SSNV176 - Identification of law ENDO_ORTH

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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

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Manual of Validation

V6.04 booklet: Nonlinear statics of the voluminal structures

HT-66/05/005/A

Organization (S):

EDF-R & D/AMA

Manual 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 piloting
3) compression

simple

4) simple compression with piloting
5) simple traction, simple compression and a biaxial test

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SSNV176 Identification of law ENDO_ORTH_BETON

Date

05/09/05

Author (S):

V. GODARD

Key

V6.04.176-A

Page:

2/12

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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)

DY (N2)

DX (N3)

DX (N2) =DY (N1)

DX (N3) =DZ (N1)

DY (N3) =DZ (N2)

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):

: FX on F1 and

3/3

FX on F4, FX<0 (traction according to X)

: FX on F1 and

3/3

FX on F4, FX<0 (compression according to X)

: FY on F2 and

3/3

FY on F4, FY<0 (traction according to y)

: FY on F2 and

3/3

FY on F4, FY<0 (compression according to y)

: FZ on F3 and

3/3

FZ on F4, FZ<0 (traction according to Z)

: FZ on F3 and

3/3

FZ on F4, FZ<0 (compression according to Z)

Blockings

N0: DX=DY=DZ=0

Linear relations:
DY (N1) =DX (N2)
DZ (N1) =DX (N3)
DZ (N2) =DY (N2)

Traction/compression in imposed displacement:
According to X DX imposed on N1
According to y DY imposed on N2
According to X DZ imposed on N3

Definition of the faces:

F1=N0 N2 N3

F2=N0 N1 N3

F3=N0 N1 N2

F4=N1 N2 N3

Traction/compression in imposed force:
According to X: FX on F1 and

3/3

FX on F4

According to y: FY on F2 and

3/3

FY on F4

According to X: FZ on F3 and

3/3

FZ on F4

Appear 1.1-a: Geometry and boundary conditions of the uniaxial tests

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SSNV176 Identification of law ENDO_ORTH_BETON

Date

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V. GODARD

Key

V6.04.176-A

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1.2

Material properties

The characteristics materials are identical for the 5 tests which are presented.

The elastic characteristics of materials are as follows:

32000

;

0.2

MPa

The breaking stresses in traction and compression are:

3, 2

;

31,8

traction

compression

rupture

MPa

= -

One uses the play of parameter following for the law of behavior:

ALPHA

K0 (Mpa) ECROB (MJ/m

)

ECROD

(MJ/m

) K

(Mpa)

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: Response of law ENDO_ORTH_BETON in simple traction

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SSNV176 Identification of law ENDO_ORTH_BETON

Date

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Author (S):

V. GODARD

Key

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Appear 1.2-b: Response of law ENDO_ORTH_BETON in simple compression

The internal variables, which are numbered in Aster, have the following significance:

V1=D

; V2=D

; V3=D

; V4=D

; V5=D

; V6=D

; 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]).

Reference solution

This test is a test of nonregression.

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SSNV176 Identification of law ENDO_ORTH_BETON

Date

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V. GODARD

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V6.04 booklet: Nonlinear statics of the voluminal structures

HT-66/05/005/A

3 Modeling

With

3.1

Characteristics of modeling

Modeling 3D

Element MECA_TETRA4.

3.2

Characteristics of the mesh

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 piloting).

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

DEPL

DX N1 3.E-04

EPSI_ELGA_DEPL

EPXX

VOLUME, point 1

3.E-04

SIEF_ELGA

SIXX

VOLUME, point 1

1.11388E+00

VARI_ELGA

V1 (D

)

VOLUME, point 1

6.59365E-01

VARI_ELGA

V7 (D)

VOLUME, point 1

2.42260E-04

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SSNV176 Identification of law ENDO_ORTH_BETON

Date

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Author (S):

V. GODARD

Key

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Page:

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V6.04 booklet: Nonlinear statics of the voluminal structures

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4 Modeling

4.1

Characteristics of modeling

Modeling 3D

Element MECA_TETRA4.

