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

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

Handbook 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 modelled 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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A

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

1
Problem of reference

1.1 Geometry



y
1 (mm)
1
4
2
3
Z
X
1 (mm)


1.2
Properties of material

Isotropic elasticity
Young modulus: E =
MPa

200000

Poisson's ratio: = 0.3
Coefficients of the model of Rousselier
Initial porosity: F
01
.
0
0 =

D = 2

MPa

500
1 =

Rational traction diagram
Deformation logarithmic curve
Rational constraint (MPa)
0.0
0.0
0.002
400.0
1.002
2400.0
Nonlocal model
Characteristic length: 0.1mm

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A

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

1.3
Boundary conditions and loadings

The bar, blocked in the direction y
However on the face [1,2], is subjected to a displacement U (T) on the face
[3, 4].



U (T)
U (mm)
1.5
4
3
T (S)
1.5
1 2



1.4 Conditions
initial

Null constraints 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 constraint of Cauchy yy in the direction y, the constraint 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 constraint 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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A

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

3 Modeling
With

3.1
Characteristics of modeling

Modeling 2D: 1 quadrangle QUAD8

y
C
D
N4
N7
N3
N8
N6
N1
N5
N2
With
B

The imposed loading is as follows:

· the nodes N1, N5 and N2 are blocked according to the direction y,
· the N1 node is blocked 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
MODELISATION
“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
MODELISATION
“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


Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A

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

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:
799.19100 799.19116 1.98
10-05
yy

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A

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

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.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/03/008/A

Outline document