Code_Aster
®
Version
7.3
Titrate:
SSNV151 - Traction/Compression with law BETON_DOUBLE_DP
Date:
13/10/04
Author (S):
J. EL GHARIB, S. MICHEL-PONNELLE
Key
:
V6.04.151-B
Page:
1/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.151
SSNV151 - Traction/Compression with the law of
behavior BETON_DOUBLE_DP
Summary
This case of validation is intended to check the model of behavior 3D
BETON_DOUBLE_DP
formulated in
tally of the thermo plasticity, for the description of the nonlinear behavior of the concrete in traction and in
compression, with the taking into account of the irreversible variations of the thermal characteristics and
mechanics of the concrete, particularly sensitive at high temperature.
The description of cracking is treated within the framework of plasticity, using an energy equivalence,
by identifying the density of energy of cracking in mode I, with the plastic work of a homogeneous medium
equivalent, where the plastic deformation is uniformly distributed in an “elementary” area. This approach
preserve the continuity of the formulation of the model, on the whole of its behavior, and contributes to avoid
possible numerical difficulties during the change of state of material.
Pathological sensitivity of the numerical solution to the space discretization (mesh), generated by
the introduction of a softening behavior of the concrete in traction and compression, is partially solved
by introducing an energy of cracking or rupture, dependant a characteristic length L
C
, related to
cut elements.
The resolution of the equations constitutive of the model is carried out by an implicit scheme.
It is about a cube with 8 nodes subjected to a uniaxial pressing, in imposed displacement to which is added
a biaxial traction when one reached an important work hardening in traction. This loading led to the case
private individual of a hydrostatic state of stress, solved by projection at the top of the cone of traction, when
one places oneself in a hydrostatic diagram forced equivalent/forced. It is about a case test of not
regression.
Code_Aster
®
Version
7.3
Titrate:
SSNV151 - Traction/Compression with law BETON_DOUBLE_DP
Date:
13/10/04
Author (S):
J. EL GHARIB, S. MICHEL-PONNELLE
Key
:
V6.04.151-B
Page:
2/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
It is about a cube with 8 nodes, whose three faces have a normal displacement no one, and the three faces
opposed have an imposed and identical normal displacement.
The cube makes 1 mm on side. In modeling A, the cube is directed according to the Oxyz reference mark.
Modeling A
1.2
Material properties
To test the establishment of thermal dilation and the withdrawal of desiccation, a field is forced
of temperature and a field of drying variables so that deformations generated by
the two phenomena are compensated, while considering that the expansion factors thermal
and of withdrawal of desiccation are equal. The values related to drying do not have any physical direction, it
test is from this point of view, purely data-processing.
For the usual linear mechanical characteristics:
Young modulus:
E = 32.000 MPa
Poisson's ratio:
= 0.18
Thermal expansion factor:
= 10
5
/°C
Coefficient of withdrawal of desiccation:
= 10
5
Temperature of reference
T
ref.
= 0 °C
Drying of reference
C
ref.
= 20
X
y
Z
Uz = 0
Ux = 0
U
1
U
2
Face1xy
Facexy
Faceyz
Face1yz
N1
N2
Face1xz
Facexz
U
3
Code_Aster
®
Version
7.3
Titrate:
SSNV151 - Traction/Compression with law BETON_DOUBLE_DP
Date:
13/10/04
Author (S):
J. EL GHARIB, S. MICHEL-PONNELLE
Key
:
V6.04.151-B
Page:
3/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/04/005/A
For the nonlinear mechanical characteristics of model BETON_DOUBLE_DP:
Resistance in uniaxial pressing:
f' C = 40 NR/mm ²
Resistance in uniaxial traction:
f' T = 4 NR/mm ²
Report/ratio of resistances in compression
biaxial/uniaxial pressing:
= 1.16
Energy of rupture in compression:
Gc =10 Nm/mm ²
Energy of rupture in traction:
WP =0.1 Nm/mm ²
Report/ratio of the limit elastic to resistance
in uniaxial pressing:
30%
1.3
Boundary conditions and loadings mechanical
Increasing field of temperature of 0°C with 20°C.
Field of drying decreasing from 20 to 0.
Lower face of the cube (facexy):
locked according to OZ.
Higher face of the cube (face1xy):
variable displacement imposed in mm
Left face of the cube (faceyz):
locked according to OX.
Right face of the cube (face1yz):
variable displacement imposed in mm
Front face of the cube (facexz):
locked according to OY.
Face postpones cube (face1xz):
variable displacement imposed in mm
The mechanical loading is applied in displacement imposed to the various faces of the cube. One
apply a compression to the face face1xz, affected by a first multiplying coefficient and one
traction according to faces' face1xy and face1yz, affected by a second multiplying coefficient, no one
during the first part at the beginning of loading, according to the following diagram:
Code_Aster
®
Version
7.3
Titrate:
SSNV151 - Traction/Compression with law BETON_DOUBLE_DP
Date:
13/10/04
Author (S):
J. EL GHARIB, S. MICHEL-PONNELLE
Key
:
V6.04.151-B
Page:
4/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/04/005/A
2 Modeling
With
2.1
Characteristics of modeling
3D (HEXA8)
1 element, stress field and uniform deformation.