4.2

Characteristics of the mesh

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 piloting 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

DEPL

DX N1 - 3.E-03

EPSI_ELGA_DEPL

EPXX

VOLUME, point 1

- 3.E-03

SIEF_ELGA

SIXX

VOLUME, point 1

- 2.74465E+01

VARI_ELGA

V2 (D

)

VOLUME, point 1

1.30416E-01

VARI_ELGA

V7 (D)

VOLUME, point 1

4.80080E-01

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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

Manual of Validation

V6.04 booklet: Nonlinear statics of the voluminal structures

HT-66/05/005/A

5 Modeling

5.1

Characteristics of modeling

Modeling 3D

Element MECA_TETRA4.

5.2

Characteristics of the mesh

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 piloting 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 piloting of the loading
PRED_ELAS (cf Doc. [R5.03.80]).

5.5 Values

tested

Moment

Name of the field

Component

Place

Aster

DEPL

DX N1 1.44744E-04

EPSI_ELGA_DEPL

EPXX

VOLUME, point 1

1.44744E-04

SIEF_ELGA

SIXX

VOLUME, point 1

2.89945E+00

VARI_ELGA

V1 (D

)

VOLUME, point 1

2.08793E-01

VARI_ELGA

V7 (D)

VOLUME, point 1

2.30235E-04

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SSNV176 Identification of law ENDO_ORTH_BETON

Date

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Author (S):

V. GODARD

Key

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Page:

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V6.04 booklet: Nonlinear statics of the voluminal structures

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6 Modeling

6.1

Characteristics of modeling

Modeling 3D

Element MECA_TETRA4.

6.2

Characteristics of the mesh

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 piloting 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 piloting of the loading
PRED_ELAS (cf Doc. [R5.03.80]).

6.5 Values

tested

Moment

Name of the field

Component

Place

Aster

DEPL

DX N1 - 1.17993E-03

EPSI_ELGA_DEPL

EPXX

VOLUME, point 1

- 1.17993E-03

SIEF_ELGA

SIXX

VOLUME, point 1

- 2.86498E+01

VARI_ELGA

V2 (D

)

VOLUME, point 1

4.73153E-02

VARI_ELGA

V7 (D)

VOLUME, point 1

1.34312E-01

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Titrate:

SSNV176 Identification of law ENDO_ORTH_BETON

Date

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Author (S):

V. GODARD

Key

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Page:

9/12

Manual of Validation

V6.04 booklet: Nonlinear statics of the voluminal structures

HT-66/05/005/A

7 Modeling

7.1

Characteristics of modeling

Modeling 3D

Element MECA_TETRA4.

7.2

Characteristics of the mesh

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) U

: Simple traction

2) U

: Compression

3) U

:Biaxial loading (traction in the direction y, compression in direction X, with one

report/ratio fixes stresses:

0.2

= -

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 stress in traction

biaxial test is lower than the stress of

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 piloting of loading PRED_ELAS, because the behavior is

polishing substance. The following loadings are applied:

1) U

: FX on F1,

3/3

FX on F4, FX<0 (Traction)

2) U

: FX on F1,

3/3

FX on F4, FX>0 (Compression)

3) U

: FX on F1,

3/3

FX on F4, FX>0 (Compression according to axis X);

FY on F2,

3/3

FY on F4, with FY= - 0,2 FX (Traction according to the axis y).

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SSNV176 Identification of law ENDO_ORTH_BETON

Date

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Author (S):

V. GODARD

Key

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Page:

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Manual of Validation

V6.04 booklet: Nonlinear statics of the voluminal structures

HT-66/05/005/A

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 stress

. One obtains

then the breaking stress in traction (U1), in compression (U2), and one checks that the stress of
traction in the biaxial test (U3) is lower than the breaking stress in simple traction (U1):

· U1:

3.20684 MPa

traction

rupture

· U2:

31.8MPa

compression

rupture

= -

· U3:

0.2

0.2 * 14.2038 MPa

traction

compression

traction

rupture

= -

Warning 1: It may be that the number of pitches 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 piloting). The maximum stress in absolute value should not be
attack for the last pitch 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 piloting reached, equal to the greatest stress
of compression

attack in absolute value, like reference to gauge K2. This is true only

if there are problems of convergence. If there is no problem of convergence for
U3 calculation, and that the maximum stress in absolute value is reached for the last pitch of time,
calculation should be continued.

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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:

11/12

Manual of Validation

V6.04 booklet: Nonlinear statics of the voluminal structures

HT-66/05/005/A

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.