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

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.129

SSNL129 ­ Validation of laws VISC_ISOT_TRAC and
VISC_ISOT_LINE on a tensile test

Summary:

This test consists in applying to an elementary volume a loading of traction. Three speeds of
loading are modelled.

Modelings A, B and C make it possible to validate the law of behavior VISC_ISOT_TRAC
(DEFORMATION=' SIMO_MIEHE') in 3D, D_PLAN and AXIS. For that, the results obtained are compared
with the viscous law of Rousselier ROUSS_VISC and degenerated DEFORMATION=' PETIT_REAC' in order to it
that the evolution of porosity is negligible. Modelings D, E and F make it possible to validate the integration of
law VISC_ISOT_LINE (DEFORMATION=' SIMO_MIEHE') in 3D, D_PLAN and AXIS. For that, results
obtained are compared with those given by law VISC_ISOT_TRAC for the same linear work hardening.

Handbook of Validation
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1
Problem of reference

1.1 Geometry

It is a question of testing the 2 viscoplastic laws of behavior VISC_ISOT_TRAC and VISC_ISOT_LINE
on Volume Elémentaire representative R of dimension 1mm, is a cube in 3D, the equivalent of one
bar in plane deformations or of a cylinder into axisymmetric.

1.2
Properties of material

Isotropic elasticity
Young modulus: E =
MPa

215000

Poisson's ratio: = 0.3
Traction diagram (MOD. With, B and C)
Traction diagram
1100
1000
900
has
)
P
M
800
T
E
(
700
T
R
has
in
N
C
O
600
500
400
0
0,2
0,4
0,6
0,8
1
deformation

Linear work hardening (MOD. D, E and F)
= 477.
MPa

1267117
y

= 529.853045MPa
T
E


Coefficient for viscous law

MPa

6176
0 =

VISC_SINH
13
0 =
10

483
3.31131121

m = 6.76


Coefficients of the model of Rousselier
9
-
f0 = 510
used to obtain the solution of
D = 0.0001
reference (MOD. With, B and C)


MPa

1575
1 =


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1.3
Boundary conditions and loadings

The element of volume is subjected to a homogeneous simple tensile test. It is thus blocked in X on
the face [3,4] and in y on the face [1,3] (and possibly in direction Z) and subjected to one
displacement U (T) in the direction y
However on the face [1, 2].
3 values of T are used 2000 S, 0.2 S and 0.002s, corresponding to speeds of deformations
& of 10-3 s-1, 10 s-1 and 103 s-1.


y

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

1 mm


1.4 Conditions
initial

Null constraints and deformations with T = 0.

2
Results of reference

For the model VISC_ISOT_TRAC which one tests in modelings A, B and C, the validation is done
by comparison with the results obtained with the model ROUSS_VISC whose parameters were
selected in order to make negligible the evolution of porosity and thus to be reduced to the model
viscoplastic “traditional”.
For model VISC_ISOT_LINE tested in modelings D, E and F, one compares the solution
obtained with VISC_ISOT_TRAC for which one defined a linear work hardening (one only preserves
the points ends of the curve used to validate this model).
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3 Modeling
With

3.1
Characteristics of modeling

Modeling 3D: 1 HEXA20

S5
S1
S2
S4
S2y
S3
X
Z
S6
Z


The imposed loading is as follows:

·
The S6 face is blocked according to the direction y,
·
The S2 face is blocked according to direction X,
·
The S1 face is blocked according to direction Z
·
The S5 face undergoes a displacement of 2 mm in 2000 S, 0.2 S or 0.002 S in 100 increments.

The law of behavior tested is law VISC_ISOT_TRAC.

3.2 Functionalities
tested

Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELISATION
3d'
DEFI_MATERIAU TRACTION


VISC_SINH


STAT_NON_LINE COMP_INCR
RELATION
“VISC_ISOT_TRAC”
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
CONVERGENCE
ITER_INTE_MAXI
10
CONVERGENCE
RESI_INTE_RELA
10-09

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4
Results of modeling A

One tests the effort of reaction on the S5 face for 3 speeds of deformation for the values of
displacement: 0.1mm, 1mm and 2mm.

