Code_Aster ®
Version
7.3
Titrate:
SSLV140 - Calcul of effective modules by a Python method
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX Key
:
V3.04.140-A Page:
1/4

Organization (S): EDF-R & D/AMA

Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
V3.04.140 document

SSLV140 - Calcul of effective modules by one
Python method

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.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSLV140 - Calcul of effective modules by a Python method
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX Key
:
V3.04.140-A Page:
2/4


1
Problem of reference

1.1 Geometry


P1
P2
P9
P5
P6
P11
P3
P4
P10
Y
P7
P8
P12
X
Z


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
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSLV140 - Calcul of effective modules by a Python method
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX Key
:
V3.04.140-A Page:
3/4


1.3
Boundary conditions and loadings

The first calculation:
It is a simple calculation of traction according to direction X:
· One imposes a linear elastic strain = 1 on surface YZ2.
xx
· 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 on surface XZ2.
yy
· 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
E and EFF
E following directions X and Y of a mixture having the form given above, is
xx
yy
given by the following formulas:

1
F
F
1
2
=
+

E EFF
E
E
xx
1
2
E EFF = F E + F E
yy
1
1
2
2

F and F are the voluminal fractions of each material, in our case:
1
2

F = F = 0.5
1
2

2.2 References
bibliographical

[1]
Mr. BORNET, T. BRETHEAU and P. GILORMINI: Homogenization in mechanics of
materials (T1). Hermes Science Publications - 2001.

Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A

Code_Aster ®
Version
7.3
Titrate:
SSLV140 - Calcul of effective modules by a Python method
Date:
06/05/04
Author (S):
T. KANIT, J.M. PROIX Key
:
V3.04.140-A Page:
4/4


3 Modeling
With

3.1
Characteristics of the grid

A number of nodes: 12.
Modeling 3D: 2 quadratic elements of volume: HEXA8.

3.2 Functionalities
tested

Commands
Options

CREA_CHAMP
TYPE_CHAM
“ELGA_SIEF_R”
OPERATION
“EXTR”
RESULTAT

NOM_CHAM
“SIEF_ELGA_DEPL”
CALC_CHAM_ELEM
MODELE

CHAM_MATER

OPTION
“COOR_ELGA”
EXTR_COMP



Python commands are inserted directly in the command file ASTER. These
commands are used to write functions of postprocessing on the fields of results,
like the averages, the trace of a tensor of deformations or constraints,… etc Les fields of
results are recovered by command 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 constraints:
xx

EFF
E
=< >
xx
xx

The second calculation:
The Young modulus following the direction Y in this case is the average of the constraints:
yy

EFF
E
=< >
yy
yy

Identification Reference
Aster %
difference
< >
133333 134134
1.00
xx
< >
150000 150000
0.00
yy

5
Summary of the results

The results obtained are in perfect agreement with the reference solution.
Handbook of Validation
V3.04 booklet: Linear statics of the voluminal systems
HT-66/04/005/A

Outline document