.66211 0.66211
- 1.88
10
4
Identification Reference
Aster %
difference
N°310
xx
1.50 10
3
1.50 10
3
2.02 10
13
xx
3.69 10
5
3.69 10
5
9.02 10
5
yy
2.09 10
3
2.09 10
3
2.39 10
4
yy
4.59 10
5
4.59 10
5
- 8.66 10
5
xy
1.41 10
3
1.41 10
3
1.23 10
13
xy
2.16 10
5
2.16 10
5
7.66 10
5
D
0.99423 0.99423
4.42
10
4
Code_Aster
®
Version
7.2
Titrate:
SSNP113 - Rotation of the main stresses (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
V6.03.113-B
Page:
6/6
Manual of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A
8
Summary of the results
With very weak variations of about 0.05% to the maximum on the stresses in the phase
non-linear and about 0.002% after complete damage on a test where
loadings are not radial, one can consider that the establishment of the model of Mazars too
well in local version that not-local, is faithful to the original model.