Code_Aster ®
Version
5.0
Titrate:
SSNV142 - Essai of clean creep (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB Key
:
V6.04.142-B Page:
1/6
Organization (S): EDF/AMA
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
Document: V6.04.142
SSNV142 - Clean Essai of creep: 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 model 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 constraint, the temperature and the hygroscopy.
In this test, the constraint, the temperature and the hygrometrical state are constant.
The cylinder is modelled by four elements quadrangles with 8 nodes.
The results obtained by Code_Aster are compared with the analytical solution of reference.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV142 - Clean Essai of creep (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB Key
:
V6.04.142-B Page:
2/6
1
Problem of reference
1.1 Geometry
Cylindrical test-tube
Z
D
C
D
a=1 m
has
R
With
B
has
1.2
Material properties
Isotropic elasticity
Relation of clean behavior of creep
E = 31000 MPa
“Granger”.
= 0.2
J1 = 0.2 MPa1
1 = 4320000 S
J2 = 0.1 MPa1
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: uz = 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.
D
1
T (S)
t0=0
t1=10
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV142 - Clean Essai of creep (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB Key
:
V6.04.142-B Page:
3/6
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.
0
0
0
That is to say the loading: 0 () 0
D T
0
0
0
The clean model of creep of Granger is such as the viscoelastic deformation corresponding to the case
of a constant loading 0 applied to the moment t0 is worth: (cf [R7.01.01])
K =8
T - T
fl (T) =
0
0 Jk (1 - exp-)
K =1
S
The model also depends on the temperature and the hygroscopy in the following way:
K
-
=8
248
T - T
fl
T
(T) =
0
0 H
Jk (1 - exp-
45
)
K =1
S
but in this test the fields of temperature and hygroscopy are selected constant and such as H and
T - 248 are worth 1 respectively.
45
When the constraint evolves/moves with time then:
K =8 T
T -
D
fl (T) = Jk (1 - exp-)
K =1
S
D
=0
one thus has for the case present:
T
2 =t
K =
1
fl
T -
1
yy =
Jk (1 - exp-) D
K =1
S
T
T =
1
0
the loading remaining constant beyond T1.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV142 - Clean Essai of creep (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB Key
:
V6.04.142-B Page:
4/6
That is to say:
K =2
fl
T - T
1
T
K
1
yy = 1 Jk 1 - exp-
1 - exp-
K =1
S T1
S
1442
4 443
4
~1
A longitudinal deflection of creep is accompanied by a transverse deformation such as:
fl
fl
xx =
- yy
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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV142 - Clean Essai of creep (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB Key
:
V6.04.142-B Page:
5/6
3 Modeling
With
3.1
Characteristics of modeling
Y
D3
N2
N5
N7
N3
N6
N4
N8
N1
N17
D4
N15
D2
N10 N11
N16
N9
N14
N21
N13 N12
N20
N19 N18
X
D1
The loading and the boundary conditions are modelled by:
FACE_IMPO: (GROUP_MA: D1, DY: 0.)
PRES_REP: (GROUP_MA: D3, PRES: 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 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 grid
A number of nodes:
21
A number of meshs and types: 4 HEXA8
3.3 Functionalities
tested
Commands
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
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV142 - Clean Essai of creep (Granger model)
Date:
23/09/02
Author (S):
J. EL GHARIB Key
:
V6.04.142-B Page:
6/6
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
flxx
5 0.80862 0.80862 0.
fl
5 4.04313 4.04313 0.
yy
fl
50 5.9701 1.19402 0.
xx
fl
50
1.19402
5.9701
0.
yy
flxx
74 1.19946 1.19946 0.
fl
74 5.99730 5.99730 0.
yy
5
Summary of the results
The results obtained with Code_Aster are close to those of the reference solution (variations
< 0.05%)
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal systems
HT-66/02/001/A
Outline document