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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
Organization (S): EDF-R & D/AMA
Handbook 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 constraints). 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 TUYAU, 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.
Handbook of Validation
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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
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
D
C
H
B
has
R or X
0
With
B
Appear 1.1-a: Géométrie 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 = 200.000 MPa modulus Young
AND = 50.000 MPa modulates tangent
= 0 3
.
(T)
y
= 0 (1 - S (T - T0) elastic limit
= 400 MPa =
0
y (T0)
S =
-
10 2 °C-1
= -
10 5 °C-1 thermal dilation coefficient
C p = 0
J/(mm3°C) heat voluminal
= -
10 3
W/(mm°C)
thermal conductivity
For isotropic material declared orthotropic, it comes:
E_L = E_T = E_N = E
Nu_LT = Nu_LN = Nu_TN = Naked =
E
G_LT = G_LN = G_TN =
(
= 76923,077
2 1+)
ALPHA_L = ALPHA_T ALPHA_N = ALPHA =
Handbook of Validation
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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
AND
0
AND
y T
()
E
Appear 1.2-a: Courbe of traction of material
1.3
Boundary conditions and loadings
Modeling A into axisymmetric: uz = 0 on the sides AB and CD (Axe OZ fixes)
Modeling B in plane constraints: uy = 0 on sides AB and CD, ux = 0 in A
T (T) = T + T0 = 1°C/S T0 = 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)
déplacemen
of
Fields
T: U = ur (R) er
(
in
blocking
Z)
U '0
0
R
R
déformatio
of
Fields
N:
(U)
= 0
0
0
according to Z
ur
0 0
R
0 0 0
R
constraint
of
Fields
S:
= L0 1 0
limits)
with
conditions
(cf.
according to Z
0 0 0
Parallelepipedic case
déplacemen
of
Fields
T: U = ux (X) E + U
X
y (y) E y
(
in
blocking
Z)
U '0
0
X
X
déformatio
of
Fields
N:
(U)
= 0
0
0
according to Z
0
0 U y '
y
0 0 0
X
constraint
of
Fields
S:
= L0 1 0
limits)
with
conditions
(cf.
according to Z
0 0 0
y
The case could be studied in plane constraints and 3D.
Handbook of Validation
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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
AND
E
y
2µ = 1+
E
3K =
E
1 - 2
The law of behavior is written (variable scalar intern p):
1
1
=
tr Id +
D + p +
O
(T - T) Id
9K
2µ
with:
1
D
= - tr Id
(diverter of the constraints)
3
3
D
3
P
&
=
p&
, with
=
D D
2
éq
2
éq
p & =
0 if F (, p) =
-
éq
R (p) < 0
p &
0 if F (, p) = 0
R (p) indicates the function of work hardening:
E E
R (p)
T
= +
p
y
E - AND
The rate &p can be expressed, when F (, p) = 0. Indeed, from &p F identically no one, one draws:
&p &f+ &p F = 0. Thus, when one is on the criterion (F =)
0, necessarily &f = 0. I.e.:
3D &
D
- R,
T
&T - R, p &p = 0
2
éq
3D &
D
E E
+ O
T
y S &
T -
&p = 0
2
E -
E
éq
T
Handbook of Validation
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Code_Aster ®
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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
From where:
E - E
D
D
T
3 &
&p
O
=
+ S
y
&T
if &p 0, for
=
éq
R (p)
E AND 2 éq
(criterion reached, in “load”)
The stress field being uniaxial, one a:
- 1 0 0
D
L
=
0 2
0
3 0 0 - 1
As follows:
=
éq
L
and:
- 1 0 0
P
&p
&
=
sgn (L) 0 2 0
2
0 0 - 1
The relation of behavior leads to:
&p
&rr = & = -
&
- sgn
L
(L) + &T (= &xx = &yy for the case of the parallelepiped)
E
2
1
&zz = 0 =
&
L + &p sgn (L) + &T
E
From where:
3
1 -
2
&rr = & = &T +
&L
2
2nd
&p = sgn (
L
L) - &
&
T -
0
if
L R (p)
E =
<
D
D
E - E
T
3 &
= max 0;
+ O
y
&
St
if not
E E
2
T
éq
I.e., in the case L = R (p) (criterion reached):
E - E
&p
Max 0;
T (sgn (
O
=
L) & + S
L
y
&T)
E E
T
Handbook of Validation
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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
2.1.1 Phase
rubber band
At the beginning of the thermal loading, L being lower than y, &p is null.
From where:
&
= - E
L
&T; &rr = & = &T (1+).
