Code_Aster
®
Version
5.0
Titrate:
SSNV142 - Clean creep test (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB
Key
:
V6.04.142-B
Page:
1/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
Document: V6.04.142
SSNV142 - Clean creep test: Granger model
Summary:
This case-test of nonlinear quasi-static mechanics relates to a creep test on a cylinder
axisymmetric. It aims to validate the relation of behavior of “Granger”, relation of
behavior which one introduced into Code_Aster to modelize the clean creep of the concretes. This model
is a linear viscoelastic model (grouping of rheological models of Kelvin in series) which allows
to take into account the history of the stress, the temperature and the hygroscopy.
In this test, the stress, the temperature and the hygrometrical state are constant.
The cylinder is modelized by four elements quadrangles with 8 nodes.
The results obtained by Code_Aster are compared with the analytical solution of reference.
Code_Aster
®
Version
5.0
Titrate:
SSNV142 - Clean creep test (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB
Key
:
V6.04.142-B
Page:
2/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Cylindrical test-tube
R
Z
D
has
has
a=1 m
With
B
C
D
1.2
Material properties
Isotropic elasticity
E = 31000 MPa
= 0.2
Relation of clean behavior of creep
“Granger”.
J
1
= 0.2 MPa
1
1
= 4320000 S
J
2
= 0.1 MPa
1
2
= 2160000 S
One does not take account of the phenomenon of ageing in the relation of behavior of
Granger.
1.3
Boundary conditions and loadings
On side AB: U
Z
= 0
One uniformly imposes on the structure a constant temperature of T = 20°C and a hygroscopy
constant h=1.
Loading: one charges in traction of 0 to 20 MPa into 10 S. And one maintains the loading during
1 year.
T
0
=0
T
1
=10
T (S)
D
1
Code_Aster
®
Version
5.0
Titrate:
SSNV142 - Clean creep test (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB
Key
:
V6.04.142-B
Page:
3/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Being given the nature of the stresses, the solution (forced
, deformations
) is homogeneous.
That is to say the loading:
0
0
0
0
0
0
0
0
D
T
()
The clean model of creep of Granger is such as the viscoelastic deformation corresponding to the case
of a constant loading
0 applied at the moment T
0
is worth: (cf [R7.01.01])
fl
K
S
K
K
T
J
T T
()
(
exp
)
=
-
- -
=
=
0
0
1
8
1
The model also depends on the temperature and the hygroscopy in the following way:
fl
K
S
K
K
T
H T
J
T T
()
(
exp
)
=
-
-
- -
=
=
0
0
1
8
248
45
1
but in this test the fields of temperature and hygroscopy are selected constant and such as
H
and
T
-
248
45
are worth 1 respectively.
When the stress evolves/moves with time then:
fl
K
S
T
K
K
T
J
T
D
D
()
(
exp
)
=
-
- -
=
=
=
1
0
1
8
one thus has for the case present:
yy
fl
K
S
T
T T
K
K
J
T
T D
=
-
- -
=
=
=
=
(
exp
)
1
1
1
0
1
2
1
the loading remaining constant beyond T
1.
Code_Aster
®
Version
5.0
Titrate:
SSNV142 - Clean creep test (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB
Key
:
V6.04.142-B
Page:
4/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
That is to say:
yy
fl
K
S
K
K
K
S
J
T T
T
T
=
-
- -
-
-
=
=
1
1
1
2
1
1
1
1
1
exp
exp
~
1
2
44
4
3
444
A longitudinal deflection of creep is accompanied by a transverse deformation such as:
xx
fl
yy
fl
= -
2.2
Results of reference
One will be interested in the values of the deformations of creep in 45 days, 245 days and 365 days.
Code_Aster
®
Version
5.0
Titrate:
SSNV142 - Clean creep test (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB
Key
:
V6.04.142-B
Page:
5/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
X
Y
D1
D3
D4
D2
N20
N19 N18
N17
N16
N15
N14
N13 N12
N11
N10
N9
N8
N7
N6
N5
N4
N3
N2
N1
N21
The loading and the boundary conditions are modelized by:
FACE_IMPO: (GROUP_MA: D1, DY: 0.)
PRES_REP: (GROUP_MA: D3, NEAR: function)
One imposes moreover one uniform and constant temperature of 20°C and a uniform field of drying
and constant of 1 on the structure using the operator
AFFE_CHAM_NO
. The curve of
sorption-desorption (user datum) makes it possible to pass from the variable drying to the hygroscopy.
3.2
Characteristics of the mesh
A number of nodes:
21
A number of meshs and types: 4 HEXA8
3.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
DEFI_MATERIAU
GRANGER_FP
AFFE_CHAM_NO
AFFE_CHAR_MECA
FACE_IMPO
PRES_REP
TEMP_CALCULEE
SECH_CALCULE
STAT_NON_LINE
COMP_INCR
RELATION
GRANGER_FP
CALC_ELEM
OPTION
EPGR_ELNO
Code_Aster
®
Version
5.0
Titrate:
SSNV142 - Clean creep test (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB
Key
:
V6.04.142-B
Page:
6/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
One tests the values with the sequence numbers corresponding to 45, 245 and 365 days
Variables number
of command
Reference
Aster %
difference
xx
fl
5 0.80862 0.80862 0.
yy
fl
5 4.04313 4.04313 0.
xx
fl
50 5.9701 1.19402 0.
yy
fl
50
1.19402
5.9701
0.
xx
fl
74 1.19946 1.19946 0.
yy
fl
74 5.99730 5.99730 0.
5
Summary of the results
The results obtained with Code_Aster are close to those of the reference solution (variations
< 0.05%)