Code_Aster ®
Version
7.4
Titrate:
Modeling 3d_INCO


Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
U3.14.06-D Page
: 1/4

Organization (S): EDF-R & D/AMA, DeltaCAD
Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
Document: U3.14.06
Modeling 3d_INCO

Summary:

This document describes for modeling 3d_INCO:

· degrees of freedom carried by the finite elements which support modeling,
· the related meshs supports,
· laws of behavior and loadings supported,
· non-linear possibilities,
· case-tests implementing modeling.

This modeling is based on finite elements adapted to the processing of the problems
quasi-incompressible. It is essential to carry out calculations of limiting analysis with the law of
Norton-Hoff and is also useful for the studies presenting of strong plastic deformations for which
traditional formulation in displacement appears insufficient (oscillation of the constraints). The formulation used
is a formulation with 3 fields: displacement-pressure-swelling [R6.03.05], usable with all them
behaviors written in incremental form. Modeling 3d_INCO has voluminal meshs supports and
accept the TETRA10, the HEXA20, and the PENTA15.
Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modeling 3d_INCO


Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
U3.14.06-D Page
: 2/4

1 Discretization

1.1
Degrees of freedom

Modeling
Ddl with all the nodes
Ddl only with the nodes nodes

3D
DX, DY, DZ
CLOSE (*), GONF

* no kinematic condition can be imposed on the degree of freedom PRES.

1.2
Net support of the matrices of rigidity

For modeling 3D, the meshs support of the finite elements can be tetrahedrons,
hexahedrons or of the prisms.

Modeling Nets
Interpolation
in
Interpolation in
displacements
pressure and swelling

3D TETRA10
Quadratic Linear
HEXA20
Quadratic Linear
PENTA15
Quadratic Linear

1.3
Net support of the surface loadings

Modeling
Net
Interpolation in displacements

3D TRIA6
Quadratic
QUAD8 Quadratique

2 Loadings
supported

The loadings available under AFFE_CHAR_MECA_ are as follows:

· “FORCE_ARETE”
Allows to apply linear forces, with an edge of voluminal element.

· “FORCE_FACE”
Allows to apply surface forces to a voluminal face of element.

· “FORCE_INTERN”
Allows to apply voluminal forces.

· “PESANTEUR”
Allows to apply a loading of the gravity type.

· “PRES_REP”
Allows to apply a pressure to a field of continuous medium.

Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modeling 3d_INCO


Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
U3.14.06-D Page
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3 Possibilities
non-linear

Attention, this modeling is accessible only starting from STAT_NON_LINE. It cannot be
used with MECA_STATIQUE or by a manual assembly.

3.1
Laws of behavior

All the laws of behavior usable on meshs of continuous mediums have a physical direction
for these modelings and are allocatable as from the moment when they are accessible from
COMP_INCR in STAT_NON_LINE (Cf. [U4.51.11]).

Let us announce that a law of behavior is specific to this modeling (dedicated to the calculation of load
limit, cf [R7.07.01]):

/“NORTON_HOFF”

3.2 Deformations

Deformations available, used in the relations of behavior under the key word
DEFORMATION for operators STAT_NON_LINE, DYNA_NON_LINE and DYNA_TRANS_EXPLI are
(Cf [U4.51.11]):

/“PETIT”
The deformations used for the relation of behavior are the deformations
linearized.

/“SIMO_MIEHE”
Allows to carry out calculations in great plastic deformations.

3.3
Method of Newton

For the resolution of the problem by the method of Newton-Raphson, the elastic matrix is not
available. It is thus necessary to use under key word NEWTON for operators STAT_NON_LINE and
DYNA_NON_LINE (cf [U4.51.11]):

/PREDICTION = “TANGENT”

The phase of prediction is carried out with the tangent matrix.

/MATRIX = “TANGENT”

The matrix used for the iterations total is the tangent matrix

Note:

The formulation used leads to nonpositive matrices and the current solveurs do not know
to solve always well the linear systems which are associated for them. In the event of difficulty of
convergence, it can thus be useful to test the other solveurs available in the code or them
other methods of renumérotations (cf [U4.50.01]).

Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Modeling 3d_INCO


Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER Key
:
U3.14.06-D Page
: 4/4

4
Examples of implementation: case-tests

· Small deformations:
SSLV130A [V3.04.130]: Analyze of a hollow roll into incompressible, subjected to a pressure
intern.

· Great deformations:
SSNV112A [V6.04.112]: Analyze of a hollow roll into incompressible in great deformations,
subjected to an internal radial displacement.

· Analyze limit:
SSNV124B [V6.04.124]: Determination of the load limits of a cube subjected to loadings
on its edges.

Handbook of Utilization
U3.14 booklet: Mechanical finite elements 3D
HT-66/05/004/A

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