A new weighted approach for homogenization of composites

A novel and simple homogenization approach is introduced to predict effective material properties of composites with high filler fractions across various material groups. The approach hypothesizes that a composite consisting of Material 1 and Material 2 can be represented as a combination of two distinct composite configurations: one where Material 2 acts as the filler in a matrix of Material 1, and the other where Material 1 serves as the filler in a matrix of Material 2. These configurations establish theoretical bounds for the composite’s material properties. Recognizing that the composite’s properties must lie within these bounds, the approach uses weight functions to assign proportions to each configuration based on the constituent volume fractions. The effective material properties are then calculated as a weighted sum of the two configurations. Two weight functions are considered: one that is independent of the constituent properties and a different function dependent on the filler-matrix modulus ratio. Predictions from this new homogenization approach are compared with experimental data and estimates from the Mori-Tanaka and self-consistent models. The results demonstrate that this weighted approach accurately predicts effective properties of composites, particularly at high filler fractions and with significant differences in constituent moduli. This approach is applicable to a wide range of composites, including ceramic-polymer, glass-polymer, metal-polymer, ceramic-metal, metal-glass, and ceramic-glass systems, as well as particulate and unidirectional fiber composites. Moreover, the approach is well-suited for the homogenization and analysis of functionally graded composite structures, which exhibit gradual changes in filler fractions along one or more directions.