Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
1/16

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

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
Document: V3.06.103

SSLA103 - Calcul of the withdrawal of desiccation and of
endogenous withdrawal on a cylinder

Summary:

The purpose of this case-test is to validate the calculation of the withdrawal of desiccation and the endogenous withdrawal. It also tests
possibility of making depend the characteristics materials on the hydration and drying (in the case of it
model of Mazars). It is about a cylinder which undergoes a drying and a uniform hydration. The temperature
also vary.

The cylinder is modelled by four elements quadrangles with 8 nodes for modelings A, C, E and F and by
an element HEXA20 for modelings B and D. Pour modelings A and B, the behavior is
presumedly elastic, which makes it possible to validate the calculation of withdrawal at the same time with STAT_NON_LINE and with
MECA_STATIQUE. Modelings C and D make it possible to validate the calculation of withdrawal with the law of MAZARS
local and not-local (without activation of the damage). Modeling E validates the calculation of withdrawal with
law ENDO_ISOT_BETON and modeling F coupling ENDO_ISOT_BETON/BETON_UMLV_FP

The results obtained by Code_Aster are identical to the analytical solution of reference.

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
2/16

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

For modelings A and B, the material is supposed to be elastic and the characteristics materials are
constants to be able to validate calculation with MECA_STATIQUE,
For modelings C and D, one uses the law of MAZARS and certain parameters depend on
the hydration and of drying.
Modeling E makes it possible to test law ENDO_ISOT_BETON, and modeling F the coupling
ENDO_ISOT_BETON/BETON_UMLV_FP, knowing that the parameters materials of the law
BETON_UMLV_FP are selected so that one does not have creep and thus which one finds it
behavior of law ENDO_ISOT_BETON. In both cases, the characteristics materials are
constants.
Let us announce that being given the loading (dilation, hydration and free drying), any
damage does not develop: one thus finds in all the cases, the elastic solution.

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
3/16

Modeling A and isotropic b: Elasticité
Modeling C and D: MAZARS
E = 30000 MPa
E = 10000 MPa for C=100l/m3
= 0.2
30000 MPa for C= 80l/m3
= 1.66 10-5 (L/m3) - 1
= 0.25 for h=0

0.15 for h=1
endo = 1.5 10-5
= 1.0 10-5 °C-1
= 1.66 10-5 (L/m3) - 1

endo = 1.5 10-5
= 1.0 10-5 °C-1

Ac = 1.4
At = 0.8 for C=100l/m3
0.6 for C= 80l/m3
Bc = 2000
LT = 10000 for h=0
11000 for h=1
d0 = 10-4
= 1.06

Modeling E: ENDO_ISOT_BETON
Modeling F:
E = 30000 MPa
ENDO_ISOT_BETON/BETON_UMLV_FP
= 0.2

= 1.66 10-5 (L/m3) - 1
See modeling E +

S
19
K = 10 MPa
endo = 1.5 10-5
R
= 1.0 10-5 °C-1
S
19
K = 10 MPa

I
T
D
19
K = 10
y = 4.0 MPa,
MPa
R
C
y = 53.4 MPa
S
19
= 10 MPa.j
E
R
T = - 1.0 103 MPa

S
19
= 10 MPa.j
I
D
19
= 10 MPa.j
R
D
19
= 10 MPa.j
I

1.3
Boundary conditions and loadings

On side AB: uz = 0

One varies uniformly on the structure:
· the temperature of T = 20°C at initial time until t=120°C at final time
· water content of 100 L/m3 at initial time up to 80 L/m3 at final time
· the hydration varies from 0. at initial time with 1. at final time.
Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
4/16

2
Reference solution

2.1
Method of calculation used for the reference solution

Being given the nature of the stresses, the total deflection is only due to the withdrawal and to
thermal dilation. Consequently, one a:

HT
rd
Re
= + + = (T - T I - C - C I - H I
ref.) D
(0
) D
D
with:

·
T, the temperature at time T
·
Tref, the temperature of reference
·
C0, water content initial (water content HR=100%).
·
C, water content at time T
·
H, the degree of hydration at time T
·
, the dilation coefficient
·
, the coefficient of withdrawal of desiccation
·
, the endogenous coefficient of withdrawal

The elastic strain being null in this problem, the constraints are null, like
the damage in the case of modelings with the law of MAZARS and ENDO_ISOT_BETON.