Displacement U = 0.1 mm

Identification Reference
Aster %
difference
Slow speed
639.207
639.294
0.014
Mean velocity
697.092
697.070
- 0.003
Fast speed
772.983 772.885 - 0.013

Displacement U = 1 mm

Identification Reference
Aster %
difference
Slow speed
484.913
484.672
- 0.050
Mean velocity
516.997
513.863
- 0.606
Fast speed
555.633 552.167 - 0.624

Displacement U = 2 mm

Identification Reference
Aster %
difference
Slow speed
347.473
347.661
0.054
Mean velocity
369.458
365.992
- 0.938
Fast speed
393.799 390.046 - 0.953

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5 Modeling
B

5.1
Characteristics of modeling

Modeling D_PLAN: 1 QUAD8

L23
2
3
L12
L34
y
X
1
L41
4


The imposed loading is as follows:

·
The L41 side is blocked in the direction y,
·
The L12 side is blocked in direction X,
·
The L23 side undergoes a displacement of 2 mm in 2000 S, 0.2 S or 0.002 S in 100 increments.

The law of behavior tested is law VMIS_ISOT_TRAC_V.

5.2 Functionalities
tested

Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELISATION
“D_PLAN”
DEFI_MATERIAU TRACTION


VISC_SINH


STAT_NON_LINE COMP_INCR
RELATION
“VISC_ISOT_TRAC”
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
CONVERGENCE
ITER_INTE_MAXI
10
CONVERGENCE
RESI_INTE_RELA
10-09

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6
Results of modeling B

One tests the effort of reaction on the L23 face for 3 speeds of deformation for the values of
displacement: 0.1mm, 1mm and 2mm.

Displacement U = 0.1 mm

Identification Reference
Aster %
difference
Slow speed
752.473
750.523
- 0.259
Mean velocity
820.703
818.465
- 0.273
Fast speed
910.274 907.610 - 0.293

Displacement U = 1 mm

Identification Reference
Aster %
difference
Slow speed
575.182
572.674
- 0.436
Mean velocity
609.788
607.023
- 0.453
Fast speed
655.218 652.093 - 0.477

Displacement U = 2 mm

Identification Reference
Aster %
difference
Slow speed
413.295
411.243
- 0.496
Mean velocity
435.051
432.815
- 0.514
Fast speed
463.612 461.120 - 0.538

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7 Modeling
C

7.1
Characteristics of modeling

Modeling AXIS: 1 QUAD8

L23
L12
L34
y
X
L41


The imposed loading is as follows:

·
The L41 side is blocked in the direction y,
·
The L23 side undergoes a displacement of 2 mm in 2000 S, 0.2 S or 0.002 S in 100 increments.

The law of behavior tested is law VISC_ISOT_TRAC.

7.2 Functionalities
tested

Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELISATION
“AXIS”
DEFI_MATERIAU TRACTION


VISC_SINH


STAT_NON_LINE COMP_INCR RELATION
“VISC_ISOT_TRAC”
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
CONVERGENCE
ITER_INTE_MAXI
10
CONVERGENCE
RESI_INTE_RELA
10-09

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8
Results of modeling C

One tests the effort of reaction on the L23 face for 3 speeds of deformation for the values of
displacement: 0.1mm, 1mm and 2mm.

Displacement U = 0.1 mm

Identification Reference
Aster %
difference
Slow speed
319.604
319.647
0.013
Mean velocity
348.483
348.535
0.015
Fast speed
386.388 386.442
0.014

Displacement U = 1 mm

Identification Reference
Aster %
difference
Slow speed
242.457
242.336
- 0.050
Mean velocity
257.078
256.931
- 0.057
Fast speed
276.269 276.084 - 0.067

Displacement U = 2 mm

Identification Reference
Aster %
difference
Slow speed
174.061
173.831
- 0.132
Mean velocity
183.251
182.996
- 0.139
Fast speed
195.314 195.023 - 0.149

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9 Modeling
D

9.1
Characteristics of modeling

Modeling 3D: 1 HEXA20

S5
S1
S2
S4
S2y
S3
X
Z
S6
Z


The imposed loading is as follows:

·
The S6 face is blocked according to the direction y,
·
The S2 face is blocked according to direction X,
·
The S1 face is blocked according to direction Z
·
The S5 face undergoes a displacement of 2 mm in 2000 S, 0.2 S or 0.002 S in 100 increments.

The law of behavior tested is law VISC_ISOT_LINE.

9.2 Functionalities
tested

Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELISATION
3d'
DEFI_MATERIAU ECRO_LINE

VISC_SINH


STAT_NON_LINE COMP_INCR RELATION
“VISC_ISOT_LINE”
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
CONVERGENCE
ITER_INTE_MAXI
10
CONVERGENCE
RESI_INTE_RELA
10-09

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10 Results of modeling D

One tests the effort of reaction on the S5 face for 3 speeds of deformation for the values of
displacement: 0.1mm, 1mm and 2mm.

