Code_Aster
®
Version
7.1
Titrate:
SSNP122 - Traction. Model of Rousselier in versions local and nonlocal
Date:
05/08/03
Author (S):
V. CANO
Key
:
V6.03.122-A
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.122
SSNP122 - Traction. Model of Rousselier in
versions local and nonlocal
Summary:
This quasi-static test consists in applying to a bar a loading of traction. Two versions are used
model of Rousselier with the kinematics of the great deformations of Simo and Miehe: the local version and
the nonlocal version (model with gradient of internal variables). For a test tensile, terms in
gradient are not activated: one thus finds the results of the local version, at least as long as the solution
local version remains homogeneous (not localization).
The bar is modelized by a quadrangular element (QUAD8) in plane deformation.
The results obtained are results of nonregression. The two models give identical results
as long as the solution of the local version does not locate. The solution of the model with gradient remains homogeneous all
with the length of the way of loading.
Code_Aster
®
Version
7.1
Titrate:
SSNP122 - Traction. Model of Rousselier in versions local and nonlocal
Date:
05/08/03
Author (S):
V. CANO
Key
:
V6.03.122-A
Page:
2/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
1 (mm)
1
2
3
4
1 (mm)
y
X
Z
1.2
Properties of material
Isotropic elasticity
Young modulus:
MPa
200000
E
=
Poisson's ratio:
= 0.3
Coefficients of the model of Rousselier
Initial porosity:
01
.
0
F
0
=
2
=
D
MPa
500
1
=
Rational traction diagram
Deformation logarithmic curve
0.0
0.002
1.002
Rational stress (MPa)
0.0
400.0
2400.0
Nonlocal model
Characteristic length: 0.1mm
Code_Aster
®
Version
7.1
Titrate:
SSNP122 - Traction. Model of Rousselier in versions local and nonlocal
Date:
05/08/03
Author (S):
V. CANO
Key
:
V6.03.122-A
Page:
3/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A
1.3
Boundary conditions and loadings
The bar, locked in the direction
y
However
on the face [1,2], is subjected to a displacement U (T) on the face
[3, 4].
1 2
3
4
U (T)
1.5
1.5
T (S)
U (mm)
1.4 Conditions
initial
Null stresses and deformations with T = 0.
2
Results of reference
We do not have reference solution.
·
As long as the solution of the local model remains homogeneous for the various points of Gauss,
i.e. for t=0.93s, one will take as reference solution the results obtained with
Code_Aster for this model. For the results of the model with gradient, one must find
exactly results obtained with the local version. At this moment, one will thus test, for
two models, the stress of Cauchy
yy
in the direction y, the stress of Cauchy
zz
in direction Z, cumulated plastic deformation p and the porosity F, calculated at the point of
Gauss n°1 of the mesh [1,2,3,4].
·
For the model with gradient, the answer must remain homogeneous in the points of Gauss all with
length of the way of loading. To test this result, one will adopt as solution of
reference, the stress of Cauchy
yy
in the direction y at the points of Gauss n°1, 2, 3 and 4
mesh [1,2,3,4] and at the final moment.
Code_Aster
®
Version
7.1
Titrate:
SSNP122 - Traction. Model of Rousselier in versions local and nonlocal
Date:
05/08/03
Author (S):
V. CANO
Key
:
V6.03.122-A
Page:
4/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 2D: 1 quadrangle QUAD8
N8
N5
N6
N1
N2
N3
With
B
C
D
y
N4
N7
The imposed loading is as follows:
·
the nodes N1, N5 and N2 are locked according to the direction y,
·
the N1 node is locked according to direction X,
·
the nodes N4, N7 and N3 undergo a displacement of 1.5mm in 1.5s distributed according to 50
increments.
3.2 Functionalities
tested
For the model of Rousselier in local version, the functionalities tested are:
Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELING
“D_PLAN_SI”
DEFI_MATERIAU ROUSSELIER
STAT_NON_LINE COMP_INCR
RELATION
“ROUSSELIER”
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
RECH_LINEAIRE
ITER_LINE_MAXI
5
CONVERGENCE
ITER_INTE_MAXI
15
CONVERGENCE
RESI_INTE_RELA
10
- 06
For the model of Rousselier in nonlocal version, the functionalities tested are:
Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELING
“D_PLAN_GRAD_VARI”
DEFI_MATERIAU ROUSSELIER
NON_LOCAL
STAT_NON_LINE COMP_INCR
RELATION
“ROUSSELIER”
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
CONVERGENCE
ITER_INTE_MAXI
15
CONVERGENCE
RESI_INTE_RELA
10
- 06
LAGR_NON_LOCAL
Code_Aster
®
Version
7.1
Titrate:
SSNP122 - Traction. Model of Rousselier in versions local and nonlocal
Date:
05/08/03
Author (S):
V. CANO
Key
:
V6.03.122-A
Page:
5/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested
The values are calculated at the point of Gauss.
At the moment of calculation T = 0.93s, one finds for the two models:
For the model of Rousselier in local version:
Identification Reference
Aster %
difference
At the point of Gauss n° 1
yy
1056.20 1056.27 0.007
zz
179.51 179.42 - 0.048
p
0.6536 0.6538 0.04
F
0.2108 0.2110 0.097
For the model of Rousselier in nonlocal version:
Identification Reference
Aster %
difference
At the point of Gauss n° 1
yy
1056.20 1056.20 - 1.37
10
- 04
zz
179.51 179.51
- 5.17
10
- 05
p
0.6536 0.6536 6.93
10
- 04
F
0.2108 0.2107
- 0.009
At the final moment T = 1.5s, one finds for the model with gradient:
Identification Reference
Aster %
difference
At the point of Gauss n° 1:
yy
799.19100 799.19116 1.98
10
- 05
At the point of Gauss n° 2:
yy
799.19100 799.19116 1.98
10
- 05
At the point of Gauss n° 3:
yy
799.19100 799.19116 1.98
10
- 05
At the point of Gauss n° 4:
yy
799.19100 799.19116 1.98
10
- 05
Code_Aster
®
Version
7.1
Titrate:
SSNP122 - Traction. Model of Rousselier in versions local and nonlocal
Date:
05/08/03
Author (S):
V. CANO
Key
:
V6.03.122-A
Page:
6/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A
5
Summary of the results
As long as the solution of the local model remains homogeneous, values obtained with the two versions of
model of Rousselier are identical.
For the model with gradient, the solution remains homogeneous throughout the loading.