Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
1/8

Organization (S): EDF-R & D/MMC

Handbook of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
Document: V6.04.181

SSNV181 - Vérification of the good taking into account
shearing in 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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
2/8

1
Problem of reference

1.1 Geometry
Z
E
H
y
X
L

Height:
H = 1,00 [m]
Width:
L = 1,00 [m]
Thickness:
E = 1,00 [m]

1.2
Properties of material

E = 31 [GPa] modulus of elasticity
=,
0 2
Poisson's ratio

Parameters specific to clean creep:


K Sr =,
1 20th + 5 [MPa]
spherical part: rigidity connects associated with the skeleton formed by
blocks of hydrates on a mesoscopic scale

K if =,
6 22E + 4 [MPa]
spherical part: rigidity connects intrinsically associated with
hydrates on a microscopic scale

K Dr. = 86
,
3
E + 4 [MPa]
deviatoric part: rigidity associated with the capacity with water adsorbed with
to transmit loads (load bearing toilets)

Sr =,
2 21E +10 [MPa.s]
spherical part:viscosity connects associated with the mechanism with
diffusion within capillary porosity

if = 16
,
4
E +10 [MPa.s]
spherical part: viscosity connects associated with the mechanism with
diffusion interlamellaire

Dr. = 19
,
6
E +10 [MPa.s]
deviatoric part:viscosity associated with the water adsorbed by the layers
hydrates

di =, 164E +12 [MPa.s]
deviatoric part: viscosity of interstitial water.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
3/8

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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
4/8

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 constraints are at the origin of a mechanism of slip (or mechanism of quasi
dislocation) of the layers of HSC in nano-porosity. Under deviatoric constraint, 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:

fd
fd
fd

=

+
éq
2.1-1
{
{
R
{
I
contribution
deformation
contribution
water
ue
déviatoriq
water
absobée
total
free

The principal component jème of the total deviatoric deformation is governed by the equations
[éq 2.1-2] and [éq 2.1-3]:

D D, J
D D, J
D J
R &r + K
,
R R
= H

éq
2.1-2

where D
Kr indicates 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.

D D, J
D J
I &
=
I
H
,







éq 2.1-3

where D
I indicates the viscosity of interstitial water.
In the case of a level of constraint xz, the corresponding deformation of creep deviatoric is
immediately deduced:


D
ki T


- D
T

F

xz = xz
+ 1
I
E
éq
2.1-4
D
I








When the elastic part is added, it follows that the total deflection of shearing is worth:



D
K



- I T
D

F
1
T
xz =
+

I
xz
+
+ 1 - E
éq
2.1-5

D
E





I





Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
5/8



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 de Code_Aster [R7.01.06] 16 p (2002).
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
6/8

3 Modeling
With

3.1
Characteristics of modeling

Modeling 3D
Z
NO7
NO6
NO8
NO5
NO2
NO3
y
NO4
NO1
X


3.2
Characteristics of the grid

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.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
7/8

3.3 Functionalities
tested

Commands
Key word


DEFI_MATERIAU ELAS_FO

FONC_DESORP

BETON_UMLV_FP
K_RS
K_IS
K_RD
V_RS
V_IS
V_RD
V_ID
CREA_CHAMP “AFFE”
NOM_CMP=' TEMP'

TYPE_CHAM=' NOEU_TEMP_R'
CREA_RESU “AFFE”
NOM_CMP=' TEMP'

TYPE_CHAM=' NOEU_TEMP_R'
AFFE_CHAR_MECA DDL_IMPO


LIAISON_UNIF
FORCE_NODALE
STAT_NON_LINE COMP_INCR
RELATION= `BETON_UMLV_FP'

3.4
Sizes tested and results

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

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
7.4
Titrate:
Checking of the good taking into account of shearing

Date:
03/01/05
Author (S):
Y. The Key POPE
:
V6.04.181-A Page:
8/8

4
Summary of the results

The values obtained with Code_Aster are in agreement with the values of the analytical solution of
reference.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A

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