Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
1/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
V7.22.100 document
HSNV100 - Thermoplasticity in simple traction
Summary:
This test treats the thermo plasticity of Von Mises with isotropic work hardening on a three-dimensional problem
(modeling A into axisymmetric) and two-dimensional (modeling B in plane stresses). Interest of the test
holds with the dependence of the elastic limit with the temperature. It also makes it possible to test the orthotropism in
thermo elasticity because it applies to an isotropic material then with an isotropic material declared orthotropic.
This makes it possible to test the functionalities of the orthotropism. One tests there also the calculation of the deformation energy.
Two modelings (C with element PIPE, D with element TUYAU_6M) are added to test
thermoplasticity in these elements.
A modeling (E) makes it possible to test the good taking into account of the variation of the coefficients of
behavior VMIS_CINE_LINE with the temperature.
A modeling (F) makes it possible to test the calculation of the thermoelastic deformation energy in the beams.
Modeling (G) makes it possible to test the same functionalities as modelings A and B, but in 3D.
The solution is analytical.
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
2/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
Axisymmetric cylinder (modeling A) or plates rectangular (modeling B) or right pipe
(modelings C and D)
Z or y
R or X
With
B
D
C
B
has
H
0
Appear 1.1-a: Geometry of the structure
Interior radius: has = 1 mm
external radius: B = 2 mm (width AB: 1 mm)
height: H = 4 mm
1.2
Property of materials
()
(
)
(
)
()
(
)
(
)
E
E
T
S T T
T
S
C
C
C
J
mm C
W
mm C
T
y
y
p
=
=
=
=
-
-
=
=
=
°
=
°
=
°
=
°
-
-
-
-
-
200 000
50 000
0 3
1
400
10
10
0
10
0
0
0
0
2
1
5
1
3
3
MPa modulus Young
MPa modulates tangent
elastic limit
MPa
thermal expansion factor
voluminal heat
thermal conductivity
.
/
/
For isotropic material declared orthotropic, it comes:
E_L
=
E_T
=
E_N
=
E
Nu_LT = Nu_LN
=
Nu_TN
=
Naked
=
G_LT
=
G_LN
=
G_TN
=
(
)
E
2 1
+
= 76923,077
ALPHA_L
=
ALPHA_T
ALPHA_N
=
ALPHA
=
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
3/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
y
T
()
E
E
T
0
E
T
Appear traction Diagram 1.2-a: of material
1.3
Boundary conditions and loadings
Modeling A into axisymmetric: U
Z
= 0 on the sides AB and CD (Axis OZ fixes)
Modeling B in plane stresses: U
y
= 0 on the sides AB and CD, U
X
= 0 in A
T (T) =
T + T
0
= 1°C/S T
0
= 0°C.
Modelings C and D: embedding in A, Dy = 0 out of C
2
Reference solution
2.1
Method of calculation used for the reference solution
Axisymmetric case (2D)
()
(
)
()
=
=
=
Z
R
Z
R
R
U
U
Z
R
U
L
R
R
R
R
according to
limits)
with
conditions
(cf.
:
S
stress
of
Fields
according to
N
déformatio
of
Fields
in
blocking
:
T
déplacemen
of
Fields
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
'
:
U
E
U
Parallelepipedic case
()
()
(
)
()
=
=
+
=
y
Z
X
y
Z
X
U
U
Z
y
U
X
U
L
y
X
y
y
X
X
according to
limits)
with
conditions
(cf.
:
S
stress
of
Fields
according to
N
déformatio
of
Fields
in
blocking
:
T
déplacemen
of
Fields
0
0
0
0
1
0
0
0
0
'
0
0
0
0
0
0
0
'
:
U
E
E
U
The case could be studied in plane stresses and 3D.
