Periodic three-dimensional mesh generation for particle reinforced composites with application to metal matrix composites

A method for the generation of three-dimensional model microstructures resembling particle reinforced composites is developed based on the periodic Voronoi tessellation. The algorithm allows for the generation of arbitrary particle volume fractions and produces periodic geometries based on the erosion procedure suggested by Christoffersen (1983). A technique for the creation of high quality periodic spatial discretizations of the particle systems for application with the finite element method is described in detail. The developed procedure is extensively applied to metal ceramic composites (Al-SiCp) at volume fractions ranging from 10 to 80%. The elastic and thermo-elastic material properties are investigated and the effect of higher statistical moments (see, e.g., Torquato, 2002), i.e. of the particle shape and relative position, is evaluated in terms of constraint point sets used in the generation of the random microstructures.