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Titrate:
Mechanical modeling 3d_GRAD_EPSI


Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.14.11-A Page
: 1/6

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

Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
U3.14.11 document

Modeling 3d_GRAD_EPSI

Summary:

This document describes for mechanical modeling 3d_GRAD_EPSI:

· degrees of freedom carried by the finite elements which support modeling,
· the related meshs supports,
· supported materials and loadings,
· options of calculations for the elementary matrices and the post processing accessible to the user,
· nonlinear possibilities as well as the options of the breaking process if they exist.

Modeling 3d_GRAD_EPSI (Phénomène: MECANIQUE) corresponds to finite elements of which meshs
supports are voluminal. This modeling enriches the finite elements 3D traditional by mechanics in
adding degrees of freedom of generalized deformations allowing to carry out nonlocal calculations,
regularization utilizing the gradient of the deformations (from where the name of modeling), for more
details to see document [R5.04.02].

Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/03/002/A

Code_Aster ®
Version
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Titrate:
Mechanical modeling 3d_GRAD_EPSI


Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.14.11-A Page
: 2/6

1 Discretization

1.1
Degrees of freedom

Modeling
Degrees of freedom
(with each node node)

3d_GRAD_EPSI
DX: displacement following X

DY: displacement following Y

DZ: displacement following Z

EPXX: generalized deformation XX

EPYY: generalized deformation YY

EPZZ: generalized deformation ZZ

EPXY: generalized deformation XY

EPXZ: generalized deformation XZ

EPYZ: generalized deformation YZ


Degrees of freedom
(with each node medium)

DX: displacement following X

DY: displacement following Y

DZ: displacement following Z

1.2
Net support of the matrices of rigidity

The meshs support of the finite elements can be tetrahedrons, pyramids, prisms or
quadratic hexahedrons: displacements are interpolated with a command higher than them
deformations generalized. One indicates in the column interpolation of the table following the couples
of interpolation (displacements/generalized deformations). The elements are isoparametric.

Modeling Nets Interpolation
Remarks

3d_GRAD_EPSI TETRA10
Quadratic/linear
3d_GRAD_EPSI PYRAM13
Quadratic/linear
3d_GRAD_EPSI PENTA15
Bilinear Serendip/
3d_GRAD_EPSI HEXA20
Trilinear Serendip/

1.3
Net support of the loadings

Modeling does not require a boundary condition specific to the generalized deformations
(boundary condition natural), one thus uses for the meshs support of the loading
modeling 3D (Cf. [U3.14.01]).

2
Significance of the symbols

·
corresponds to a functionality available

corresponds to a functionality which could exist but not
currently available
Name of
corresponds to a test implementing the functionality
case-test
Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/03/002/A

Code_Aster ®
Version
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Titrate:
Mechanical modeling 3d_GRAD_EPSI


Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.14.11-A Page
: 3/6

3 Materials
supported

DEFI_MATERIAU
3d_GRAD_EPSI

% General elastic Behaviors

ELAS
SSNV157A
% General nonlinear mechanical Behaviors

ECRO_LINE
SSNV157A
BETON_ECRO_LINE
SSNV157D
MAZARS
SSNV157E

The case of the nonlinear operators is approached further.

4 Loadings
supported

The loadings are to be affected on a modeling 3D, Cf. [§1.3].

5 Possibilities
non-linear

This modeling has direction only into non-linear.

5.1
STAT_NON_LINE

COMP_INCR RELATION
3d_GRAD_EPSI

ENDO_FRAGILE
SSNV157A

ENDO_ISOT_BETON
SSNV157D

MAZARS SSNV157E

COMP_INCR DEFORMATION
3d_GRAD_EPSI

“PETIT”
SSNV157A

5.2
DYNA_NON_LINE

COMP_INCR RELATION
3d_GRAD_EPSI

ENDO_FRAGILE
·

ENDO_ISOT_BETON
·

MAZARS
·

COMP_INCR DEFORMATION
3d_GRAD_EPSI

“PETIT”
·
Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/03/002/A

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Titrate:
Mechanical modeling 3d_GRAD_EPSI


Date:
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:
U3.14.11-A Page
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6
Postprocessing of calculation

6.1 Option
CALC_ELEM


3d_GRAD_EPSI

ECIN_ELEM_DEPL
·
ENEL_ELGA
·
ENEL_ELNO_ELGA
·
EPME_ELGA_DEPL
·
EPME_ELNO_DEPL
·
EPOT_ELEM_DEPL
·
EPSI_ELGA_DEPL
·
EPSI_ELNO_DEPL
·
EQUI_ELGA_EPME
·
EQUI_ELGA_EPSI
·
EQUI_ELGA_SIGM
·
EQUI_ELNO_EPME
·
EQUI_ELNO_EPSI
·
EQUI_ELNO_SIGM
·
SIEF_ELGA_DEPL
·
SIEF_ELNO_ELGA
·
VARI_ELNO_ELGA
·

6.2 Option
CALC_CHAM_ELEM


3d_GRAD_EPSI

ECIN_ELEM_DEPL


EPOT_ELEM_DEPL
·
ENEL_ELGA
·
ENEL_ELNO_ELGA
·
EPSI_ELNO_DEPL
·
EQUI_ELGA_EPSI
·
EQUI_ELGA_SIGM
·
EQUI_ELNO_EPSI
·
EQUI_ELNO_SIGM
·
SIEF_ELGA_DEPL
·
Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/03/002/A

Code_Aster ®
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Titrate:
Mechanical modeling 3d_GRAD_EPSI


Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.14.11-A Page
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6.3 Option
CALC_NO


3d_GRAD_EPSI

FORC_NODA'
·
REAC_NODA'
·
ENEL_NOEU_ELGA'
·
EPME_NOEU_DEPL'
·
EPSI_NOEU_DEPL'
·
EQUI_NOEU_EPME'
·
EQUI_NOEU_EPSI'
·
EQUI_NOEU_SIGM'
·
SIEF_NOEU_ELGA'
·
VARI_NOEU_ELGA'
·

6.4 Option
POST_ELEM


3d_GRAD_EPSI

MASS_INER
·
ENER_POT
·
ENER_CIN


ENER_TOTALE
·
ENER_ELAS
·
Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/03/002/A

Code_Aster ®
Version
6.4
Titrate:
Mechanical modeling 3d_GRAD_EPSI


Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.14.11-A Page
: 6/6

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Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/03/002/A

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