Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/MMC
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
Document: V6.04.181
SSNV181 - Checking of the good taking into account
shearing in the model
BETON_UMLV_FP
Summary:
This test makes it possible to validate the good taking into account of shearing in the law of behavior
BETON_UMLV_FP
. The results of this test are compared with an analytical solution.
Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
Z
X
y
L
H
E
Height:
H = 1,00 [m]
Width:
L = 1,00 [m]
Thickness:
E = 1,00 [m]
1.2
Properties of material
31
=
E
[GPa] modulus of elasticity
2
,
0
=
Poisson's ratio
Parameters specific to clean creep:
5
20
,
1
+
=
E
K
Sr
[MPa]
spherical part: rigidity connects associated with the skeleton formed by
blocks of hydrates on a mesoscopic scale
4
22
,
6
+
=
E
K
S
I
[MPa]
spherical part: rigidity connects intrinsically associated with
hydrates on a microscopic scale
4
86
,
3
+
=
E
K
D
R
[MPa]
deviatoric part: rigidity associated with the capacity with water adsorbed with
to transmit loads (load bearing toilets)
10
21
,
2
+
=
E
S
R
[MPa.s]
spherical part:viscosity connects associated with the mechanism with
dissemination within capillary porosity
10
16
,
4
+
=
E
if
[MPa.s]
spherical part: viscosity connects associated with the mechanism with
dissemination interlamellaire
10
19
,
6
+
=
E
D
R
[MPa.s]
deviatoric part:viscosity associated with the water adsorbed by the layers
hydrates
12
64
,
1
+
=
E
D
I
[MPa.s]
deviatoric part: viscosity of interstitial water.
Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
1.3
Boundary conditions and loadings
In this test, one creates a field of homogeneous and constant drying in the structure.
The mechanical loading corresponds to a shearing in the xz plan; its intensity is of
10 [MPa]. The load is applied in 1s and is maintained constant for 750 days.
1.4 Conditions
initial
The beginning of calculation is supposed the moment 1. At this moment there is neither field of drying, nor forced
mechanics.
At moment 0, one applies a field of drying corresponding to 100% of hygroscopy.
Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation
The analytical solution rests on the resolution of the two differential equations which control
deviatoric part of the behavior (cf [R7.01.06]).
The deviatoric stresses are at the origin of a mechanism of slip (or mechanism of quasi
dislocation) of the layers of HSC in nano-porosity. Under deviatoric stress, creep
be carried out with constant volume. In addition, the law of creep UMLV supposes the isotropy of creep
deviatoric. Phénoménologiquement, the mechanism of slip comprises a contribution
reversible viscoelastic of the water strongly adsorbed with the layers of HSC and a contribution
irreversible viscous of interstitial water:
{
{
{
free
water
one
contributi
fd
I
absobée
water
one
contributi
fd
R
total
ue
déviatoriq N
déformatio
fd
+
=
éq
2.1-1
The J
ème
main component of the total deviatoric deformation is governed by the equations
[éq 2.1-2] and [éq 2.1-3]:
J
D
J
D
R
D
R
J
D
R
D
R
H
K
,
,
,
=
+
&
éq
2.1-2
where
D
R
K
indicate rigidity associated with the capacity with water adsorbed to transmit loads (load
bearing toilets);
and
D
R
viscosity associated with the water adsorbed by the layers with hydrates.
J
D
J
D
I
D
I
H
,
,
=
&
éq 2.1-3
where
D
I
indicate the viscosity of interstitial water.
In the case of a level of stress
xz
, the corresponding deformation of creep deviatoric is
immediately deduced:
-
+
=
-
D
I
D
I
T
K
D
I
xz
fxz
E
T
1
éq
2.1-4
When the elastic part is added, it follows that the total deflection of shearing is worth:
-
+
+
+
=
-
D
I
D
I
T
K
D
I
xz
fxz
E
T
E
1
1
éq
2.1-5
Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
5/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
2.2
Sizes and results of reference
The test is homogeneous. One tests the deformation in an unspecified node.
2.3
Uncertainties on the solution
Analytical solution.
2.4 References
bibliographical
[1]
POPE Y.: Relation of behavior UMLV for the clean creep of the concrete,
Reference material of Code_Aster [R7.01.06] 16 p (2002).
Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
6/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D
Z
X
y
NO2
NO1
NO3
NO4
NO8
NO7
NO5
NO6
3.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs: 1 of type HEXA 8
6 of type QUAD 4
The following meshs are defined:
S_ARR
NO3 NO7 NO8 NO4
S_AVT
NO1 NO2 NO6 NO5
S_DRT
NO1 NO5 NO8 NO4
S_GCH
NO3 NO2 NO6 NO7
S_INF
NO1 NO2 NO3 NO4
S_SUP
NO5 NO6 NO7 NO8
The boundary conditions in displacement imposed are:
On nodes NO1, NO2, NO3 and NO4: DZ = 0
On nodes NO3, NO7, NO8 and NO4: DY = 0
On nodes NO2, NO6, NO7 and NO8: DX = 0
The loading is consisted of the same field of drying and the same nodal force 1/4 applied
on the four nodes of S_SUP.
Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
3.3 Functionalities
tested
Controls
Key word
DEFI_MATERIAU ELAS_FO
BETON_UMLV_FP
FONC_DESORP
K_RS
K_IS
K_RD
V_RS
V_IS
V_RD
V_ID
CREA_CHAMP “AFFE”
TYPE_CHAM=' NOEU_TEMP_R'
NOM_CMP=' TEMP'
CREA_RESU “AFFE”
TYPE_CHAM=' NOEU_TEMP_R'
NOM_CMP=' TEMP'
AFFE_CHAR_MECA DDL_IMPO
LIAISON_UNIF
FORCE_NODALE
STAT_NON_LINE COMP_INCR
RELATION= `BETON_UMLV_FP'
3.4
Sizes tested and results
The component
xx
with node NO6 was tested.
Moment Reference
Aster %
difference
64800
+3.975E-04
+3.997E-04
0.063
648000
+4.770E-04
4.771E-04
0.035
6480000
+6.811E-04
+6.811E-04
0.003
64800000
+10.413E-04
+10.413E-04
- 0.001
Code_Aster
®
Version
7.4
Titrate:
Checking of the good taking into account of shearing
Date:
03/01/05
Author (S):
Y. The POPE
Key
:
V6.04.181-A
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
4
Summary of the results
The values obtained with Code_Aster are in agreement with the values of the analytical solution of
reference.