Code_Aster ®
Version
7.2
Titrate:
SSNP113 - Rotation of the principal constraints (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
V6.03.113-B Page:
1/6

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

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.113

SSNP113 - Rotation of the principal constraints
(law of MAZARS)

Summary:

This case test of mechanics is inspired by work of Willam [bib1] and was used in the benchmark
Three-dimensional EDF/Division R & D “Modèles 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 principal constraints. 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 (Ecole Centrale of Nantes).

Handbook of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP113 - Rotation of the principal constraints (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
V6.03.113-B Page:
2/6

1
Problem of reference

1.1
Geometry and boundary conditions

P4
P3

y
length of the edges: has = 0.56 m, thickness 0.1 m

X

P
P

1
2

Appear 1.1-a: Géométrie and boundary conditions

The loading is such as one obtains a homogeneous state of plane forced constraint 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 constraint
(initiation of the lenitive phase)
2) direction
(xx, yy, xy) = (1, 1.5, 1) up to xx = 0.0015

-
xx: displacement on the side delimited by side 2
P - 3
P in direction OX
-
yy: displacement on the side delimited by side 3
P - 4
P in direction OY
-
xy: displacement on the side delimited by side 2
P - 3
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:
E = 32.000 MPa, = 2
.
0
Damaging behavior:

=
.
375
.
9
10 4
-; Ac = 15
.
1
; At = 8
.
0; Bc =
3
.
1391; LT = 10.000;
06
.
1
D 0
=

Handbook of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP113 - Rotation of the principal constraints (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
V6.03.113-B Page:
3/6

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 (Ecole Centrale 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 constraints.
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, Evaluation tests one models off non-linear behavior off cracking concrete using
three dimensional modelling, Benchmark EDF/Division R & D ­ S. Ghavamian
Handbook of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP113 - Rotation of the principal constraints (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
V6.03.113-B Page:
4/6

4 Modeling
With

4.1
Characteristics of modeling

Modeling 3D
Element MECA_HEXA8

4.2
Characteristics of the grid

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 steps 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
9.375 10­5
9.375 10­5 5.8
10­14
xx
3.00 106
3.00 106 4.7
10­14
yy
­ 1.875 10­5
­ 1.875 10­5 9.0
10­14
yy
0.
­ 2.83 10­10
­ 2.83 10­10
xy
0. 0.
-
xy
0.
0. -
D
0. 2.22
10­16 2.22
10­16

Identification Reference
Aster %
difference
N°25 xx
1.64 10­4
1.64 10­4 0.065
xx
2.04 106
2.04 106 - 0.048
yy
8.67 10­5
8.68 10­5
0.099
yy
1.35 106
1.35 106
- 0.016
xy
7.03 10­5
7.04 10­5
0.081
xy
6.34 105
6.33 105
- 0.016
D
0.66211 0.66238
0.040

Identification Reference
Aster
%
difference
N°310 xx
1.50 10­3
1.50 10­3
0.06
xx
3.69 105
3.69 105
- 0.002
yy
2.09 10­3
2.09 10­3
0.064
yy
4.59 105
4.59 105
5.22 10­4
xy
1.41 10­3
1.41 10­3
0.063
xy
2.16 105
2.16 105
6.85 10­4
D
0.99423 0.99424 8.07
10­4

Handbook of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP113 - Rotation of the principal constraints (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
V6.03.113-B Page:
5/6

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 grid

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 steps 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
9.375 10­5
9.375 10­5 2.02
10­13
xx
3.00 106
3.00 106 - 2.33
10­13
yy
­ 1.875 10­5
­ 1.875 10­5 5.42
10­14
yy
0.
5.98 10­10
5.98 10­10
xy
0. 6.88
10­21
6.88 10­21
xy
0.
0. -
D
0. 3.88
10­15 3.88
10­15

Identification Reference
Aster %
difference
N°25 xx
1.64 10­4
1.64 10­4 0.038
xx
2.04 106
2.04 106 - 1.89
10­4
yy
8.67 10­5
8.67 10­5
0.022
yy
1.35 106
1.35 106
- 3.39 10­4
xy
7.03 10­5
7.03 10­5
0.018
xy
6.34 105
6.34 105
1.4 10­5
D
0.66211 0.66211
- 1.88
10­4

Identification Reference
Aster %
difference
N°310 xx
1.50 10­3
1.50 10­3
2.02 10­13
xx
3.69 105
3.69 105
9.02 10­5
yy
2.09 10­3
2.09 10­3
­ 2.39 10­4
yy
4.59 105
4.59 105
- 8.66 10­5
xy
1.41 10­3
1.41 10­3
1.23 10­13
xy
2.16 105
2.16 105
7.66 10­5
D
0.99423 0.99423
4.42
10­4
Handbook of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
SSNP113 - Rotation of the principal constraints (law of MAZARS)
Date:
19/02/04
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
V6.03.113-B Page:
6/6

8
Summary of the results

With very weak variations of about 0.05% to the maximum on the constraints 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.

Handbook of Validation
V6.03 booklet: Non-linear statics of the plane systems
HT-66/04/005/A

Outline document