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
4/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
E
T
E
y
2
µ
=
E
1
+
3K
=
E
1
- 2
The law of behavior is written (variable scalar intern
p
):
(
)
(
)
()
()
()
µ
=
+
+
+
-
=
-
=
=
=
=
-
<
=
1
9
1
2
1
3
3
2
3
2
0
0
0
0
K
T T
p
p
p
p
p
p
D
p
O
D
P
D
éq
éq
D
D
éq
tr
tr
&
&
,
&
F
,
&
F
,
Id
Id
Id
with:
diverter of the stresses
with
if
if
R
()
R
p
indicate the function of work hardening:
()
R
p
E E
E E
p
y
T
T
=
+
-
The rate
&p
can be expressed, when
()
F
,
p
= 0
. Indeed, of
& F
p
identically no one, one fires:
& &f & & F
p
p
+
= 0
. Thus, when one is on the criterion
(
)
F
= 0
, necessarily
&f = 0
. I.e.:
&
&
&
&
&
&
,
,
3
2
0
3
2
0
-
-
=
+
-
-
=
D
D
éq
T
p
D
D
éq
yo
T
T
T
p
S T
E E
E E
p
R
R
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
5/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
From where:
()
(
)
&
&
&
&
,
p
E E
E E
S T
p
p
T
T
D
D
éq
yo
éq
=
-
+
=
3
2
0
if
for
criterion reached, of of “charges”
R
The stress field being uniaxial, one a:
D
L
=
-
-
3
1 0
0
0
2
0
0
0
1
As follows:
éq
L
=
and:
()
&
& sgn
P
L
p
=
-
-
2
1 0
0
0
2
0
0
0
1
The relation of behavior leads to:
()
(
)
()
&
&
&
& sgn
&
&
&
&
&
& sgn
&
rr
L
L
xx
yy
zz
L
L
E
p
T
E
p
T
=
= -
-
+
=
=
=
=
+
+
2
0
1
for the case of the parallelepiped
From where:
()
()
&
&
&
&
&
sgn
&
&
Max
;
&
&
rr
L
L
L
L
T
T
D
D
éq
yo
T
E
p
T
E
p
E E
E E
St
=
=
+ -
=
-
-
=
<
=
-
+
3
2
1 2
2
0
0
3
2
if
if not
R
I.e., in the case
()
L
p
=
R
(criterion reached):
()
(
)
&
Max
;
sgn
&
&
p
E E
E E
S T
T
T
L
L
yo
=
-
+
0
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
6/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
2.1.1 Phase
rubber band
At the beginning of the thermal loading,
L
being lower than
y
,
&p
is null.
From where:
(
)
&
&; &
&
&
L
rr
E
T
T
= -
=
=
+
1
.
As follows:
(
)
(
)
L
L
rr
E
T
T
= -
<
=
=
+
compression
0
1
Validity of the elastic solution
The criterion is:
()
()
(
)
L
Y
yo
T
T
E
T
S T
-
=
=
-
-
1
0
The criterion is not crossed for
[]
T
T
y
= 0,
, with:
(
)
T
E
S
y
yo
yo
=
+
T
y
-
L
y
O
T
y
At the moment
T
y
:
()
L y
yo
yo
T
E
E
S
= -
+
The density of deformation energy is worth:
()
()
2
2
1
T
E
T
W
y
-
=
The total deformation energy is worth in the parallelepipedic case:
()
()
H
X
X
T
E
T
W
With
B
y
).
.(
2
1
2
-
-
=
The total deformation energy is worth in the axisymmetric case:
()
()
H
R
R
T
E
T
W
With
B
y
2
).
(
.
2
1
2
2
2
-
-
=
(for 1 radian)
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
7/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
2.1.2 Phase
elastoplastic
T T
y
. One is on the criterion. Then:
()
(
)
&
Max
;
& sgn
&
p
E E
E E
S T
T
T
L
L
yo
=
-
+
0
By admitting that one is “charges some”
(
)
&p > 0
, then one eliminates
&p
to have:
()
&
&
sgn
L
T
L
T
T
yo
E T
E E
E E
S
= -
+
-
then:
()
&
&
sgn
p
E E
E
T
S
E
T
L
yo
=
-
-
+
With
T T
y
=
,
L
y
E
T
= -
< 0
; one integrates these expressions then for
(
)
T T T
y
=
&
:
()
()
()
()
[
]
()
L
T
y
T
T
yo
L y
T
yo
y
T
E
T T
E E
E E
S
T
p T
E E
E
E S
T T
= -
-
- -
-
=
-
+
-
2
Maybe, after rearrangement,
()
T T
y
:
()
()
(
)
L
yo
T
y
yo
T
y
T
S T
E
E
T
T
p T
E E
E
T
T
=
- +
-
=
-
-
1
1
1
2
Validity of this elastoplastic solution
It should be made sure that
()
L
T
remain negative. Knowing that
S T
< 1
, and that
T T
y
>
, the preceding result
confirm that
()
L
T
< 0
.
