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Version
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Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
1/12
Organization (S): EDF-R & D/AMA
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.176
SSNV176 Identification of the law
ENDO_ORTH_BETON
Summary:
One presents here the tests of law ENDO_ORTH_BETON on a single element allowing to identify them
parameters of the model. Insofar as there is not empirical formula making it possible to gauge them
parameters, the user will be able to use some of the cases tests presented here to adjust his parameters. The study
parameters of the model is in documentation [R7.01.09]. The 5 tests suggested are as follows:
1) traction
simple
2) simple traction with control
3) compression
simple
4) simple compression with control
5) simple traction, simple compression and a biaxial test
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
2/12
1
Problem of reference
1.1
Geometry and boundary conditions
The element used is a tetrahedron at a point of gauss. There is thus no problem of homogeneity
fields in the element.
The conditions of blockings and the relations linear between the nodes which should be applied are summarized
on [Figure 1.1-a]. Edges N0N1, N0N2 and N0N3 are length 1.
Taking into account the geometry of the element, conditions of blockings and relations linear,
deformation is directly connected to displacements of the nodes:
= DX (N1)
xx
= DY (N2)
yy
= DX (N3)
zz
= DX (N2) =DY (N1)
xy
= DX (N3) =DZ (N1)
xz
= DY (N3) =DZ (N2)
yz
If one works with imposed deformation, it is thus enough to impose displacement on the adequate nodes.
If one wishes to work with imposed force, as it is the case for modeling E, it is necessary to impose them
following loadings (see it [Figure 1.1-a] for the definition of the faces F1, F2, F3 and F4):
> 0: FX on F1 and - 3/3FX on F4, FX<0 (traction according to X)
xx
< 0: FX on F1 and - 3/3FX on F4, FX<0 (compression according to X)
xx
> 0: FY on F2 and - 3/3FY on F4, FY<0 (traction according to y)
yy
< 0: FY on F2 and - 3/3FY on F4, FY<0 (compression according to y)
yy
> 0: FZ on F3 and - 3/3FZ on F4, FZ<0 (traction according to Z)
zz
< 0: FZ on F3 and - 3/3FZ on F4, FZ<0 (compression according to Z)
zz
N2
Blockings
:
N0: DX=DY=DZ=0
N0
Linear relations:
Traction/compression in imposed displacement:
N1
DY (N1) =DX (N2)
According to X DX imposed on N1
DZ (N1) =DX (N3)
According to y DY imposed on N2
DZ (N2) =DY (N2)
According to X DZ imposed on N3
N3
Definition of the faces:
Traction/compression in imposed force:
y
F1=N0 N2 N3
According to X: FX on F1 and - 3/3 FX on F4
F2=N0 N1 N3
According to y: FY on F2 and - 3/3 FY on F4
X
F3=N0 N1 N2
According to X: FZ on F3 and - 3/3 FZ on F4
Z
F4=N1 N2 N3
Appear 1.1-a: Géométrie and boundary conditions of the uniaxial tests
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
3/12
1.2
Material properties
The characteristics materials are identical for the 5 tests which are presented.
The elastic characteristics of materials are as follows:
E = 32000 MPa; = 0.2
The breaking stresses in traction and compression are:
traction
= 3, 2 MPa;
compression
= 3
- 1,8 MPa
rupture
rupture
One uses the play of parameter following for the law of behavior:
ALPHA
K0 (Mpa) ECROB (MJ/m3)
ECROD (MJ/m3) K1 (Mpa)
K2
0.87 3.10-4 1.10-3 6.10-2 10.5
6.10-4
Note:
There are several sets of parameters which provide the same breaking stresses.
parameters were identified so that the envelope of rupture of the biaxial tests does not present
of swelling (cf Doc. [R7.01.09]).
The answers of the model for the uniaxial tests are represented below.
Appear 1.2-a: Réponse of law ENDO_ORTH_BETON in simple traction
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
4/12
Appear 1.2-b: Réponse of law ENDO_ORTH_BETON in simple compression
The internal variables, which are numbered in Aster, have the following significance:
V1=Dxx; V2=Dyy; V3=Dzz; V4=Dxy; V5=Dxz; V6=Dyz; V7=d;
Where D is the tensor representing the orthotropic damage of traction, and D is the damage
isotropic of compression (cf Doc. [R7.01.09]).