2.2
Results of reference

One checks the value of the deformation after 3600 days, as well as the constraint. One also checks
that the plastic deformation is null, as well as the damage for modelings
concerned. The results are tested with STAT_NON_LINE like with MECA_STATIQUE (for
modelings A and B)

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
5/16

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 =_F (GROUP_MA = D1, DY= 0.)
TEMP_CALCULEE=TEMP1
SECH_CALCULEE=SECH1
HYDR_CALCULEE=HYDR1

3.2
Characteristics of the grid

A number of nodes:
21
A number of meshs and types: 4 QUAD8

3.3 Functionalities
tested

Commands


DEFI_MATERIAU ELAS_FO
ALPHA


K_DESSIC


B_ENDOGE

AFFE_MATERIAU AFFE
SECH_REF
AFFE_CHAR_MECA FACE_IMPO


TEMP_CALCULEE
SECH_CALCULEE
HYDR_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION ELAS
CALC_ELEM OPTION “EPSP_ELNO”

MECA_STATIQUE


CALC_ELEM OPTION “SIGM_ELNO_DEPL”


Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
6/16

3.4
Results of modeling A

For calculation with STAT_NON_LINE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIEF_NOEU_ELGA are
null as well as the plastic deformation (EPSP_NOEU).
For calculation with MECA_STATIQUE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIGM_NOEU_DEPL are
null.

Calculation STAT_NON_LINE

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 8.30
10-14

3600 6.53
10-4
6.53 10-4 - 4.98
10-14
yy
p
xx
3600 0.
1.15
10-8 -
p

3600 0.
- 1.63
10-8 -
yy
xx
3600 0.
- 6.63
10-19 -

3600 0.
2.42
10-19 -
yy

Calculation MECA_STATIQUE

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 1.83
10-13

3600 6.53
10-4 6.53
10-4 - 3.15
10-13
yy
xx
3600 0.
1.66
10-9 -

3600 0.
- 8.04
10-8 -
yy

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
7/16

4 Modeling
B

4.1
Characteristics of modeling

face
C yz
face
C xz
Z
y
F
F it
C xy
X


The loading and the boundary conditions are modelled by:


FACE_IMPO = (_F (GROUP_MA = “FACEXY”, DZ= 0.),
_F (GROUP_MA
=
“FACEXZ”,
DY=
0.),
_F (GROUP_MA
=
“FACEYZ”,
DX=
0.))
TEMP_CALCULEE=TEMP1
SECH_CALCULEE=SECH1
HYDR_CALCULEE=HYDR1

4.2
Characteristics of the grid

A number of nodes:
20
A number of meshs and types: 1 HEXA20

4.3 Functionalities
tested

Commands


DEFI_MATERIAU ELAS_FO
ALPHA


K_DESSIC


B_ENDOGE

AFFE_MATERIAU AFFE
SECH_REF
AFFE_CHAR_MECA FACE_IMPO


TEMP_CALCULEE
SECH_CALCULEE
HYDR_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION ELAS
CALC_ELEM OPTION “EPSP_ELNO”

MECA_STATIQUE


CALC_ELEM OPTION “SIGM_ELNO_DEPL”


Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
8/16

4.4
Results of modeling B

For calculation with STAT_NON_LINE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIEF_NOEU_ELGA are
null as well as the plastic deformation (EPSP_NOEU).
For calculation with MECA_STATIQUE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIGM_NOEU_DEPL are
null.