Lastly, it is noticed that:
()
(
)
sgn
& &
&
L
rr
p
T
1 2
2
1
-
+
=
+
from where:
()
()
(
)
()
[
]
rr
y
end
T
T
T
p T
T
T T
=
=
+
+ -
1
1 2
2
,
,
(since
()
L
T
< 0
).
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
8/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
2.2
Results of reference
rr
xx
zz
y
p
T
or and
in
,
and with beyond:
Elastic phase: for
T T
y
<
(
)
(
)
L
rr
xx
E
T
T
T
= -
=
=
+
=
+
1
1
into axisymmetric
in plane stresses.
The yield stress is reached in
(
)
T
E
S
y
=
+
=
0
0
66,666 S
from where
()
L y
T
S
E
= -
+
1
0
Elastoplastic phase: for
T T
y
()
()
(
)
(
)
()
(
)
()
L
T
y
T
y
rr
xx
T
S
T
E
E
T
T
p T
E E
E
T
T
T
p T
T
p T
=
- +
-
=
-
-
=
=
+
+ -
=
=
+
+ -
0
0
2
1
1
1
1
1 2
2
1
1 2
2
into axisymmetric
or
in plane stresses
E
MPa
C
S
MPa
T
C
S
C
T
S
E
MPa
yo
O
end
T
=
=
=
°
=
=
= °
=
°
<
=
-
-
-
-
-
200 000
0 3
10
10
400
0
10
100
50 000
5
1
1
2
1
;
,
;
;
.
;
;
;
From where:
()
()
()
T
S
T
MPa
T
T
y
L y
rr
y
y
=
= -
=
=
-
66 6666
133 333
0 86666610
3
.
.
.
.
elastic phase
w=4.44410- ²
W=0.17778 (PLANE or 3D)
W=0.26666 (axi)
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
9/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
Then, elastoplastic phase:
()
()
()
()
()
()
()
()
with
with
T
S
T
S
=
= -
=
=
=
=
= -
=
=
=
-
-
-
80:
90:
L
rr
L
rr
MPa
p
MPa
p
80
100 0
80
0 300010
80
80
110010
90
75 00
90
0 525010
90
90
127510
3
3
3
3
.
.
.
.
.
.
.
.
.
.
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
10/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
QUAD4 - Axisymmetric
With
B
D
C
Z
N3
N4
GRN03
GRN04
GRN02
N1
N2
GRN01
Appear 3.1-a: Modeling A
3.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 1
QUAD4
, 4
SEG2
3.3 Functionalities
tested
Controls
DEFI_MATERIAU ELAS_ORTH
DEFI_MATERIAU TRACTION
SIGM
AFFE_CHAR_MECA DDL_IMPO
TEMP_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION
VMIS_ISOT_TRAC
CALC_ELEM OPTION
EPSI_ELNO_DEPL
CALC_ELEM OPTION
EPOT_ELEM_DEPL
CALC_ELEM OPTION
ENEL_ELGA
POST_ELEM ENER_TOTALE
3.4 Remarks
Functionality
AFFE_CARTE
is also tested but it is not documented in the test.
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
11/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested
Variables Moments
(S) Reference
Aster %
error
relative
Tolerance
T = 66.666
8.6666 10
4
8.66658
10
4
0 0.1
rr
=
T = 80
1.1000 10
3
1.10029
10
3
0.026 0.1
T = 90
1.2750 10
3
1.27529
10
3
0.023 0.1
T = 66.666
0
0
0
0.1
p
T = 80
3.0000 10
4
3.0000 10
4
0 0.1
T = 90
5.2500 10
4
5.2500 10
4
0 0.1
T = 66.666
133.333
133.332
0.001
0.1
zz
T = 80
100.000
100.00
0
0.1
T = 90
75.000
75.000
0
0.1
ENEL_ELGA
T = 66.666
4.444. 10
- 2
4.444.
10
- 2
0.00 0.1
ENER_TOTALE
T = 66.666
0.2666
0.2666
0.00
0.1
ENER_POT
T = 66.666
0.2666
0.2666
0.00
0.1
4.2 Notice
One obtains well the same results with isotropic material declared orthotropic as with material
isotropic in thermo elasticity, i.e. for the sequence number 1 with T = 66.666 S.
