Homogenization of Random Composite Materials: Sensitivity to Mechanical Parameters and Scaling Measures

Several composite materials used in engineering, such as rocks, ceramic materials, concrete, masonry-like materials, innovative meta-materials, have an internal micro-structure characterized by a random distribution of inclusions embedded in a matrix. Mechanical properties of this type of materials depend on the characteristics of the microstructure: mechanical properties of components, geometrical shape and size of inclusions. The evaluation of effective mechanical properties of this typology of materials is a topical issue. A statistically-based homogenization procedure, previously developed by some of the authors [1‐3], is adopted. This procedure allows us obtaining effective elastic properties of homogeneous micro-polar continua able to naturally account for scale and skew–symmetric shear effects. The so‐called Representative Volume Element (RVE) used to perform the homogenization procedure is obtained by increasing a scale factor representing the ratio between the size of a control window, referred as Statistical Volume Element (SVE), and the particle size until the statistical convergence is reached. In this work, in order to evaluate the effect of microstructure on the properties of such materials, a series of parametric analyses are developed for two dimensional samples of composites with disk-shaped inclusions. Two material cases are considered: inclusions stiffer or softer than the matrix. Attention is paid to the phase contrast in elastic moduli (ratio between inclusions and matrix moduli). The sensitivity of the effective material parameters to several material contrast is investigated. Moreover, the convergence trend of properly defined scaling‐measures is analyzed. The results obtained for different kind of composites - ranging from metal or ceramic matrix composites up to concrete, masonry-like and geo-materials - highlight the importance of taking into account the spatial randomness of inclusions in identifying the bulk, shear and bending behavior of composites as well as the effectiveness of the micro-polar continuum modeling.Several composite materials used in engineering, such as rocks, ceramic materials, concrete, masonry-like materials, innovative meta-materials, have an internal micro-structure characterized by a random distribution of inclusions embedded in a matrix. Mechanical properties of this type of materials depend on the characteristics of the microstructure: mechanical properties of components, geometrical shape and size of inclusions. The evaluation of effective mechanical properties of this typology of materials is a topical issue. A statistically-based homogenization procedure, previously developed by some of the authors [1‐3], is adopted. This procedure allows us obtaining effective elastic properties of homogeneous micro-polar continua able to naturally account for scale and skew–symmetric shear effects. The so‐called Representative Volume Element (RVE) used to perform the homogenization procedure is obtained by increasing a scale factor representing the ratio between the size of a control window, referred as Statistical Volume Element (SVE), and the particle size until the statistical convergence is reached. In this work, in order to evaluate the effect of microstructure on the properties of such materials, a series of parametric analyses are developed for two dimensional samples of composites with disk-shaped inclusions. Two material cases are considered: inclusions stiffer or softer than the matrix. Attention is paid to the phase contrast in elastic moduli (ratio between inclusions and matrix moduli). The sensitivity of the effective material parameters to several material contrast is investigated. Moreover, the convergence trend of properly defined scaling‐measures is analyzed. The results obtained for different kind of composites - ranging from metal or ceramic matrix composites up to concrete, masonry-like and geo-materials - highlight the importance of taking into account the spatial randomness of inclusions in identifying the bulk, shear and bending behavior of composites as well as the effectiveness of the micro-polar continuum modeling