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

Abstract

a b s t r a c tA 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-SiC p ) 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.

Nonuniform transformation field analysis of materials with morphological anisotropy

“…Based on an algorithm for the generation of periodic unstructured meshes for polycrystalline aggregates (Fritzen et al, 2009), the authors have recently proposed an extension for particle reinforced composites (Fritzen and Böhlke, 2010b). The generated model microstructures are based on the Voronoi tessellation and allow for arbitrary particle volume fractions.…”

“…While the method presented in (Fritzen and Böhlke, 2010b) is suitable for the description of near isotropic materials, some materials exhibit a pronounced morphological anisotropy. The latter is, e.g., caused by an extrusion or rolling processes during the production of the composite material.…”

“…• Generate a periodic volume mesh based on the generated particle geometry (step 5) using the hierarchical mesh generation algorithm used by Fritzen et al (2009);Fritzen and Böhlke (2010b). The libraries triangle (Shewchuk, 1996) and tetgen (Si and Gaertner, 2005) are used.…”

“…Based on the Eshelby solution for an ellipsoidal inclusion, efficient algorithms for the prediction of the linear properties of particulate structures with near isotropic inclusions were found by Mori and Tanaka (1973). Self-consistent estimates (Kröner, 1958) were developed, which overpredict the stiffness of the particle reinforcement systems with high phase contrast (see, e.g., Fritzen and Böhlke (2010b)). All these methods rely on the linearity of the material response.…”

“…Therefore, a modification of the mesh generation technique developed by Fritzen and Böhlke (2010b) is presented in section 2 in order to account for a class of morphological anisotropy. The generated model microstructures are used in combination with the non-uniform transformation field analysis briefly revisited in section 3 to generate reduced constitutive equations for the microstructured material on the macroscopic scale.…”