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Titrate:
HSNV129 - Essai of compression-dilation


Date:
14/10/02
Author (S):
Key S. MICHEL-PONNELLE
:
V7.22.129-A Page:
1/8

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

Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
Document: V7.22.129-A

HSNV129 - Essai of compression-dilation for
study of the coupling thermics-cracking

Summary:

One applies to an element of volume obeying the law of Mazars (local and not-local version) a loading
thermomechanical in order to check the good taking into account of the dependence of the parameters materials
with the temperature as well as the taking into account of thermal dilation. The loading is homogeneous and
also break up: compression with imposed displacement and constant temperature, then application of a cycle
of heating-cooling.
Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
HSNV129 - Essai of compression-dilation


Date:
14/10/02
Author (S):
Key S. MICHEL-PONNELLE
:
V7.22.129-A Page:
2/8

1
Problem of reference

1.1
Geometry and boundary conditions

Element of volume materialized by a unit cube on side (m):

Z
F
G
E
y
B
C
With
D
X

Appear 1.1-a: Geometry

The loading is such as one obtains a uniform stress and strain state in volume.
Blockings are as follows:
face ABCD: DZ = 0.
face BCGF: DX = 0.
face ABFE: DY = 0.
face EFGH: displacement Uz (T)
The temperature T (T) is supposed to be uniform on the cube; the temperature of reference is worth 0°C.
Uz and T vary according to time in the following way:

moment T
0.100.200 300
Uz (T)
0 Mr.
­ 10­3 Mr.
­ 10­3 Mr.
­ 10­3 Mr.
T (T)
0°C 0°C
200
°C
0°C

A purely mechanical loading is thus carried out, then one heats by blocking the Uz direction,
before cooling. This makes it possible to check the separation of the thermal and mechanical deformations
as well as the non-recouvrance of the mechanical properties after heating.

1.2
Properties of material

For the model of Mazars, the following parameters were used (value with 0°C):

Elastic behavior:
5
-
1
E = 32.000 MPa, = 0. ,
2 = 1.2 10
-
°C
Thermal characteristics:
1
-
1
-
6
3
-
1
= 2
.
2 W m K
, C p = 2
.
2 10
-
J m
K
Damaging behavior:
D = 0
.
1 10 4
-; C
To = 15
.
1
; T
To = 0 8
. ; C
B =
.
2000; T
B = 10.000;
06
.
1
0
=


It is considered in addition that E and Bc vary with the temperature. Their evolution is given on
figures [Figure 1.2-a] and [Figure 1.2-b].
Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
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Titrate:
HSNV129 - Essai of compression-dilation


Date:
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Key S. MICHEL-PONNELLE
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V7.22.129-A Page:
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35000
30000
25000
has) 20000
(MP
E 15000
10000
5000
0
0
50
100
150
200
T (°C)

Appear 1.2-a: Evolution of the Young modulus with the temperature

2500
2000
1500
Bc
1000
500
0
0
50
100
150
200
T (°C)

Appear 1.2-b: Evolution of BC with the temperature

Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

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HSNV129 - Essai of compression-dilation


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2
Reference solution

One can analytically determine the solution of the problem arising.
One notes:
· 0 deformation applied in direction Z,
· 1, 2 and 3 principal deformations

2.1
First stage of the loading: simple compression

- 0
0
0


· The tensor of the deformations is worth: 0
- 0 0 with 0 < 0


0
0
0
· The equivalent deformation is worth consequently
:
~
2
2
2
=
E
+ E
+ E
= -

2
1
2
3
0

+
+
+
· Since ~
> d0, there is evolution of the damage which is worth:
d0 (1 - C
With)
With
D = 1
C
-
~
-


[~
exp B (-)
C
D 0]
· Finally the constraint zz is worth: zz = E 1 (- D) 0

2.2 Second stage of the loading
: thermal dilation in
plane deformations

· The tensor of the total deflections is worth:

- 0 + (T - T
1
) (
ref.
+)
0
0



0
- 0 + (T - T
1
) (
ref.
+) 0 with 0 < 0 fixed



0
0
0

· Elastic strain being worth E
= - T
(- ref.
T
) Id, the equivalent deformation is worth:
~
= 2 ((T -
)
ref.
T
- 0)

· The damage is worth:

-
d0 (1 - C
With)
With

D = MAX D 1, -
-
C


~

[~
exp B (
C -
)
D 0]
· Finally the constraint zz is worth:

zz = E (1 - D) [- (T - T)
0
ref.]
Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
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Titrate:
HSNV129 - Essai of compression-dilation


Date:
14/10/02
Author (S):
Key S. MICHEL-PONNELLE
:
V7.22.129-A Page:
5/8

Note:

· In a given state, the parameters materials used are those defined in the temperature
maximum sight by material and not at the current temperature.
· The evaluation of the damage D utilizes the concept of maximum reaches with the course
history of the loading; the solution is thus not completely analytical but
imply a discretization. If there is no influence of thermics, it
is enough to take ~ equivalent with the maximum equivalent deformation reached. When one
takes into account the thermal aspect, the heating can contribute “to decrease” or
“to delay” the damage with deformation given; it is the case with the evolution of Bc
reserve. In this case, it is necessary in makes rather finely discretize the loading to have
the good value of damage D (which presents indeed a maximum in our
case).

