Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
1/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA, CS IF
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
V6.04.143 document
SSNV143 - Biaxial traction with the law of
behavior
BETON_DOUBLE_DP
Summary:
This case of validation is intended to check the model of behavior 3D
BETON_DOUBLE_DP
formulated in
tally of the thermo plasticity, for the description of the nonlinear behavior of the concrete, in traction, and in
compression, with the taking into account of the irreversible variations of the thermal characteristics and
mechanics of the concrete, particularly sensitive at high temperature.
The description of cracking is treated within the framework of plasticity, using an energy equivalence,
by identifying the density of energy of cracking in mode I, with the plastic work of a homogeneous medium
equivalent, where the plastic deformation is uniformly distributed, in an “elementary” area. This approach
preserve the continuity of the formulation of the model, on the whole of its behavior, and contributes to avoid
possible numerical difficulties during the change of state of material.
Pathological sensitivity of the numerical solution to the space discretization (mesh), generated by
the introduction of a softening behavior of the concrete in traction and compression, is partially solved
by introducing an energy of cracking or rupture, dependant a characteristic length L
C
, related to
cut elements.
The case test includes/understands two modelings 3D, the loading consists of a load followed by a discharge.
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
2/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
It is about a cube with 8 nodes, whose two faces have a normal displacement no one, and the two faces
opposed have an imposed normal displacement, different one from the other of a coefficient 2.
The cube makes 1 mm on side. The cases tests are composed of a load, followed by a discharge. In
modeling A, the cube is directed according to the Oxyz reference mark. In modeling B, it is turned of 30°
by around axis OY.
Modeling A
Modeling B
U
2
= 2.U
1
X
y
Z
Uz = 0
Ux = 0
U
1
U
2
Face1xy
Facexy
Faceyz
Face1yz
N1
N2
X
y
Z
One = 0
One = 0
U
1
U
2
Face1xy
Faceyz
Face1yz
Facexy
N1
N2
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
3/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
1.2
Material properties
To test the evolution of the mechanical characteristics in an irreversible way with the temperature, one
apply a field of temperature decreasing. Certain variables depend on the temperature,
others of drying. Lastly, one applies a coefficient of withdrawal of desiccation not no one, equal to
thermal expansion factor, to test “data-processing” operation. Deformations
thermics thus equal and will be opposed to the deformations of withdrawal of desiccation. These
dependences intervene only for checks purely data-processing, the characteristics
mechanics can be regarded as constants.
For the usual linear mechanical characteristics:
Young modulus:
E = 32.000 MPa
of
0°C with 20°C
E = 15.000 MPa
with
400°C (linear decrease)
E = 5.000 MPa
with
800°C (linear decrease)
Poisson's ratio:
= 0.18
Thermal expansion factor:
= 10
- 5
Coefficient of withdrawal of desiccation:
= 10
- 5
For the nonlinear mechanical characteristics of the model
BETON_DOUBLE_DP
:
Resistance in uniaxial pressing:
f' C = 40 NR/mm ˛
of 0°C with 400°C
f' C = 15 NR/mm ˛
with
800°C (linear decrease)
Resistance in uniaxial traction:
f' T = 4 NR/mm ˛
of 0°C with 400°C
f' T = 1.5 NR/mm ˛
with
800°C (linear decrease)
Report/ratio of resistances in compression
biaxial/uniaxial pressing:
= 1.16
Energy of rupture in compression:
Gc =10 Nm/mm ˛
Energy of rupture in traction:
WP =0.1 Nm/mm ˛
Report/ratio of the limit elastic to resistance
in uniaxial pressing:
30%
1.3
Boundary conditions and loadings mechanical
Field of temperature decreasing of 20°C with 0°C.
Lower face of the cube (facexy):
locked according to OZ.
Higher face of the cube (face1xy):
displacement 0.30 mm imposed followed by a discharge of
0.1 mm
Left face of the cube (faceyz):
locked according to OX.