2
Reference solution
This test is a test of nonregression.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
5/12
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D
Element MECA_TETRA4.
3.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 TETRA4
3.3 Functionalities
tested
The law of behavior ENDO_ORTH_BETON in simple traction (without control).
3.4
Way of loading
The element is subjected to a uniaxial traction in direction X. displacement DX is imposed on
N1 node.
3.5 Values
tested
Moment
Name of the field
Component
Place
Aster
50
DEPL
DX N1 3.E-04
50
EPSI_ELGA_DEPL
EPXX
VOLUME, point 1
3.E-04
50
SIEF_ELGA
SIXX
VOLUME, point 1
1.11388E+00
50
VARI_ELGA
V1 (Dxx)
VOLUME, point 1
6.59365E-01
50
VARI_ELGA
V7 (D)
VOLUME, point 1
2.42260E-04
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
6/12
4 Modeling
B
4.1
Characteristics of modeling
Modeling 3D
Element MECA_TETRA4.
4.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 TETRA4
4.3 Functionalities
tested
The law of behavior ENDO_ORTH_BETON in simple compression (without control of the loading).
4.4
Way of loading
The element is subjected to a uniaxial traction in direction X. displacement DX is imposed on
N1 node.
4.5 Values
tested
Moment
Name of the field
Component
Place
Aster
50
DEPL
DX N1 - 3.E-03
50
EPSI_ELGA_DEPL
EPXX
VOLUME, point 1
- 3.E-03
50
SIEF_ELGA
SIXX
VOLUME, point 1
- 2.74465E+01
50
VARI_ELGA
V2 (Dyy)
VOLUME, point 1
1.30416E-01
50
VARI_ELGA
V7 (D)
VOLUME, point 1
4.80080E-01
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
7/12
5 Modeling
C
5.1
Characteristics of modeling
Modeling 3D
Element MECA_TETRA4.
5.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 TETRA4
5.3 Functionalities
tested
The law of behavior ENDO_ORTH_BETON in simple traction (with control of the loading).
5.4
Way of loading
The element is subjected to a uniaxial traction in direction X. displacement DX is imposed on
N1 node. The difference with modeling A is that one uses the method of control of the loading
PRED_ELAS (cf Doc. [R5.03.80]).
5.5 Values
tested
Moment
Name of the field
Component
Place
Aster
51
DEPL
DX N1 1.44744E-04
51
EPSI_ELGA_DEPL
EPXX
VOLUME, point 1
1.44744E-04
51
SIEF_ELGA
SIXX
VOLUME, point 1
2.89945E+00
51
VARI_ELGA
V1 (Dxx)
VOLUME, point 1
2.08793E-01
51
VARI_ELGA
V7 (D)
VOLUME, point 1
2.30235E-04
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
8/12
6 Modeling
D
6.1
Characteristics of modeling
Modeling 3D
Element MECA_TETRA4.
6.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 TETRA4
6.3 Functionalities
tested
The law of behavior ENDO_ORTH_BETON in simple compression (with control of the loading).
6.4
Way of loading
The element is subjected to a uniaxial traction in direction X. displacement DX is imposed on
N1 node. The difference with modeling B is that one uses the method of control of the loading
PRED_ELAS (cf Doc. [R5.03.80]).
6.5 Values
tested
Moment
Name of the field
Component
Place
Aster
51
DEPL
DX N1 - 1.17993E-03
51
EPSI_ELGA_DEPL
EPXX
VOLUME, point 1
- 1.17993E-03
51
SIEF_ELGA
SIXX
VOLUME, point 1
- 2.86498E+01
51
VARI_ELGA
V2 (Dyy)
VOLUME, point 1
4.73153E-02
51
VARI_ELGA
V7 (D)
VOLUME, point 1
1.34312E-01
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
9/12
7 Modeling
E
7.1
Characteristics of modeling
Modeling 3D
Element MECA_TETRA4.
