Effective properties of suspensions, composites and porous materials

Three effective properties of heterogeneous systems are discussed from the viewpoint of rational mechanics and micromechanics: viscosity of suspensions and the tensile modulus and thermal conductivity of solid composites, including porous materials. Rigorous bounds (Voigt–Reuss and Hashin–Shtrikman bounds) are given as well as model relations for prediction and fitting purposes (dilute approximations, power-law relations, exponential relations, Coble–Kingery relations and new relations recently proposed by the authors). The semi-empirical nonlinear relations for the volume fraction (or porosity) dependence, including exponential and power-law relations with and without percolation threshold, are presented in a new systematic way which emphasizes the formal analogies between these relations and might become a useful tool in the future education of materials scientists and engineers.