Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA, CNEPE/GC
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.135
SSNV135 - Triaxial compression test drained with model CJS
(level 1)
Summary
This test makes it possible to validate level 1 of model CJS. It is about a triaxial compression test in drained condition. Three
levels of containment are simulated: 100, 200, then 400 kPa.
By reason of symmetry, one is interested only in the eighth of a sample subjected to a triaxial compression test.
The results obtained with model CJS1 are compared with the analytical solution.
Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Z
X
y
E
L
H
C
With
B
height:
H = 1 m
width:
L = 1 m
thickness: E = 1 m
Co-ordinates of the points (in meters):
With
B
C
X 0. 0.
0.5
y 0. 1.
0.5
Z 0. 0.
0.5
1.2
Material property
E = 22,4 10
3
kPa
= 0,3
Parameters CJS1:
= 0,03
= 0,82
R
m
= 0,289
P
has
= 100 kPa
1.3
Initial conditions, boundary conditions, and loading
Phase 1:
One brings the sample in a homogeneous state:
xx
yy
zz
0
0
0
=
=
, by imposing the pressure of
containment corresponding on the front, side straight line and higher faces. Displacements are
locked on the faces postpones (
U
X
= 0
), side left (
U
y
= 0
) and lower (
U
Z
= 0
).
Phase 2:
One maintains displacements locked on the faces postpones (
U
X
= 0
), side left (
U
y
= 0
) and
lower (
U
Z
= 0
), as well as the confining pressure on the front faces and side straight line. One
apply a displacement imposed to the higher face:
()
U T
Z
, in order to obtain a deformation
zz
= - 20%
(counted starting from the beginning of phase 2).
Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Development of the analytical solution for CJS1
One has permanently:
xx
yy
xx
=
=
0
where
xx
you
C
0
=
represent the confining pressure.
Remain to determine
zz
.
Elastic phase:
By writing the elastic law simply, one a:
(
)
µ
xx
xx
zz
xx
xx
0
0
2
=
+
+
+
+
(
)
µ
zz
zz
zz
xx
=
+
+
+
0
2
2
where here
µ
and
are the coefficients of Lamé.
While eliminating
xx
between these two equations, one finds:
(
)
(
)
µ
µ
µ
zz
zz
zz
=
+
+
+
0
3
2
Plastic phase:
One a:
I
zz
xx
1
0
2
=
+
where
xx
you
C
0
=
represent the confining pressure.
One deduces some for the components from the diverter
S
:
S
I
zz
xx
=
-
2 13
1
0
and
S
I
xx
xx
=
-
0
1
1
3
that is to say:
S
I
II
xx
=
-
6
1
3
0
1
and
()
det S
I
xx
=
-
2 13
1
0
3
Consequently:
()
(
)
H
S
= -
1
1 6
/
In addition, when one reaches the criterion of the mechanism déviatoire:
()
S H
R I
II
S
m
+
=
1
0
from where the relation:
(
)
I
R
xx
m
1
0
1 6
6
2
3
1
=
- -
/
Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
and finally, one has for the vertical stress:
(
)
zz
xx
m
xx
R
=
- -
-
6
2
3
1
2
0
1 6
0
/
Moreover, one can calculate that the transition enters the states rubber band and perfectly plastic is done
for an axial deformation equalizes with:
(
)
(
)
(
)
µ
µ
µ
zz
xx
m
xx
R
=
+
+
- -
-
3
2
6
2
3
1
2
0
1 6
0
/
2.2
Results of reference
Stresses
xx
,
yy
and
zz
at points A, B and C.
2.3
Uncertainty on the solution
Analytical solution for CJS1.
Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
5/8
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:
Z
X
y
B
Cutting: 2 in height, in width and thickness.
Loading of phase 1:
Confining pressure:
xx
yy
zz
0
0
0
=
=
: successively 100 kPa, 200 kPa and 400 kPa.
Level 1 of model CJS
3.2
Characteristic of the mesh
A number of nodes: 27
A number of meshs and types: 8
HEXA8
and 24
QUA4
3.3 Functionalities
tested
Controls
DEFI_MATERIAU CJS
STAT_NON_LINE COMP_INCR
RELATION
“CJS”
Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
6/8
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
For
xx
yy
zz
0
0
0
=
=
: 100 kPa
Localization Number
of command
deformation
axial
zz
(%)
stress
(kPa)
Reference
Aster %
difference
Not A, B and C
10 0.8
%
xx
100.0 100.0
<
10
5
100
20.0
%
xx
100.0 100.0
< 10
5
10 0.8
%
yy
100.0 100.0
< 10
5
100
20.0
%
yy
100.0 100.0
< 10
5
10 0.8
%
zz
279.2
279.2 <
10
5
20
1.6
%
zz
367.159
367.1587 <
10
5
40
3.2
%
zz
367.159
367.1587 <
10
5
60
7.2
%
zz
367.159
367.1587 <
10
5
100
20.0
%
zz
367.159
367.1587 <
10
5
For
xx
yy
zz
0
0
0
=
=
: 200 kPa
Localization Number
of command
deformation
axial
zz
(%)
stress
(kPa)
Reference
Aster %
difference
Not A, B and C
10
0.8%
xx
200.0 200.0
<
10
5
100
20.0
%
xx
200.0 200.0
< 10
5
10 0.8
%
yy
200.0 200.0
< 10
5
100
20.0
%
yy
200.0 200.0
< 10
5
10 0.8
%
zz
379.2
379.2 <
10
5
20
1.6
%
zz
558.4
558.4 <
10
5
40
3.2
%
zz
734.317
734.3174 <
10
5
60
7.2
%
zz
734.317
734.3174 <
10
5
100
20.0
%
zz
734.317
734.3174 <
10
5
For
xx
yy
zz
0
0
0
=
=
: 400 kPa
Localization Number
of command
deformation
axial
zz
(%)
stress
(kPa)
Reference
Aster %
difference
Not A, B and C
10
0.8%
xx
400.0 400.0
<
10
5
100
20.0
%
xx
400.0 400.0
< 10
5
10 0.8
%
yy
400.0 400.0
< 10
5
100
20.0
%
yy
400.0 400.0
< 10
5
10 0.8
%
zz
579.2
579.2 <
10
5
20
1.6
%
zz
758.4
758.4 <
10
5
40
3.2
%
zz
1116.8
1116.8 <
10
5
60
7.2
%
zz
1458.6348
1468.6348 <
10
5
100
20.0
%
zz
1458.6348
1468.6348 <
10
5
4.2 Parameters
of execution
Version: 5.03.08
Machine: SGI - ORIGIN 2000 - R12000
System: IRIX 64
Overall dimension memory: 16 Mo
Time CPU To use: 120 S
Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
5
Summary of the results
The values of Code_Aster are in triad with the values of the analytical solution of
reference.
Code_Aster
®
Version
5.0
Titrate:
SSNV135 triaxial Compression test drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. AUBERT
Key
:
V6.04.135-A
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Intentionally white left page.