As follows:
= - E
L
T
(compressionL <) 0
=
rr
= (1+) T
Validity of the elastic solution
The criterion is:
() - () =
= - O
T
T
E
T
(1 - S
L
Y
y
T) 0
The criterion is not crossed for T = [0, ty], with:
O
T
y
y
=
(E
O
+ S
y
)
y - L
OY
T
T y
At the moment ty:
E O
y
L (ty) =
-
E + OY S
1
The density of deformation energy is worth: (
W T =
y)
E (T) 2
2
The total deformation energy is worth in the parallelepipedic case:
1
W (T
2
=
.(-).
y)
E (T) X
X
H
B
With
2
1
(R 2 -
2
R 2).
The total deformation energy is worth in the axisymmetric case: W (T =
.
y)
E (T)
B
With
H
2
2
(for 1 radian)
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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
2.1.2 Phase
elastoplastic
T ty. One is on the criterion. Then:
E - E
&p
Max 0;
T (& sgn
O
=
L
(L) + S
y
&T)
E E
T
By admitting that one is “charges some” (&p >)
0, then one eliminate &p to have:
E - E
&
= - E &T + sgn ()
T
S O
L
T
L
y
E AND
then:
E - E
S O
y
&p
T
=
&T- sgn (
L) +
E
E
With T = ty, = - E
L
ty < 0; one integrates then these expressions for T T (T
y & =):
E - E
(T) = - E
T
O
L
T
(T - ty) -
S -
y
L (ty)
E E
T
(
E - E
p T)
T
=
2
[E +soy] (t-ty)
E
Maybe, after rearrangement, (T ty):
E
T
(T) = bone
T
1
1
L
y
T - +
-
E
T
y
O
y (E - AND)
(
T
p T) =
-
1
E 2
T
y
Validity of this elastoplastic solution
It should be made sure that ()
L T remains negative. Knowing that S T < 1, and that T > T y, the preceding result
confirm that ()
L T < 0.
Lastly, it is noticed that:
1 -
2
sgn (L)
p +
= (1+)
& &rr
&T
2
from where:
1 -
(
2
T) = (T)
rr
= (1+) T +
(
p T), T [
ty, T fine]
2
(since ()
L T < 0).
Handbook of Validation
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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
2.2
Results of reference
,
rr
xx
zz
or and p
ty
in
and with beyond:
Elastic phase: for T < ty
= - E T =
L
rr
= (1+) T
into axisymmetric
= (
1+)
xx
T
in plane constraints.
The yield stress is reached in T
0
y =
66,666 S from where
(
=
E + S
0)
L (ty) = - 1+ S
0
E
Elastoplastic phase: for T ty
E
T
(T) = S
T
1
1
L
T - +
-
0
E
T
y
0 (E - E
T)
(
T
p T) =
-
1
E 2
T
y
1 -
2
=
rr
= (1+) T +
(
p T) into axisymmetric
2
1 -
2
or
=
xx
= (1+) T +
(
p T) in plane constraints
2
E = 200.000 MPa; = 0 3
,
; =
-
10 5 °C-1; = 10
. s-1
O
= 400 MPa; To = 0 °C; S = -
10 2 °C-1; T
< 100s
y
end
E
= 50.000 MPa
T
From where:
T
= 66 6666
.
S
y
133 333
.
L
(ty) = -
MPa
elastic phase
-
rr
(ty) = (ty) = 0866666
.
10 3
.
w=4.44410- ²
W=0.17778 (PLAN or 3D)
W=0.26666 (axi)
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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
Then, elastoplastic phase:
with T =
S
80:
()
80
= -
L
100 0
. MPa
(
p
)
80
=
-
0 3000
.
10 3
.
()
80
= ()
80
=
- 3
rr
1100
.
10
.
with T =
S
90:
()
90
= -
L
75 00
.
MPa
(
p
)
90
=
-
0 5250
.
10 3
.
()
90
= ()
90
=
3
rr
1275
.
10
.
2.3
Uncertainty on the solution
Analytical solution.
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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
3 Modeling
With
3.1
Characteristics of modeling
QUAD4 - Axisymétrique
GRN03
Z
N4
N3
D
C
GRN04
GRN02
With
B
N1
N2
GRN01
Appear 3.1-a: Modeling A
3.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 QUAD4, 4 SEG2
3.3 Functionalities
tested
Commands
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.