3 Modeling
With

3.1
Characteristics of modeling

Modeling 3D
Element MECA_HEXA8

3.2
Characteristics of the grid

A number of nodes: 8
A number of meshs and types: 1 HEXA8

3.3 Functionalities
tested

The law of behavior MAZARS_FO combined with ELAS_FO.

4
Results of modeling A

4.1 Values
tested

One compares the damage D and the constraint zz with various moments

Identification Reference
Aster
% difference
T = 50
D
0
0
-

­ 16.0
­ 16.0
2.33 10­14
zz (MPa)
T = 100
D
0.1702
0.1702
0.007

­ 26.5532
­ 26.5532
6.46 10­5
zz (MPa)
T = 150
D
0.4247
0.4247
­ 0.005

­ 30.3768
­ 30.3769
2.91 10­4
zz (MPa)
T = 200
D
0.4626
0.4625
­ 0.014

­ 29.2327
­ 29.2382
0.019
zz (MPa)
T = 250
D
0.4626
0.4625
­ 0.014

­ 18.9153
­ 18.9188
0.019
zz (MPa)
T = 300
D
0.4626
0.4625
­ 0.014

­ 8.5979
­ 8.5994
0.018
zz (MPa)

4.2 Notice

Actually, the maximum damage, i.e. 0.4626 is reached at time T 180 S. Ensuite, it
do not evolve/move any more because of the reduction of Bc when the temperature increases.
Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
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Titrate:
HSNV129 - Essai of compression-dilation


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Key S. MICHEL-PONNELLE
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5 Modeling
B

5.1
Characteristics of modeling

The use of the delocalized version of the model of Mazars passes by the use of modeling
3d_GRAD_EPSI and implies the use of quadratic elements.
The test is carried out with a null characteristic length.

Modeling 3d_GRAD_EPSI
Element MGCA_HEXA20

5.2
Characteristics of the grid

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

5.3 Functionalities
tested

The law of behavior MAZARS_FO combined with ELAS_FO within the framework of modeling
not-local 3d_GRAD_EPSI.

6
Results of modeling B

6.1 Values
tested

One compares the damage D and the constraint zz with various moments

Identification Reference
Aster %
difference
T = 50
D
0
0
-

­ 16.0
­ 16.0
2.33 10­14
zz (MPa)
T = 100
D
0.1702
0.1702
0.007

­ 26.5532
­ 26.5532
6.46 10­5
zz (MPa)
T = 150
D
0.4247
0.4247
­ 0.005

­ 30.3768
­ 30.3770
8.06 10­4
zz (MPa)
T = 200
D
0.4626
0.4625
­ 0.014

­ 29.2327
­ 29.2382
0.019
zz (MPa)
T = 250
D
0.4626
0.4625
­ 0.014

­ 18.9153
­ 18.9188
0.019
zz (MPa)
T = 300
D
0.4626
0.4625
­ 0.014

­ 8.5979
­ 8.5994
0.018
zz (MPa)

6.2 Notice

Actually, the maximum damage, i.e. 0.4626 is reached at time T 180 S. Ensuite, it
do not evolve/move any more because of the reduction of Bc when the temperature increases.
Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
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Titrate:
HSNV129 - Essai of compression-dilation


Date:
14/10/02
Author (S):
Key S. MICHEL-PONNELLE
:
V7.22.129-A Page:
7/8

7
Summary of the results

One obtains the analytical solution with a precision lower than 0.02% what makes it possible to be ensured of
good establishment of the model of Mazars including when the temperature intervenes. Let us point out them
choices which were made for the coupling cracking-thermics and which are checked here:

· linear thermal dilation,
· evolution of the damage only under the effect of the elastic strain and not
thermics,
· dependence of the parameters materials with the maximum temperature, i.e. not
reversibility of the modifications of the mechanical properties when the concrete is heated then
cooled.
Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
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Titrate:
HSNV129 - Essai of compression-dilation


Date:
14/10/02
Author (S):
Key S. MICHEL-PONNELLE
:
V7.22.129-A Page:
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Handbook of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A

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