Calculation STAT_NON_LINE

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 - 8.30
10-14

3600 6.53
10-4 6.53
10-4 - 4.98
10-14
yy
p
xx
3600 0.
9.39
10-9 -
p

3600 0.
1.56
10-8 -
yy
xx
3600 0.
- 1.85
10-19 -

3600 0.
- 2.94
10-19 -
yy

Calculation MECA_STATIQUE

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 - 6.64
10-14

3600 6.53
10-4 6.53
10-4 8.30
10-14
yy
xx
3600 0.
6.09
10-9 -

3600 0.
2.30
10-8 -
yy

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
9/16

5 Modeling
C

5.1
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 =_F (GROUP_MA = D1, DY= 0.)
TEMP_CALCULEE=TEMP1
SECH_CALCULEE=SECH1
HYDR_CALCULEE=HYDR1

5.2
Characteristics of the grid

A number of nodes:
21
A number of meshs and types: 4 QUAD8

5.3 Functionalities
tested

Commands


DEFI_MATERIAU ELAS_FO
ALPHA


K_DESSIC


B_ENDOGE

MAZARS_FO


AFFE_MATERIAU AFFE
SECH_REF
AFFE_CHAR_MECA FACE_IMPO


TEMP_CALCULEE
SECH_CALCULEE
HYDR_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION MAZARS
CALC_ELEM OPTION “EPSP_ELNO”

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
10/16

5.4
Results of modeling C

For calculation with STAT_NON_LINE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIEF_NOEU_ELGA are
null as well as the plastic deformation (EPSP_NOEU) and the variable of damage
(VARI_NOEU_ELGA, V1).

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 - 5.65
10-5

3600 6.53
10-4 6.53
10-4 - 3.58
10-5
yy
p
xx
3600 0.
0.619
-
p

3600 0.
0.032
-
yy
xx
3600 0.
- 3.91
10-10 -

3600 0.
- 2.05
10-10 -
yy
D
3600 0.
0.0
-

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
11/16

6 Modeling
D

6.1
Characteristics of modeling

face
C yz
face
C xz
Z
y
F
F it
C xy
X


The loading and the boundary conditions are modelled by:

FACE_IMPO = (_F (GROUP_MA = “FACEXY”, DZ= 0.),
_F (GROUP_MA
=
“FACEXZ”,
DY=
0.),
_F (GROUP_MA
=
“FACEYZ”,
DX=
0.))
TEMP_CALCULEE=TEMP1
SECH_CALCULEE=SECH1
HYDR_CALCULEE=HYDR1

6.2
Characteristics of the grid

A number of nodes:
20
A number of meshs and types: 1 HEXA20

6.3 Functionalities
tested

Commands


DEFI_MATERIAU ELAS_FO
ALPHA


K_DESSIC


B_ENDOGE

MAZARS_FO


NON_LOCAL


AFFE_MODELE


AFFE_MATERIAU AFFE
SECH_REF
AFFE_CHAR_MECA FACE_IMPO


TEMP_CALCULEE
SECH_CALCULEE
HYDR_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION MAZARS
CALC_ELEM OPTION “EPSP_ELNO”

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
12/16

6.4
Results of modeling D

For calculation with STAT_NON_LINE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIEF_NOEU_ELGA are
null as well as the plastic deformation (EPSP_NOEU) and the variable of damage
VARI_NOEU_ELGA, V1.