Handbook of Validation
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Code_Aster ®
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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
4
Results of modeling A
4.1 Values
tested
Variables Moments
(S) Référence
Aster %
error
Tolerance
relative
T = 66.666
8.6666 104 8.66658
104
0 0.1
rr =
T = 80
1.1000 103 1.10029
103
0.026 0.1
T = 90
1.2750 103 1.27529
103
0.023 0.1
T = 66.666
0
0
0
0.1
p
T = 80
3.0000 104
3.0000 104
0 0.1
T = 90
5.2500 104
5.2500 104
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.
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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
5 Modeling
B
5.1
Characteristics of modeling
QUAD4 - Contraintes plane
y
N4
N3
D
C
With
B
N1
N2
Appear 5.1-a: Modeling B
5.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 QUAD4, 4 SEG2
5.3 Functionalities
tested
Commands
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
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
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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
6
Results of modeling B
6.1 Values
tested
Variables Moments
(S) Référence
Aster %
error
Tolerance
relative
T = 66.666
8.6666 104 8.66658
104
0 0.1
xx
T = 80
1.1000 103
1.1000 103
0 0.1
T = 90
1.2750 103
1.2750 103
0 0.1
T = 66.666
0
0
0
0.1
p
T = 80
3.0000 104
3.0000 104
0 0.1
T = 90
5.2500 104
5.2500 104
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
Handbook of Validation
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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
7 Modeling
C
7.1
Characteristics of modeling
1 element TUYAU
C
With
7.2
Characteristics of the grid
1 element TUYAU
7.3 Functionalities
tested
Commands
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) Référence
Aster %
difference
T = 66.666
0
0
0
p
T = 80
3. 104
3.003 104 0.1
T = 90
5.25 104 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
Handbook of Validation
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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
9 Modeling
D
9.1
Characteristics of modeling
1 element TUYAU 6M
C
With
9.2
Characteristics of the grid
1 element TUYAU
9.3 Functionalities
tested
Commands
AFFE_MODELE
MODELISATION 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) Référence
Aster %
difference
T = 66.666
0
0
0
p
T = 80
3. 104
3.003 104 0.1
T = 90
5.25 104 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
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
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Version
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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
11 Modeling
E
11.1 Characteristics of modeling
QUAD4 - Axisymétrique. Test of the variation of the coefficients of VMIS_CINE_LINE according to
temperature, in this case AND (given by D_SIGM_EPSI) varies like: AND = 105 (1102 (TT0)).
2nd E
constant of Prager is worth: C
T
=
.
3rd - AND
GRN03
Z
N4
N3
D
C
GRN04
GRN02
With
B
N1
N2
GRN01
Appear 3.1-a: Modeling E
11.2 Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 1 QUAD4, 4 SEG2
11.3 Functionalities
tested
Commands
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 AND (D_SIGM_EPSI) with the temperature per comparison with
behavior VMIS_ECMI_TRAC where C (constant of Prager) varies with the temperature in way
similar (not of analytical solution).
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
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
12 Results of modeling E
12.1 Values
tested
Variables
Moments (S)
Reference (Aster)
Aster
% error
Tolerance
(VMIS_ECMI_TRAC) (VMIS_CINE_LINE)
relative
T = 66.666
8.6666 104 8.66658
104 0
0.1
rr =
T = 80
1.112 103 1.112
103 0 0.1
T = 90
1.303 103 1.303
103 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.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
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
13 Modeling
F
13.1 Characteristics of modeling
1 element POU_D_T
C
With
13.2 Characteristics of the grid
1 mesh SEG2
13.3 Functionalities
tested
Commands
AFFE_MODELE
MODELISATION 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) Référence
Aster %
difference
yy
T = 66.666
1.333
1.3313
0.16
ENER_POT
T = 66.666
0.3555
0.3555
0.00
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
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
15 Modeling
G
15.1 Characteristics of modeling
3D, H=1
y
N4
N3
D
C
With
B
N1
N2
Appear 5.1-a: Modeling G
15.2 Characteristics of the grid
A number of nodes: 8
A number of meshs and types: 1 HEXA8
15.3 Functionalities
tested
Commands
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
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
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
16 Results of modeling G
16.1 Values
tested
Variables Moments
(S) Référence
Aster %
error
Tolerance
relative
T = 66.666
8.6666 104 8.66658
104
0 0.1
xx
T = 80
1.1000 103
1.1000 103
0 0.1
T = 90
1.2750 103
1.2750 103
0 0.1
T = 66.666
0
0
0
0.1
p
T = 80
3.0000 104
3.0000 104
0 0.1
T = 90
5.2500 104
5.2500 104
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 constraints or axisymetry) and elements TUYAU.
One notes in particular a good modeling of the variation of the elastic limit and
constant of Prager with the temperature.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/03/008/A
Outline document