7.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 TETRA4
7.3 Functionalities
tested
One tests here the law of behavior ENDO_ORTH_BETON in 3 cases of loading:
1) U1: Simple traction
2) U2: Compression
3) U3:Biaxial loading (traction in the direction y, compression in direction X, with one
report/ratio fixes constraints:
= - 0.2
yy
xx
This case test makes it possible to check that the set of parameters chosen by the user respects the data
following:
· breaking stresses in traction,
· breaking stresses in compression,
· no the swelling of the envelope of rupture for biaxial tests. That consists in checking
that the maximum constraint in traction of the biaxial test is lower than the constraint of
yy
rupture in simple traction.
7.4
Way of loading
With the difference in modelings A, B, C and D, it is the force, and not the displacement, which is here
imposed. One uses the method of control of loading PRED_ELAS, because the behavior is
polishing substance. The following loadings are applied:
1) U
-
1: FX on F1,
3/3FX on F4, FX<0 (Traction)
2) U
-
2: FX on F1,
3/3FX on F4, FX>0 (Compression)
3) U
-
3: FX on F1,
3/3FX on F4, FX>0 (Compression according to axis X);
FY on F2, - 3/3FY on F4, with FY= - 0,2 FX (Traction according to the axis y).
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
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Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
10/12
7.5 Values
tested
Moment Result
Name of the field
Component
Place
Aster
42 U1 SIEF_ELGA
SIXX
VOLUME, point 1
3.20684E+00
76 U2 SIEF_ELGA
SIXX
VOLUME, point 1
- 3.18000E+01
74 U3 SIEF_ELGA
SIXX
VOLUME, point 1
- 1.42038E+01
One tests for each calculation, the maximum value (in absolute value) of the constraint. One obtains
xx
then the breaking stress in traction (U1), in compression (U2), and one checks that the constraint of
traction in the biaxial test (U3) is lower than the breaking stress in simple traction (U1):
· U1: traction
= 3.20684 MPa
rupture
· U2: compression
= 31.8
-
MPa
rupture
· U3: traction
= - 0.2 compression
= 0.2 * 14.2038 MPa
traction
traction
<
U 3
U 3
U 3
rupture
Warning 1: It may be that the number of steps of time is insufficient to reach the phase
lenitive. The user will thus check that for calculations U1 and U2, U3 calculation being subjected to one
warning additional (cf warning 2), it is well in the lenitive phase
(reduction in the parameter of control). The maximum constraint in absolute value should not be
attack for the last step of time. In the contrary case, it is necessary to continue calculation until the phase
lenitive.
Warning 2: It is possible, for certain set of parameters, to observe difficulties of
convergence for U3 calculation at the time of the lenitive phase. Indeed, the law of behavior ensures
the existence and the unicity of the solution in imposed deformation, but not in imposed force. These
problems of convergence appearing only in the lenitive phase, the user will be able
to consider the greatest value of the parameter of control reached, equal to the greatest constraint
of compression reached in absolute value, like reference to gauge K2. This is true only
xx
if there are problems of convergence. If there is no problem of convergence for
U3 calculation, and that the maximum constraint in absolute value is reached for the last step of time,
calculation should be continued.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
11/12
8
Summary of the results
The objective of the modelings presented in this document is to identify the parameters of the law
ENDO_ORTH_BETON. Insofar as there is not empirical formula for the values of
parameters to be used, the user will have to gauge his parameters step by step on the various tests
proposed. The method to gauge the parameters, which is in the document [R7.01.09], can
to be summarized as follows:
· choice of ALPHA: (0,85 to 0,9),
· calibration of K0, ECROB on modelings A, C or E (U1 calculation). Once these parameters
gauged, it should not be modified in the phase of calibration of the other parameters,
· calibration of K1, K2 and ECROD on modelings B (or D) and E. In fact, modeling E
(calculations U2 and U3) is enough. It makes it possible to check the value of the breaking stress in
simple compression, and to ensure that the envelope of rupture for biaxial tests
do not inflate. It is not necessary to gauge the K2 parameter in a very fine way bus it
rise from a qualitative argument, and no experimental data is never available for
to identify.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/05/005/A
Code_Aster ®
Version
7.4
Titrate:
SSNV176 Identification of law ENDO_ORTH_BETON
Date
:
05/09/05
Author (S):
V. GODARD Key
:
V6.04.176-A Page:
12/12
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