Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
1/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
Document: V7.22.129-A
HSNV129 - Test 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.
Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
2/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1
Geometry and boundary conditions
Element of volume materialized by a unit cube on side (m):
With
E
F
Z
G
C
D
y
X
B
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.
10
3
Mr.
10
3
Mr.
10
3
Mr.
T (T)
0°C 0°C
200
°C
0°C
A purely mechanical loading is thus carried out, then one heats by locking 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:
1
5
10
2
.
1
,
2
.
0
,
000
32
-
-
°
=
=
=
C
MPa
E
Thermal characteristics:
1
3
6
1
1
10
2
.
2
,
2
.
2
-
-
-
-
=
=
K
m
J
C
K
m
W
p
Damaging behavior:
06
.
1
;
000
10
;
.
2000
;
8
.
0
;
15
.
1
;
10
0
.
1
4
0
=
=
=
=
=
=
-
T
C
T
C
D
B
B
With
With
It is considered in addition that
E
and
B
C
vary with the temperature. Their evolution is given on
figures [Figure 1.2-a] and [Figure 1.2-b].
Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
3/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
0
5000
10000
15000
20000
25000
30000
35000
0
50
100
150
200
T (°C)
E
(MP
has)
Appear 1.2-a: Evolution of the Young modulus with the temperature
0
500
1000
1500
2000
2500
0
50
100
150
200
T (°C)
Bc
Appear 1.2-b: Evolution of B
C
with the temperature
Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
4/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
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
main deformations
2.1
First stage of the loading: simple compression
·
The tensor of the deformations is worth:
-
-
0
0
0
0
0
0
0
0
0
with
0
< 0
·
The equivalent deformation is worth consequently
:
2
~
0
2
3
2
2
2
1
-
=
+
+
=
+
+
+
E
E
E
·
Since
0
~
D
>
, there is evolution of the damage which is worth:
(
)
[
]
)
~
(
exp
~
1
1
0
0
D
C
C
C
D
B
With
With
D
-
-
-
-
=
·
Finally the stress
zz
is worth:
0
)
1
(
-
=
D
E
zz
2.2 Second stage of the loading
: thermal dilation in
plane deformations
·
The tensor of the total deflections is worth:
+
-
+
-
+
-
+
-
0
0
0
0
0
0
)
1
) (
(
0
0
0
)
1
) (
(
T
T
T
T
ref.
ref.
with
0
< 0 fixed
·
Elastic strain being worth
D
ref.
E
T
T
I
)
(
-
-
=
, the equivalent deformation is worth:
(
)
0
)
(
2
~
-
-
=
ref.
T
T
·
The damage is worth:
(
)
[
]
-
-
-
-
=
-
)
~
(
exp
~
1
1
,
0
0
D
C
C
C
D
B
With
With
D
MAX
D
·
Finally the stress
zz
is worth:
(
)
[
]
)
(
1
0
ref.
zz
T
T
D
E
-
-
-
=
Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
5/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
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 B
C
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 mesh
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 stress
zz
at various moments
Identification Reference
Aster
% difference
T = 50
D
zz
(MPa)
0
16.0
0
16.0
-
2.33 10
14
T = 100
D
zz
(MPa)
0.1702
26.5532
0.1702
26.5532
0.007
6.46 10
5
T = 150
D
zz
(MPa)
0.4247
30.3768
0.4247
30.3769
0.005
2.91 10
4
T = 200
D
zz
(MPa)
0.4626
29.2327
0.4625
29.2382
0.014
0.019
T = 250
D
zz
(MPa)
0.4626
18.9153
0.4625
18.9188
0.014
0.019
T = 300
D
zz
(MPa)
0.4626
8.5979
0.4625
8.5994
0.014
0.018
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 B
C
when the temperature increases.
Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
6/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
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 the use of quadratic elements implies.
The test is carried out with a null characteristic length.
Modeling
3d_GRAD_EPSI
Element MGCA_HEXA20
5.2
Characteristics of the mesh
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 stress
zz
at various moments
Identification Reference
Aster %
difference
T = 50
D
zz
(MPa)
0
16.0
0
16.0
-
2.33 10
14
T = 100
D
zz
(MPa)
0.1702
26.5532
0.1702
26.5532
0.007
6.46 10
5
T = 150
D
zz
(MPa)
0.4247
30.3768
0.4247
30.3770
0.005
8.06 10
4
T = 200
D
zz
(MPa)
0.4626
29.2327
0.4625
29.2382
0.014
0.019
T = 250
D
zz
(MPa)
0.4626
18.9153
0.4625
18.9188
0.014
0.019
T = 300
D
zz
(MPa)
0.4626
8.5979
0.4625
8.5994
0.014
0.018
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 B
C
when the temperature increases.
Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
7/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
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 amendments of the mechanical properties when the concrete is heated then
cooled.
Code_Aster
®
Version
6.0
Titrate:
HSNV129 - Test of compression-dilation
Date:
14/10/02
Author (S):
S. MICHEL-PONNELLE
Key
:
V7.22.129-A
Page:
8/8
Manual of Validation
V7.22 booklet: Thermomechanical non-linear statics of the voluminal structures
HT-66/02/001/A
Intentionally white left page.