Elastic percolation of composite structures with regular tessellations of microstructure

Enhancing the mechanical properties of materials by adding inclusions (particles) into microstructure is a favorite research area for material science researchers. In this paper, overall elastic properties of a microstructure are computed taking into account the effects of different geometrical shapes of inclusions. Representative volume elements (RVE) of the material's microstructures with different tessellations are constructed using a random generation method. The resulting RVEs obtained from the mentioned method were meshed and finite element method (FEM) was used to analyze the deformation of the microstructure including particles under tension and shear loadings. The FE results were then used to compute the stiffness the microstructure. Numerical results are compared with the available theoretical relations. The results show that the dependency of tensile and shearing properties of the microstructure on volume fraction of particles can completely have different trends in some ranges of volume fractions. Also the effects of mechanical percolation on the elastic properties of microstructures were obtained. The presented approach opens a systematic method for investigating the enhanced properties of microstructures with different shapes of tessellations.