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
12/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling
QUAD4 - Plane stresses
With
D
y
N4
C
N3
B
N2
N1
Appear 5.1-a: Modeling B
5.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 1
QUAD4
, 4
SEG2
5.3 Functionalities
tested
Controls
DEFI_MATERIAU TRACTION
SIGM
AFFE_CHAR_MECA DDL_IMPO
TEMP_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION
VMIS_ISOT_TRAC
CALC_ELEM OPTION
EPSI_ELNO_DEPL
CALC_ELEM OPTION
EPOT_ELEM_DEPL
CALC_ELEM OPTION
ENEL_ELGA
POST_ELEM ENER_TOTALE
POST_ELEM ENER_POT
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
13/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
6
Results of modeling B
6.1 Values
tested
Variables Moments
(S) Reference
Aster %
error
relative
Tolerance
T = 66.666
8.6666 10
4
8.66658
10
4
0 0.1
xx
T = 80
1.1000 10
3
1.1000 10
3
0 0.1
T = 90
1.2750 10
3
1.2750 10
3
0 0.1
T = 66.666
0
0
0
0.1
p
T = 80
3.0000 10
4
3.0000 10
4
0 0.1
T = 90
5.2500 10
4
5.2500 10
4
0 0.1
T = 66.666
133.333
133.332
0.001
0.1
yy
T = 80
100.
100.00
0
0.1
T = 90
75.000
75.00
0.001
0.1
ENEL_ELGA
T = 66.666
4.444. 10
- 2
4.444.
10
- 2
0.00 0.1
ENER_TOTALE
T = 66.666
0.17777
0.17777
0.00
0.1
ENER_POT
T = 66.666
0.17777
0.17777
0.00
0.1
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
14/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
7 Modeling
C
7.1
Characteristics of modeling
1 element PIPE
With
C
7.2
Characteristics of the mesh
1 element PIPE
7.3 Functionalities
tested
Controls
AFFE_MODELE
MODELING PIPE
STAT_NON_LINE COMP_INCR
RELATION
VMIS_ISOT_TRAC
TUYAU_NCOU
1
TUYAU_NSEC
16
8
Results of modeling C
8.1 Values
tested
Variables Moments
(S) Reference
Aster %
difference
T = 66.666
0
0
0
p
T = 80
3. 10
4
3.003 10
4
0.1
T = 90
5.25 10
4
5.2526
0.05
T = 66.666
1.333
1.3313
0.16
yy
T = 80
100
99.82
0.18
T = 90
75
74.85
0.2
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
15/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
9 Modeling
D
9.1
Characteristics of modeling
1 element PIPE 6M
With
C
9.2
Characteristics of the mesh
1 element PIPE
9.3 Functionalities
tested
Controls
AFFE_MODELE
MODELING TUYAU_6M
STAT_NON_LINE COMP_INCR
RELATION
VMIS_ISOT_TRAC
TUYAU_NCOU
1
TUYAU_NSEC
16
10 Results of modeling D
10.1 Values
tested
Variables Moments
(S) Reference
Aster %
difference
T = 66.666
0
0
0
p
T = 80
3. 10
4
3.003 10
4
0.1
T = 90
5.25 10
4
5.2526
0.05
T = 66.666
1.333
1.3313
0.16
yy
T = 80
100
99.82
0.18
T = 90
75
74.85
0.2
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
16/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
11 Modeling
E
11.1 Characteristics of modeling
QUAD4 - Axisymmetric. Test of the variation of the coefficients of VMIS_CINE_LINE according to
temperature, in this case
E
T
(given by D_SIGM_EPSI) varies like:
E
T
= 10
5
(110
2
(TT
0
)).
constant of Prager is worth:
C
E E
E E
T
T
=
-
2
3
.
With
B
D
C
Z
N3
N4
GRN03
GRN04
GRN02
N1
N2
GRN01
Appear 3.1-a: Modeling E
11.2 Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 1
QUAD4
, 4
SEG2
11.3 Functionalities
tested
Controls
DEFI_MATERIAU ECRO_LINE_FO D_SIGM_EPSI
DEFI_MATERIAU PRAGER_FO
C
DEFI_MATERIAU TRACTION
SIGM
AFFE_CHAR_MECA DDL_IMPO
TEMP_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION
VMIS_ECMI_TRAC
CALC_ELEM OPTION
EPSI_ELNO_DEPL
STAT_NON_LINE COMP_INCR
RELATION
VMIS_CINE_LINE
11.4 Notice
One tests the variation of
E
T
(D_SIGM_EPSI) with the temperature by comparison with
behavior VMIS_ECMI_TRAC where
C
(constant of Prager) varies with the temperature in way
similar (not of analytical solution).