Right face of the cube (face1yz):
displacement 0.15 mm imposed followed by a discharge of
0.05 mm
Lower nodes front face (NR
1
, NR
2
):
locked according to OY (Suppression of the movements of
solid body).
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
4/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is calculated in an semi-analytical way, knowing that in traction, only the criterion
of traction is activated. It is thus necessary to solve a system of an equation to an unknown factor, which allows
to obtain by dichotomy for example, plastic deformation cumulated in traction. The aforementioned allows
to calculate strains and stresses then. This is possible, knowing displacement, and thus
deformation in the two imposed directions. Displacement in the third direction is then
an unknown factor of the problem.
The reference solution is calculated only in traction. The solution is determined by one
program resolution by dichotomy in independent FORTRAN. In compression, discharge,
exact solution was not recomputed, and constitutes a solution of nonregression of the code, been dependant on
version 5.02.14.
For modeling B, the results result by rotation from the tensor from stress from
modeling A, of the intrinsic reference mark of the cube to the reference mark user, the stress field of both
configurations being identical in the intrinsic reference mark of the cube.
2.2
Calculation of the reference solution of reference
For more details on the notations and the setting in equation, one will refer to the document of
reference. Only, the main equations are pointed out here.
One notes “has”, imposed displacement following direction X, and “2.a” following imposed displacement
direction Z. The tensor of deformation is form (has,
y, 2.a, 0., 0., 0.) by taking the notations
usual of Code_Aster (three main components, three components of shearing).
The tensor of stress is form (
X, 0.,
Z, 0., 0., 0.), in modeling A.
The criterion of traction is expressed in the form:
()
()
F
C
D
F
D
C
D
F
trac
Oct.
Oct.
T
T
eq
H
T
T
=
+
-
=
+
-
.
2
3
The constitutive equations are written by distinguishing the isotropic part of the deviatoric part of
tensors of stresses and deformations.
()
H
tr
=
1
3
()
S
tr
I
= -
1
3
()
H
tr
=
1
3
()
~
= -
1
3 tr
I
= +
S
I
H
= +
~
H
I
The equivalent stress is written then:
()
eq
tr S
=
3
2
In the case of an incremental formulation, and of a variable law of behavior, while noting with one
exponent “E” the elastic components of the stress and the deformation, one obtains:
S
S
E
=
+
+
- -
+
µ
µ
µ
2
~
and
H E
H
H
K
K
K
=
+
+
-
-
+
3
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
5/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
The criteria in compression and traction are expressed in the following way:
()
()
F
has
B
F
B
has
B
F
comp
Oct.
Oct.
C
C
eq
H
C
C
=
+
-
=
+
-
.
2
3
()
()
F
C
D
F
D
C
D
F
trac
Oct.
Oct.
T
T
eq
H
T
T
=
+
-
=
+
-
.
2
3
The plastic deformations in traction and compression are expressed:
~
PC
C
eq
B
S
=
2
p Hc
C
has
B
=
3
~
p T
T
eq
D
S
=
2
p HT
T
C
D
=
3
One obtains for the stress:
(
)
S S
E
PC
p T
=
-
+
+
2
µ
~
~
(
)
H
H E
H PC
H p T
K
=
-
+
+
3
S
B
D
S
C
T
E eq
E
= -
+
+
1 2
2
2
1
µ
H
H E
C
T
K
has
B
C
D
=
-
+
+
3
3
3
for the equivalent stress:
µ
eq
E eq
C
T
B
D
=
-
+
+
2
2
2
The two criteria lead then to a system of two equations to two unknown factors
C
and
T
with
to solve:
(
)
(
)
2
3
2
3
2
3
0
2
3
2
3
2
3
0
2
2
2
2
2
2
B
has
B
B
K has
B
data base
K ac
data base
F
D
C
D
data base
K ac
data base
D
K C
D
F
E eq
H E
C
T
C
C
C
E eq
H E
C
T
T
T
T
µ
µ
µ
µ
+
-
+
-
+
-
+
=
+
-
+
-
+
-
+
=
+
+
+
+
-
+
+
+
+
-
In a similar way, in the case of the only criterion of traction activated, configuration of the case test, one
a system of an equation to an unknown factor obtains
T
to solve:
(
)
2
3
2
3
0
2
2
2
D
C
D
D
K C
D
F
E eq
H E
T
T
T
T
µ
+
-
+
-
+
=
+
+
-
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
6/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
One thus seeks to solve this system, by using the particular shape of the tensors of stresses
and of deformations, uniforms on the structure.
