Code_Aster
®
Version
7.3
Titrate:
SSLV140 - Calculation of effective modules by a method Python
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX
Key
:
V3.04.140-A
Page:
1/4
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
V3.04.140 document
SSLV140 - Calculation of effective modules by one
method Python
Summary:
One presents a test here having an analytical reference. The treated geometry is a whole of two cubes
having different elastic properties. The goal is to find the Young modulus of the mixture made up of
these two cubes along two directions.
Code_Aster
®
Version
7.3
Titrate:
SSLV140 - Calculation of effective modules by a method Python
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX
Key
:
V3.04.140-A
Page:
2/4
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
Following surfaces are defined:
· Face YZ1: containing the nodes P1, P3, P5 and P7.
· Face YZ2: containing the nodes P9, P10, P11 and P12.
· Face XY1: containing the nodes P1, P2, P9, P3, P4 and P10.
· Face XY2: containing the nodes P5, P6, P11, P7, P8 and P12.
· Face XZ1: containing the nodes P3, P4, P10, P7, P8 and P12.
· Face XZ2: containing the nodes P1, P2, P9, P5, P6 and P11.
and following elements:
· M1 element: containing the nodes P1, P2, P3, P4, P5, P6, P7 and P8.
· Element m2: containing the nodes P2, P9, P4, P10, P6, P11, P8 and P12.
1.2
Material properties
Two materials are used:
· Material MAT1 allotted to the M1 element:
Young modulus: E1 = 200000 MPa
Poisson's ratio:
1 = 0.3
· Material MAT2 allotted to the element m2:
Young modulus: E2 = 100000 MPa
Poisson's ratio:
2 = 0.3
X
Y
Z
P1
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
P11
P12
Code_Aster
®
Version
7.3
Titrate:
SSLV140 - Calculation of effective modules by a method Python
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX
Key
:
V3.04.140-A
Page:
3/4
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
1.3
Boundary conditions and loadings
The first calculation:
It is a simple calculation of traction according to direction X:
· A linear elastic strain is imposed
1
=
xx
on surface YZ2.
· Surface YZ1 does not move according to direction X.
The second calculation:
It is a simple calculation of traction according to the direction Y:
· A linear elastic strain is imposed
1
=
yy
on surface XZ2.
· Surface XZ1 does not move according to direction Y.
2
Reference solution
2.1
Method of calculation
According to the general theory of the homogenization of composite materials [bib1], the Young moduli
manpower
EFF
xx
E
and
EFF
yy
E
according to directions X and Y of a mixture having the form given above, are
given by the following formulas:
2
2
1
1
1
E
F
E
F
E
EFF
xx
+
=
2
2
1
1
E
F
E
F
E
EFF
yy
+
=
1
F
and
2
F
are the voluminal fractions of each material, in our case:
5
.
0
2
1
=
= F
F
2.2 References
bibliographical
[1]
Mr. BORNET, T. BRETHEAU and P. GILORMINI: Homogenization in mechanics of
materials (T1). Hermes Science Publications - 2001.
Code_Aster
®
Version
7.3
Titrate:
SSLV140 - Calculation of effective modules by a method Python
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX
Key
:
V3.04.140-A
Page:
4/4
Manual of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of the mesh
A number of nodes: 12.
Modeling 3D: 2 quadratic elements of volume: HEXA8.
3.2 Functionalities
tested
Controls
Options
CREA_CHAMP
TYPE_CHAM
OPERATION
RESULT
NOM_CHAM
“ELGA_SIEF_R”
“EXTR”
“SIEF_ELGA_DEPL”
CALC_CHAM_ELEM
MODEL
CHAM_MATER
OPTION
“COOR_ELGA”
EXTR_COMP
Python controls are inserted directly in the command file ASTER. These
controls are used to write functions of postprocessing on the fields of results,
like the averages, the trace of a tensor of deformations or stresses,… etc fields of
results are recovered by control EXTR_COMP.
4
Results of modeling A
4.1 Values
tested
The first calculation:
The Young modulus following direction X in this case is the average of the stresses
xx
:
>
=<
xx
EFF
xx
E
The second calculation:
The Young modulus following the direction Y in this case is the average of the stresses
yy
:
>
=<
yy
EFF
yy
E
Identification Reference
Aster %
difference
>
<
xx
133333 134134
1.00
>
<
yy
150000 150000
0.00
5
Summary of the results
The results obtained are in perfect agreement with the reference solution.