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Manuscript Title: Calculation of Effective Conductivity of 2D and 3D Composite Materials with Anisotropic Constituents and Different Inclusion Shapes in Mathematica
Authors: José Luis Gómez-Muñoz, Julián Bravo-Castillero
Program title: CompositeMaterials
Catalogue identifier: AEAU_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 179(2008)275
Programming language: Mathematica 6.0.
Computer: Any that can run Mathematica 6.0 and where the open-source free C-programs Triangle (http://www.cs.cmu.edu/~quake/triangle.html) and TetGen (http://tetgen.berlios.de/) can be compiled and executed. Tested on Intel Pentium computers.
Operating system: Any that can run Mathematica 6.0 and where the open-source free C-programs Triangle (http://www.cs.cmu.edu/~quake/triangle.html) and TetGen (http://tetgen.berlios.de/) can be compiled and executed. Tested in Windows XP.
RAM: Small two-dimensional calculations require less than 100 MB. Large three-dimensional calculations require 500 MB or more.
Keywords: Composite Materials, Asymptotic Homogenization, Effective Coefficients, Cell Problem, FEM.
PACS: 72.80.Tm, 02.70.Dc, 77.84.Lf.
Classification: 7.9.

External routines: One Mathematica Add-on and two external programs: The free Mathematica Add-On IMS (http://www.imtek.uni-freiburg.de/simulation/Mathematica/IMSweb/), The open-source free C-program Triangle (http://www.cs.cmu.edu/~quake/triangle.html) The open-source free C-program TetGen (http://tetgen.berlios.de/).
The distribution file contains Windows executables for Triangle and tetgen.

Nature of problem:
The calculation of effective thermal conductivity tensor for two-dimensional and three-dimensional composite materials with anisotropic constituents and different inclusion shapes.

Solution method:
Asymptotic Homogenization Method, with the Cell Problems solved with Finite Element Method

Unusual features:
Different inclusion shapes can be easily created. The constituents can be anisotropic. The intermediate stages and the final results can be graphed and analyzed with all the power of Mathematica 6.0. The use of the external meshing programs Triangle and TetGen is totally transparent for the end user. A typical calculation requires the use of only four special commands that follow standard Mathematica syntax.

Additional comments:
  • The executable binary files for Triangle and TetGen must be accessible from the directory specified by Mathematica's variable $HomeDirectory. The IMS add-on and the CompositeMaterials package, which is the package presented in this work, must be installed in the directory specified by Mathematica's variable $BaseDirectory or in the variable $UserBaseDirectory.
  • The 2D calculations of Composite Materials will run successfully in Mathematica 5.2 and 6.0 but for the 3D calculations it is necessary to use Mathematica 6.0 or higher.

Running time:
Simple two-dimensional calculations can be done in less than a minute. Complex three dimensional calculations can take an hour or more.