On the basis of
(
)
(
)
.
0
.,
0
.,
0
,
.,
0
,
.
0
.,
0
.,
0
,
.
2
,
,
Z
X
of
and
has
has
y
=
=
. one obtains:
The elastic tensor of stress
(
) () ()
+
+
+
=
+
+
+
=
+
+
+
=
µ
µ
µ
2
.
2
.
.
2
2
.
.
2
2
has
has
has
has
has
has
y
Z
y
y
y
X
The elastic diverter of stress
S
S
has
S
has
X
y
y
y
Z
y
= -
= -
+
=
-
2
3
2
4
3
2
2
3
.
.
.
.
.
µ
µ
µ
µ
µ
The elastic hydrostatic stress
(
)
µ
E H
y
has
=
+
+
3
2
1
3.
The elastic equivalent stress
µ
E eq
y
y
has
has
=
-
+
4
12
12
2
2
.
.
In the case of a curve of linear work hardening post-peak in traction, the expression of the parameter
of work hardening is as follows:
(
)
()
()
()
F
F
T
tp
T
tp
U
,
,
=
=
-
1
with
()
()
()
U
F
C
T
G
L F
=
2.
.
One thus seeks to solve the equation:
2
3
2
3
1
2
0
2
2
2
D
C
D
D
K C
D
F
L F
G
E eq
H E
T
T
T C
T
T
µ
+
-
+
-
-
=
+
+
.
.
éq
2.2-1
Knowing that the stress in the direction is null there, one second equation is obtained:
µ
y
y
H
T
E eq
E y
E H
S
D
S
=
+
= =
-
+
+
0
1
2
1
µ
µ
µ
y
T
E eq
y
E H
T
D
has
K C D
= =
-
-
+
-
+
0
1
2
1
4
3
2
.
.
From where:
µ
µ
µ
µ
µ
T
y
E H
E eq
y
has
D
has
K Cd
=
-
+
-
+
4
3
2
2
4
3
2
.
.
.
that one can substitute in the expression of the criterion
[éq 2.2-1].
Knowing has, imposed displacement, one obtains a nonlinear equation with an unknown factor, that one
can solve simply by dichotomy, and which makes it possible to calculate the deformation
y, then the unit
unknown factors of the system.
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
7/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
2.3
Uncertainty on the solution
It is negligible, about the precision machine.
2.4 References
bibliographical
The model was defined starting from the following theses:
[1]
J.F. GEORGIN, at the time of its thesis “Contribution to the numerical modeling of the behavior
concrete concrete and structures reinforced under mechanical thermo stresses with high
temperature ",
[2]
G. HEINFLING, at the time of its thesis “Contribution to the modeling of the concrete under stress of
fast dynamics. The taking into account of the effect speed by viscoplasticity ", and is described
in the report/ratio of specification:
[3]
SCSA/128IQ1/RAP/00.034 Version 1.2, Development of a model of behavior 3D
concrete with double criterion of plasticity in Code_Aster - Specifications “.
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
8/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
3D (HEXA8)
1 element, stress field and uniform deformation.