Displacement U = 0.1 mm

Identification Reference
Aster %
difference
Slow speed
498.936
499.026
0.018
Mean velocity
556.844
556.945
0.018
Fast speed
632.832 362.948 0.018

Displacement U = 1 mm

Identification Reference
Aster %
difference
Slow speed
433.411
433.422
0.003
Mean velocity
462.578
462.591
0.003
Fast speed
500.853 500.868 0.003

Displacement U = 2 mm

Identification Reference
Aster %
difference
Slow speed
360.757
360.740
- 0.005
Mean velocity
379.083
379.066
- 0.005
Fast speed
403.131 403.113 - 0.004

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11 Modeling
E

11.1 Characteristics of modeling

Modeling D_PLAN: 1 QUAD8

L23
L12
L34
y
X
L41


The imposed loading is as follows:

·
The L41 side is blocked in the direction y,
·
The L23 side undergoes a displacement of 2 mm in 2000 S, 0.2 S or 0.002 S in 100 increments.

The law of behavior tested is law VISC_ISOT_LINE.

11.2 Functionalities
tested

Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELISATION
“D_PLAN”
DEFI_MATERIAU ECRO_LINE

VISC_SINH


STAT_NON_LINE COMP_INCR RELATION
“VISC_ISOT_LINE”
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
CONVERGENCE
ITER_INTE_MAXI
10
CONVERGENCE
RESI_INTE_RELA
10-09

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12 Results of modeling E

One tests the effort of reaction on the L23 face for 3 speeds of deformation for the values of
displacement: 0.1mm, 1mm and 2mm.

Displacement U = 0.1 mm

Identification Reference
Aster %
difference
Slow speed
583.729
583.873
0.025
Mean velocity
651.843
652.008
0.025
Fast speed
741.214 741.406 0.026

Displacement U = 1 mm

Identification Reference
Aster %
difference
Slow speed
530.975
531.065
0.017
Mean velocity
565.249
565.350
0.018
Fast speed
610.221 610.335 0.019

Displacement U = 2 mm

Identification Reference
Aster %
difference
Slow speed
448.942
449.007
0.014
Mean velocity
470.456
470.528
0.015
Fast speed
498.687 498.767 0.016

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13 Modeling
F

13.1 Characteristics of modeling

Modeling AXIS: 1 QUAD8

L23
L12
L34
y
X
L41


The imposed loading is as follows:

·
The L41 side is blocked in the direction y,
·
The L23 side undergoes a displacement of 2 mm in 2000 S, 0.2 S or 0.002 S in 100 increments.

The law of behavior tested is law VMIS_ISOT_LINE

13.2 Functionalities
tested

Order
Key word factor
Simple key word
Argument
AFFE_MODELE AFFE
MODELISATION
“AXIS”
DEFI_MATERIAU ECRO_LINE

VISC_SINH


STAT_NON_LINE COMP_INCR RELATION
'VMIS_ISOT_LINE
COMP_INCR
DEFORMATION
“SIMO_MIEHE”
CONVERGENCE
ITER_INTE_MAXI
10
CONVERGENCE
RESI_INTE_RELA
10-09

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14 Results of modeling F

One tests the effort of reaction on the L23 face for 3 speeds of deformation for the values of
displacement: 0.1mm, 1mm and 2mm.

Displacement U = 0.1 mm

Identification Reference
Aster %
difference
Slow speed
249.468
249.513
0.018
Mean velocity
278.422
278.473
0.018
Fast speed
316.416 316.474 0.018

Displacement U = 1 mm

Identification Reference
Aster %
difference
Slow speed
216.706
216.711
0.002
Mean velocity
231.289
231.296
0.003
Fast speed
250.426 250.434 0.003

Displacement U = 2 mm

Identification Reference
Aster %
difference
Slow speed
180.379
180.370
- 0.005
Mean velocity
189.542
189.533
- 0.005
Fast speed
201.566 201.557 - 0.005

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15 Summary of the results

With less than 1% of difference between model ROUSS_VISC (degenerated) and the model
VISC_ISOT_TRAC whatever the rate loading applied, one can admit that the addition
viscous component in model VISC_ISOT_TRAC is correct.
In addition very weak variations (lower than 0.02%) observed between the solutions obtained with
VISC_ISOT_LINE and VISC_ISOT_TRAC for a linear work hardening, also allow
to validate the establishment of model VISC_ISOT_LINE.
In all the cases, less than 10 local iterations are necessary to reach convergence
(precision 10-9).
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