Code_Aster ®
Version
6.2
Titrate:
SSNP117 - Modèle of ROUSSELIER in 2D - DP


Date:
09/09/03
Author (S):
R. MASSON, Key Mr. BONNAMY
:
V6.03.117-A Page:
1/4

Organization (S): EDF-R & D/MMC, AUSY

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.117

SSNP117 - Modèle de Rousselier in 2D - DP

Summary:

This test of nonlinear quasi-static mechanics makes it possible to validate the model of Rousselier in 2D
plane deformations for the following configurations: elastoplastic basic model, model germination and
viscoplastic model with theta-method for integration of the law of behavior.

Modeling is carried out with a quadratic element 2D, in plane deformation.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A

Code_Aster ®
Version
6.2
Titrate:
SSNP117 - Modèle of ROUSSELIER in 2D - DP


Date:
09/09/03
Author (S):
R. MASSON, Key Mr. BONNAMY
:
V6.03.117-A Page:
2/4

1
Problem of reference

1.1 Geometry

One considers a mesh square 2D:

Y

P1
L32
P2

L21

L43

X

P3
P4
L14

The sides L21, L32, L43, L14 measure each one 10 Misters.

1.2
Properties of material

One takes: E=200 GPa, and = 0,3.
The traction diagram employed is given in the following table:


0.0001 0.00338 0.03
0.04
0.05 0.07 0.10 0.15 0.2.0.3.0.4
27.30 222.72 519.58 580.94 633.48 721.82 828.96 970.19 1084.75 1269.57 1419.48


0.5.0.7.1.0 1.5 2.0






1547.86 1763.72 2025.50
2370.59 2650.53

The model of Rousselier is employed in three configurations with the following parameters:


Elastoplastic basic model
Elastoplastic model
Viscoplastic model
(ROUSS_PR)
(ROUSS_PR) with germination
(VISCOROUSS) and theta-method
· D = 2.
· D = 2.
· D = 2.
· 1 = 600 MPa
· 1 = 600 MPa
· 1 = 600 MPa
· = 1.
· = 1.
· = 1.
· f0 = 1.e-4 (initial porosity)
· f0 = 1.e-4
· f0 = 1.e-4
· FC = 1. (porosity criticizes)
· FC = 1.
· FC = 1.
· To = 1.
· To = 1.
· To = 1.
· Year = 0.6
· 0 = 27 MPa
· 0 = 1.e-2
· = 0.57
· m = 2

Handbook of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A

Code_Aster ®
Version
6.2
Titrate:
SSNP117 - Modèle of ROUSSELIER in 2D - DP


Date:
09/09/03
Author (S):
R. MASSON, Key Mr. BONNAMY
:
V6.03.117-A Page:
3/4

1.3
Boundary conditions and loadings

While referring to the figure [§1.1] boundary conditions are as follows:

· on the edge L32 displacement L imposed following direction OY (monotonous traction),
· blocked displacements of L21 following X,
· blocked displacements of L14 following Y.

The evolution temporal of lengthening L are deferred in the following table:

Time [S]
0.
10.
Displacement L [mm]
0. 10.

The evolution is linear between the two moments.

1.4 Conditions
initial

Null constraints and deformations.

2
Reference solutions

2.1
Method of calculation

Without object.

2.2
Sizes and results of reference

Values of porosity at the final moment at the points of Gauss.

2.3
Uncertainties on the solution

Without object.

3 Modeling
With

3.1
Characteristics of the grid

A number of nodes: 8
A number of meshs and types: 1 (QUA8)

3.2
Characteristics of modeling

Plane deformations with under-integration (DP_SI).
Handbook of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A

Code_Aster ®
Version
6.2
Titrate:
SSNP117 - Modèle of ROUSSELIER in 2D - DP


Date:
09/09/03
Author (S):
R. MASSON, Key Mr. BONNAMY
:
V6.03.117-A Page:
4/4

3.3 Functionalities
tested

Commands




DEFI_MATERIAU ROUSSELIER PORO_INIT



D_SIGM_EPSI_NORM

PORO_CRIT

D

SIGM_1

PORO_ACCE
VISCOROUSS
SIGM_1

SIGM_0

M

EPSI_0
ELAS
TRACTION
STAT_NON_LINE COMP_INCR RELATION
ROUSS_PR

DEFORMATION
PETIT_REAC
STAT_NON_LINE COMP_INCR RELATION
VISCOROUSS

DEFORMATION
PETIT_REAC

3.4
Sizes tested and results

Model
Code_Aster

porosity F (t=10s.)
Basic model
0,03257572
Model with nucleation
0,39058042
Viscoplastic model (= 0,57)
0,03352194

4
Summary of the results

The results obtained by Code_Aster show that the model of Rousselier functions and gives
coherent results with the awaited theoretical results.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A

Outline document