Abstract: Matter conductivities are crucial physical properties that directly determine the engineering application value of materials. In reality, the majority of materials are multiphase composites. However, there is currently a lack of theoretical models to accurately predict the conductivities of composite materials. In this study, we develop a unified mixed conductivity (UMC) model, achieving unity in three aspects: (1) a unified description and prediction for different conductivities, including elastic modulus, thermal conductivity, electrical conductivity, magnetic permeability, liquid permeability coefficient, and gas diffusion coefficient; (2) a unified-form governing equation for mixed conductivities of various composite structures, conforming to the Riccati equation; (3) a unified-form composite structure, i.e., a three-dimensional multiphase interpenetrating cuboid structure, encompassing over a dozen of typical composite structures as its specific cases. The UMC model is applicable for predicting the conductivity across six different types of physical fields and over a dozen different composite structures, providing a broad range of applications. Therefore, the current study deepens our understanding of the conduction phenomena and offers a powerful theoretical tool for predicting the conductivities of composite materials and optimizing their structures, which holds significant scientific and engineering implications.

Key words: Composite materials, Conductivity, Elastic modulus, Permeability coefficient, Diffusion coefficient, Multiphase interpenetrating structure