2.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and type: 1 HEXA8
2.3 Functionalities
tested
Controls Options
“MECHANICAL” AFFE_MODELE
“3D”
DEFI_MATERIAU “BETON_DOUBLE_DP”
DEFI_MATERIAU “ELAS_FO”
“K_DESSIC”
AFFE_CHAR_MECA “SECH_CALCULEE”
STAT_NON_LINE “BETON_DOUBLE_DP”
X
y
Z
Uz = 0
Ux = 0
U
1
U
2
Face1xy
Facexy
Faceyz
Face1yz
N1
N2
Face1xz
Facexz
U
3
Code_Aster
®
Version
7.3
Titrate:
SSNV151 - Traction/Compression with law BETON_DOUBLE_DP
Date:
13/10/04
Author (S):
J. EL GHARIB, S. MICHEL-PONNELLE
Key
:
V6.04.151-B
Page:
5/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/04/005/A
3
Results of modeling A
3.1 Values
tested
Components xx and yy of the stress field were tested
SIEF_ELNO_ELGA
, deformation
figure cumulated in compression, plastic deformation cumulated in traction (first and
second internal variable, second component of the field
VARI_ELNO_ELGA)
and
the plastic state (
fourth variable of the field
VARI_ELNO_ELGA)
. The plastic state is worth 1 in compression, 11 afterwards
projection at the top of the cone of compression, 2 in traction, 22 after projection at the top of the criterion
of traction, 3 in compression and traction together, and 33 after projection out of the two nodes of
two cones. Displacement being imposed, the field
EPSI_ELNO_DEPL
is not tested.
The values given here correspond to version 7.2.25.
Component field SIEF_ELNO_ELGA SIXX
Identification Reference
Aster %
difference
For a displacement imposed in
U
3
= 1. and U
1
= U
2
= 0.
For a displacement imposed in
U
3
= 1.725 and U
1
= U
2
= 0.010
2.5737449
For a displacement imposed in
U
3
= 1.8
and U
1
= U
2
= 0.02872
0.6767446
For a displacement imposed in
U
3
= 2. and U
1
= U
2
= 0.1
2.666667
10
- 6
Component field SIEF_ELNO_ELGA SIYY
Identification Reference
Aster %
difference
For a displacement imposed in
U
3
= 1. and U
1
= U
2
= 0.
17.4575632
For a displacement imposed in
U
3
= 1.725 and U
1
= U
2
= 0.010
2.5737449
For a displacement imposed in
U
3
= 1.8
and U
1
= U
2
= 0.02872
0.6767446
For a displacement imposed in
U
3
= 2. and U
1
= U
2
= 0.1
- 3.622988
10
- 5
Field
VARI_ELNO_ELGA
component
V1
(plastic deformation cumulated in compression)
Identification Reference
Aster %
difference
For a displacement imposed in
U
3
= - 1. and U
1
= U
2
= 0.
- 0.1995285
-
For a displacement imposed in
U
3
= - 1.725 and U
1
= U
2
= 0.010
- 0.3429299
-
For a displacement imposed in
U
3
= - 1.8
and U
1
= U
2
= 0.02872
- 0.3449657
-
For a displacement imposed in
U
3
= - 2. and U
1
= U
2
= 0.1
- 0.3849539
-
Code_Aster
®
Version
7.3
Titrate:
SSNV151 - Traction/Compression with law BETON_DOUBLE_DP
Date:
13/10/04
Author (S):
J. EL GHARIB, S. MICHEL-PONNELLE
Key
:
V6.04.151-B
Page:
6/6
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/04/005/A
Component field VARI_ELNO_ELGA V2 (plastic deformation cumulated in traction)
Identification Reference
Aster %
difference
For a displacement imposed in
U
3
= - 1. and U
1
= U
2
= 0.
- -
-
For a displacement imposed in
U
3
= - 1.725 and U
1
= U
2
= 0.010
- 1.231450e-03
-
For a displacement imposed in
U
3
= - 1.725 and U
1
= U
2
= 0.02872
- 2.638289e-02
-
For a displacement imposed in
U
3
= - 2. and U
1
= U
2
= 0.1
- 8.373868e-02
-
Component field VARI_ELNO_ELGA V4 (plastic state)
Identification Reference
Aster %
difference
For a displacement imposed in
U
3
= - 1. and U
1
= U
2
= 0.
- 1.
-
For a displacement imposed in
U
3
= - 1.725 and U
1
= U
2
= 0.010
- 22.
-
For a displacement imposed in
U
3
= - 1.725 and U
1
= U
2
= 0.02872
- 22.
-
For a displacement imposed in
U
3
= - 2. and U
1
= U
2
= 0.1
- 3.
-