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
17/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
12 Results of modeling E
12.1 Values
tested
Variables
Moments (S)
Reference (Aster)
(VMIS_ECMI_TRAC)
Aster
(VMIS_CINE_LINE)
% error
relative
Tolerance
T = 66.666
8.6666 10
4
8.66658
10
4
0
0.1
rr
=
T = 80
1.112 10
3
1.112
10
3
0 0.1
T = 90
1.303 10
3
1.303
10
3
0 0.1
T = 66.666
133.333
133.332
0
0.1
zz
T = 80
88
88
0
0.1
T = 90
47
47
0
0.1
12.2 Notice
One obtains well the same results with behavior VMIS_CINE_LINE as with
behavior VMIS_ECMI_TRAC what validates the taking into account of the temperature in this model.
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
18/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
13 Modeling
F
13.1 Characteristics of modeling
1 element POU_D_T
With
C
13.2 Characteristics of the mesh
1 mesh SEG2
13.3 Functionalities
tested
Controls
AFFE_MODELE
MODELING TUYAU_6M
STAT_NON_LINE COMP_INCR
RELATION
ELAS
CALC_ELEM OPTION
EPOT_ELEM_DEPL
POST_ELEM ENER_POT
14 Results of modeling D
14.1 Values
tested
Variables Moments
(S) Reference
Aster %
difference
yy
T = 66.666
1.333
1.3313
0.16
ENER_POT
T = 66.666
0.3555
0.3555
0.00
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
19/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
15 Modeling
G
15.1 Characteristics of modeling
3D, H=1
With
D
y
N4
C
N3
B
N2
N1
Appear 5.1-a: Modeling G
15.2 Characteristics of the mesh
A number of nodes: 8
A number of meshs and types: 1
HEXA8
15.3 Functionalities
tested
Controls
DEFI_MATERIAU TRACTION
SIGM
AFFE_CHAR_MECA DDL_IMPO
TEMP_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION
VMIS_ISOT_TRAC
CALC_ELEM OPTION
EPSI_ELNO_DEPL
CALC_ELEM OPTION
EPOT_ELEM_DEPL
CALC_ELEM OPTION
ENEL_ELGA
POST_ELEM ENER_TOTALE
POST_ELEM ENER_POT
Code_Aster
®
Version
6.4
Titrate:
HSNV100 - Thermoplasticity in simple traction
Date:
03/11/03
Author (S):
J.M. PROIX, I. DEBOST-EYMARD, F.VOLDOIRE
Key
:
V7.22.100-C
Page:
20/20
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
16 Results of modeling G
16.1 Values
tested
Variables Moments
(S) Reference
Aster %
error
relative
Tolerance
T = 66.666
8.6666 10
4
8.66658
10
4
0 0.1
xx
T = 80
1.1000 10
3
1.1000 10
3
0 0.1
T = 90
1.2750 10
3
1.2750 10
3
0 0.1
T = 66.666
0
0
0
0.1
p
T = 80
3.0000 10
4
3.0000 10
4
0 0.1
T = 90
5.2500 10
4
5.2500 10
4
0 0.1
T = 66.666
133.333
133.332
0.001
0.1
yy
T = 80
100.
100.00
0
0.1
T = 90
75.000
75.00
0.001
0.1
ENEL_ELGA
T = 66.666
4.444. 10
- 2
4.444.
10
- 2
0.00 0.1
ENER_TOTALE
T = 66.666
4.444. 10
- 2
4.444.
10
- 2
0.00 0.1
ENER_POT
T = 66.666
4.444. 10
- 2
4.444.
10
- 2
0.00 0.1
17 Summary of the results
The results are satisfactory and validate the behaviors thermoplastic of Von Mises with
isotropic work hardening and linear kinematics. The finite elements used are the elements 2D
(quadrilaterals in plane stresses or axisymetry) and the elements PIPE.
One notes in particular a good modeling of the variation of the elastic limit and
constant of Prager with the temperature.