3.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and type: 1 HEXA8
3.3 Functionalities
tested
Controls Options
AFFE_MODELE
“MECHANICAL”
“3D”
DEFI_MATERIAU
“BETON_DOUBLE_DP”
DEFI_MATERIAU
“ELAS_FO”
“K_DESSIC”
AFFE_CHAR_MECA
“SECH_CALCULEE”
STAT_NON_LINE
“BETON_DOUBLE_DP”
X
y
Z
Uz = 0
Ux = 0
U
1
U
2
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
9/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
The nonnull components of the stress field were tested
SIEF_ELNO_ELGA
(component
xx and zz), the component yy of the field of deformation
EPSI_ELNO_DEPL
, which constitutes an unknown factor
system (deformations in the two other directions being imposed), deformation
figure cumulated in traction (second variable internal, second component of the field
VARI_ELNO_ELGA
), and finally, only for the fourth case of loading (discharge),
plastic deformation cumulated in compression, (first internal variable, first component of
field
VARI_ELNO_ELGA
).
The first three loadings correspond to the load, and have results of reference.
The fourth loading corresponds to the discharge, and constitutes a result of nonregression of
code.
Field
SIEF_ELNO_ELGA
component
SIXX
Identification Reference
Aster
% difference
For a displacement imposed in
charge U
1
=0.1 and U
2
= 0.05
0.1235611 0.1235380 0.019
For a displacement imposed in
charge U
1
=0.2 and U
2
= 0.10
6.882374.10
2
6.878218.10
2
0.060
For a displacement imposed in
charge U
1
=0.3 and U
2
= 0.15
1.408764.10
2
1.402639.10
2
0.435
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 4.195092.10
5
-
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Field
SIEF_ELNO_ELGA
component
SIZZ
Identification Reference
Aster
% difference
For a displacement imposed in
charge U
1
=0.1 and U
2
= 0.05
0.239212 0.239174 0.016
For a displacement imposed in
charge U
1
=0.2 and U
2
= 0.10
0.133243 0.133165 0.059
For a displacement imposed in
charge U
1
=0.3 and U
2
= 0.15
2.727403.10
2
2.725569.10
2
0.434
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 4.959258.10
5
-
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
10/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Field
EPSI_ELNO_DEPL
component
EPYY
Identification Reference
Aster
% difference
For a displacement imposed in
charge U
1
=0.1 and U
2
= 0.05
3.419463.10
3
3.419464.10
3
2.10
7
For a displacement imposed in
charge U
1
=0.2 and U
2
= 0.10
6.835813.10
3
6.835815.10
3
2.10
7
For a displacement imposed in
charge U
1
=0.3 and U
2
= 0.15
1.025216.10
2
1.025216.10
2
2.10
7
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 4.357498.10
1
-
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Field
VARI_ELNO_ELGA
component
VARI_2
(plastic deformation cumulated in traction)
Identification Reference
Aster
% difference
For an imposed displacement
U
1
=0.1 and U
2
= 0.05
1.085728.10
2
1.085728.10
2
5.10
9
For an imposed displacement
U
1
=0.2 and U
2
= 0.10
2.171556.10
2
2.171556.10
2
5.10
9
For an imposed displacement
U
1
=0.3 and U
2
= 0.15
3.257385.10
2
3.257385.10
2
4.10
9
For an imposed displacement
U
1
=0.1 and U
2
= 0.05
3.257385.10
2
3.257385.10
2
4.10
9
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Field
VARI_ELNO_ELGA
component
VARI_1
(plastic deformation cumulated in
compression)
Identification Reference
Aster
% difference
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 3.528401.10
1
-
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
11/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
3D (HEXA8)
1 element, stress field and uniform deformation.
5.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and type: 1 HEXA8
5.3
Functionalities tested
Controls Options
AFFE_MODELE
“MECHANICAL”
“3D”
DEFI_MATERIAU
“BETON_DOUBLE_DP”
DEFI_MATERIAU
“ELAS_FO”
“K_DESSIC”
AFFE_CHAR_MECA
“SECH_CALCULEE”
STAT_NON_LINE
“BETON_DOUBLE_DP”
X
y
Z
One = 0
One = 0
U
1
U
2
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
12/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
6
Results of modeling B
The nonnull components of the stress field were tested
SIEF_ELNO_ELGA
(component
xx, zz and xz), plastic deformation cumulated in traction (second variable internal, second
component of the field
VARI_ELNO_ELGA
), and finally, only for the fourth case of loading
(discharge), plastic deformation cumulated in compression, (first internal variable, first
component of the field
VARI_ELNO_ELGA
).
