Homogenization-based constitutive modelling for diffusion problems (INVITED)

Abstract eng:
This work investigates the effective thermodynamic and transport properties of inhomogeneous media in which one mobile species can diffuse. These properties are important for a variety of applications, including energy-storage materials and soft materials, where they further couple with the mechanical properties. Here we develop a first-order homogenization framework according to which the effective chemical behaviour can be obtained based on an analysis on a RVE of the microstructure. Based on a Hill-Mandel macrohomogeneity condition, expressions for the effective concentration rates and fluxes (conjugated respectively to the macroscopic chemical potential and its gradient) are derived. The framework is used to identify and calibrate non-classical, homogenized constitutive relations. In particular, we show that the commonly adopted assumption of local chemical equilibrium generally does not hold at the macroscopic scale.

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