Code_Aster
®
Version
6.2
Titrate:
SSNP117 - Model of ROUSSELIER in 2D - DP
Date:
09/09/03
Author (S):
R. MASSON, Mr. BONNAMY
Key
:
V6.03.117-A
Page:
1/4
Manual of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A
Organization (S):
EDF-R & D/MMC, AUSY
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.117
SSNP117 - Model of 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.
Code_Aster
®
Version
6.2
Titrate:
SSNP117 - Model of ROUSSELIER in 2D - DP
Date:
09/09/03
Author (S):
R. MASSON, Mr. BONNAMY
Key
:
V6.03.117-A
Page:
2/4
Manual of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A
1
Problem of reference
1.1 Geometry
One considers a mesh square 2D:
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
(
ROUSS_PR
)
Elastoplastic model
(
ROUSS_PR
) with germination
Viscoplastic model
(
VISCOROUSS
) and theta-method
·
D = 2.
·
1
= 600 MPa
·
= 1.
·
f0 = 1.e-4 (initial porosity)
·
FC = 1. (porosity criticizes)
·
To = 1.
·
D = 2.
·
1
= 600 MPa
·
= 1.
·
f0 = 1.e-4
·
FC = 1.
·
To = 1.
·
Year = 0.6
·
D = 2.
·
1
= 600 MPa
·
= 1.
·
f0 = 1.e-4
·
FC = 1.
·
To = 1.
·
0
= 27 MPa
·
0
= 1.e-2
·
= 0.57
·
m = 2
X
Y
P2
P1
P3
P4
L43
L32
L21
L14
Code_Aster
®
Version
6.2
Titrate:
SSNP117 - Model of ROUSSELIER in 2D - DP
Date:
09/09/03
Author (S):
R. MASSON, Mr. BONNAMY
Key
:
V6.03.117-A
Page:
3/4
Manual of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A
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 according to direction OY (monotonous traction),
·
locked displacements of L21 following X,
·
locked displacements of L14 following Y.
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 stresses 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 mesh
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
).
Code_Aster
®
Version
6.2
Titrate:
SSNP117 - Model of ROUSSELIER in 2D - DP
Date:
09/09/03
Author (S):
R. MASSON, Mr. BONNAMY
Key
:
V6.03.117-A
Page:
4/4
Manual of Validation
V6.03 booklet: Nonlinear statics of the system plans
HT-26/03/023/A
3.3 Functionalities
tested
Controls
DEFI_MATERIAU ROUSSELIER
VISCOROUSS
ELAS
TRACTION
PORO_INIT
D_SIGM_EPSI_NORM
PORO_CRIT
D
SIGM_1
PORO_ACCE
SIGM_1
SIGM_0
M
EPSI_0
STAT_NON_LINE COMP_INCR RELATION
DEFORMATION
ROUSS_PR
PETIT_REAC
STAT_NON_LINE COMP_INCR RELATION
DEFORMATION
VISCOROUSS
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.