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 1.16
10-13

3600 6.53
10-4 6.53
10-4 8.30
10-14
yy
p
xx
3600 0.
1.7510-8 -
p

3600 0.
2.95
10-8 -
yy
xx
3600 0.
- 2.91
10-20 -

3600 0.
- 8.78
10-19 -
yy
D
3600 0.
0.
-

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
13/16

7 Modeling
E

7.1
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 =_F (GROUP_MA = D1, DY= 0.)
TEMP_CALCULEE=TEMP1
SECH_CALCULEE=SECH1
HYDR_CALCULEE=HYDR1

7.2
Characteristics of the grid

A number of nodes:
21
A number of meshs and types: 4 QUAD8

7.3 Functionalities
tested

Commands
DEFI_MATERIAU ELAS_FO
ALPHA


K_DESSIC


B_ENDOGE

BETON_ECR_LINE


AFFE_MATERIAU AFFE
SECH_REF

AFFE_CHAR_MECA FACE_IMPO


TEMP_CALCULEE
SECH_CALCULEE
HYDR_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION
ENDO_ISOT_BETON
CALC_ELEM OPTION “EPSP_ELNO”


Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
14/16

7.4
Results of modeling E

For calculation with STAT_NON_LINE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIEF_NOEU_ELGA are
null as well as the plastic deformation (EPSP_NOEU) and the variable of damage
(VARI_NOEU_ELGA, V1).

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 1.33
10-13

3600 6.53
10-4 6.53
10-4 4.98
10-14
yy
p
xx
3600 0.
2.30
10-8
-
p

3600 0.
- 3.30
10-10
-
yy
xx
3600 0.
- 4.49
10-19 -

3600 0.
- 1.78
10-19 -
yy
D
3600 0.
0.0
-

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
15/16

8 Modeling
F

8.1
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 =_F (GROUP_MA = D1, DY= 0.)
TEMP_CALCULEE=TEMP1
SECH_CALCULEE=SECH1
HYDR_CALCULEE=HYDR1

8.2
Characteristics of the grid

A number of nodes:
21
A number of meshs and types: 4 QUAD8

8.3 Functionalities
tested

Commands


DEFI_MATERIAU ELAS_FO
ALPHA


K_DESSIC


B_ENDOGE

BETON_ECRO_LINE


BETON_UMLV_FP


AFFE_MATERIAU AFFE
SECH_REF
AFFE_CHAR_MECA FACE_IMPO


TEMP_CALCULEE
SECH_CALCULEE
HYDR_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION KIT_DDI
CALC_ELEM OPTION “EPSP_ELNO”

Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
SSLA103 - Calcul of the withdrawal of desiccation and the endogenous withdrawal
Date:
01/09/05
Author (S):
S. MICHEL-PONNELLE, J. EL GHARIB Key
:
V3.06.103-B Page:
16/16

8.4
Results of modeling F

For calculation with STAT_NON_LINE, one tests the components of the tensor of the deformations
EPSI_NOEU_DEPL after 3600 days. It is also checked that constraints SIEF_NOEU_ELGA are
null as well as the plastic deformation (EPSP_NOEU) and the variable of damage
(VARI_NOEU_ELGA, V1).

Variables Moment Reference
Aster %
difference
xx
3600 6.53
10-4 6.53
10-4 1.06
10-12

3600 6.53
10-4 6.53
10-4 8.97
10-13
yy
p
xx
3600 0.
2.46
10-7
-
p

3600 0.
2.38
10-7 -
yy
xx
3600 0.
1.44
10-18 -

3600 0.
7.74
10-19 -
yy
D
3600 0.
0.0
-

9
Summary of the results

The results obtained with Code_Aster are identical to the analytical solution. It was thus validated
calculation of thermal dilation and the endogenous withdrawal and desiccation for the elastic model,
that it is with STAT_NON_LINE or MECA_STATIQUE, like for the law of Mazars, local version
or not-local, for law ENDO_ISOT_BETON and the case of the coupling
BETON_UMLV_FP/ENDO_ISOT_BETON. Let us announce that modelings A and B also allow
to validate the calculation of the withdrawals for laws VMIS_ISOT_TRAC and VMIS_ISOT_LINE which uses
even routine that ELAS.
Handbook of Validation
V3.06 booklet: Linear statics of the axisymmetric structures
HT-66/05/005/A

Outline document