Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
1/8
Organization (S): EDF/AMA, CNEPE/GC
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.135
SSNV135 - Triaxial Essai 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.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
2/8
1
Problem of reference
1.1 Geometry
Z
E
height:
H = 1 m
width:
L = 1 m
thickness: E = 1 m
C
H
With
y
B
X
L
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 = 22,4 103 kPa
= 0,3
Parameters CJS1: = 0,03
= 0,82
Rm = 0,289
Pa = 100 kPa
1.3
Initial conditions, boundary conditions, and loading
Phase 1:
One brings the sample in a homogeneous state: 0 = 0 = 0
xx
yy
zz, by imposing the pressure of
containment corresponding on the front, side straight line and higher faces. Displacements are
blocked on the faces postpones (ux = 0), side left (uy = 0) and lower (uz = 0).
Phase 2:
One maintains displacements blocked on the faces postpones (ux = 0), side left (uy = 0) and
lower (uz = 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).
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
3/8
2
Reference solution
2.1
Development of the analytical solution for CJS1
One has permanently:
= = 0
xx
yy
xx
where 0
you
xx = C represents the confining pressure.
Remain to determine zz.
Elastic phase:
By writing the elastic law simply, one a:
0 = 0 + + (+ 2 µ) +
xx
xx
zz
xx
xx
= 0 + (+ 2 µ) + 2
zz
zz
zz
xx
where here and µ is the coefficients of Lamé.
By eliminating xx between these two equations, one finds:
µ (3 + 2 µ)
= 0 +
(
zz
zz
+ µ)
zz
Plastic phase:
One a:
I
0
0
you
1 = zz + 2 xx where xx = C represents the confining pressure.
One deduces some for the components from the diverter S:
1
0
1
S = 2
I
zz
- xx
and S
= 0 - I
3 1
xx
xx
1
3
1
3
0
1
0
that is to say: S
= 6 - I
II
xx
and det (S) = 2
I -
3 1
xx
3 1
1/6
Consequently: (
H S) = (1 -)
In addition, when one reaches the criterion of the mechanism déviatoire: S
(H) + R I
II
S
m
=
1
0
from where the relation:
0
6
I
xx
1 =
2
Rm
-
3
(1 -) 1/6
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
4/8
and finally, one has for the vertical constraint:
6 0
xx
=
- 2 0
zz
xx
2
Rm
-
3 (1 -) 1/6
Moreover, one can calculate that the transition enters the states rubber band and perfectly plastic is done
for an axial deformation equalizes with:
µ (3 + 2 µ)
6 0
xx
=
0
(
- 2
zz
+ µ)
xx
2
R
m
-
3
1/6
(1 -)
2.2
Results of reference
Constraints xx, yy and zz at points A, B and C.
2.3
Uncertainty on the solution
Analytical solution for CJS1.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
5/8
3 Modeling
With
3.1
Characteristics of modeling
3D:
Z
B
y
X
Cutting: 2 in height, in width and thickness.
Loading of phase 1:
Confining pressure: 0 = 0 = 0
xx
yy
zz: successively 100 kPa, 200 kPa and 400 kPa.
Level 1 of model CJS
3.2
Characteristic of the grid
A number of nodes: 27
A number of meshs and types: 8 HEXA8 and 24 QUA4
3.3 Functionalities
tested
Commands
DEFI_MATERIAU CJS
STAT_NON_LINE COMP_INCR
RELATION
“CJS”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
6/8
4
Results of modeling A
4.1 Values
tested
For 0 = 0 = 0
xx
yy
zz: 100 kPa
Localization Numéro deformation
constraint
Reference
Aster %
difference
of command axial
(kPa)
zz (%)
Not A, B and C
10 0.8
% xx
100.0 100.0
<
105
100
20.0
%
xx
100.0 100.0
< 105
10 0.8
% yy
100.0 100.0
< 105
100
20.0
%
yy
100.0 100.0
< 105
10 0.8
% zz
279.2
279.2 <
105
20
1.6
%
zz
367.159
367.1587 <
105
40
3.2
%
zz
367.159
367.1587 <
105
60
7.2
%
zz
367.159
367.1587 <
105
100
20.0
%
zz
367.159
367.1587 <
105
For 0 = 0 = 0
xx
yy
zz: 200 kPa
Localization Numéro deformation
Référence constraint
Aster %
difference
of command
axial
(kPa)
zz (%)
Not A, B and C
10
0.8%
xx
200.0 200.0
<
105
100
20.0
%
xx
200.0 200.0
< 105
10 0.8
% yy
200.0 200.0
< 105
100
20.0
%
yy
200.0 200.0
< 105
10 0.8
% zz
379.2
379.2 <
105
20
1.6
%
zz
558.4
558.4 <
105
40
3.2
%
zz
734.317
734.3174 <
105
60
7.2
%
zz
734.317
734.3174 <
105
100
20.0
%
zz
734.317
734.3174 <
105
For 0 = 0 = 0
xx
yy
zz: 400 kPa
Localization Numéro deformation
Référence constraint
Aster %
difference
of command
axial
(kPa)
zz (%)
Not A, B and C
10
0.8%
xx
400.0 400.0
<
105
100
20.0
%
xx
400.0 400.0
< 105
10 0.8
% yy
400.0 400.0
< 105
100
20.0
%
yy
400.0 400.0
< 105
10 0.8
%
zz
579.2
579.2 <
105
20
1.6
%
zz
758.4
758.4 <
105
40
3.2
%
zz
1116.8
1116.8 <
105
60
7.2
%
zz
1458.6348
1468.6348 <
105
100
20.0
%
zz
1458.6348
1468.6348 <
105
4.2 Parameters
of execution
Version: 5.03.08
Machine: SGI - ORIGIN 2000 - R12000
System: IRIX 64
Obstruction memory: 16 Mo
Time CPU To use: 120 S
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
7/8
5
Summary of the results
The values of Code_Aster are in triad with the values of the analytical solution of
reference.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
SSNV135 triaxial Essai drained with model CJS (level 1)
Date:
05/02/02
Author (S):
C. CHAVANT, pH. Key AUBERT
:
V6.04.135-A Page:
8/8
Intentionally white left page.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Outline document