The first three loadings correspond to the load, and have results of reference.
The fourth loading corresponds to the discharge, and constitutes a result of nonregression of
code.
6.1 Values
tested
Field
SIEF_ELNO_ELGA
component
SIXX
Identification Reference
Aster
% difference
For a displacement imposed in
charge U
1
=0.1 and U
2
= 0.05
0.152474 0.1524472 0.018
For a displacement imposed in
charge U
1
=0.2 and U
2
= 0.10
8.492877.10
2
8.487797.10
2
0.060
For a displacement imposed in
charge U
1
=0.3 and U
2
= 0.15
1.732484.10
2
1.730871.10
2
0.434
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 4.386134.10
5
-
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Field
SIEF_ELNO_ELGA
component
SIZZ
Identification Reference
Aster
% difference
For a displacement imposed in
charge U
1
=0.1 and U
2
= 0.05
0.210300 0.210265 0.016
For a displacement imposed in
charge U
1
=0.2 and U
2
= 0.10
0.117138 0.117069 0.059
For a displacement imposed in
charge U
1
=0.3 and U
2
= 0.15
2.397743.10
2
2.387336.10
2
0.434
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 4.768217.10
5
-
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
13/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Field
SIEF_ELNO_ELGA
component
SIXZ
Identification Reference
Aster
% difference
For a displacement imposed in
charge U
1
=0.1 and U
2
= 0.05
5.007871.10
2
5.007226.10
2
0.013
For a displacement imposed in
charge U
1
=0.2 and U
2
= 0.10
2.789472.10
2
2.787871.10
2
0.057
For a displacement imposed in
charge U
1
=0.3 and U
2
= 0.15
5.709873.10
3
5.685155.10
3
0.433
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 3.308936.10
6
-
(*) discharges some, one carries out a test of nonregression. There is no analytical solution.
Field
VARI_ELNO_ELGA
component
VARI_2
(plastic deformation cumulated in traction)
Identification Reference
Aster
% difference
For a displacement imposed in
charge U
1
=0.1 and U
2
= 0.05
1.085728.10
2
1.085728.10
2
5.10
9
For a displacement imposed in
charge U
1
=0.2 and U
2
= 0.10
2.171556.10
2
2.171556.10
2
5.10
9
For a displacement imposed in
charge U
1
=0.3 and U
2
= 0.15
3.257385.10
2
3.257385.10
2
4.10
9
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
3.257385.10
2
3.257385.10
2
4.10
9
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Field
VARI_ELNO_ELGA
component
VARI_1
(plastic deformation cumulated in
compression)
Identification Reference
Aster
% difference
For a displacement imposed in
discharge U
1
=0.1 and U
2
= 0.05
(*) 3.528401.10
1
-
(*) discharges some, one carries out a test of nonregression. There is no calculated analytical solution.
Code_Aster
®
Version
5.2
Titrate:
SSNV143 - Biaxial traction with the law
BETON_DOUBLE_DP
Date
:
23/09/02
Author (S):
C. CHAVANT, B. CIREE
Key
:
V6.04.143-A
Page:
14/14
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
7
Summary of the results
This case test offers satisfactory results compared to the results of reference, lower than 0.06%
for the first two cases of loading, more important for the third, which is explained by one
relatively low level of stress (one reaches the end of the curve of work hardening in traction).
The test discharges some (fourth loading) makes it possible to check nonthe regression of the code.
The iteration count is relatively important with the first pitch of calculation, about 13, then
drop to 7, 4 and 1, which is explained by the passage of the plastic threshold to the first pitch of calculation, for
to reach a quasi linear behavior thereafter (curved post-peak linear).
One obtains also a more significant number of iterations to pitch 31 (beginning of the fourth case of
loading), then an iteration count dropping up to 1, because of the passage in discharge, with one
change of behavior, follow-up of a quasi linear behavior thereafter (curved post-peak
linear).