Variationally consistent homogenization of diffusion in particle composites with material interfaces using dual macroscale chemical potentials
摘要
Computational homogenization of particle-matrix composites with material interfaces is considered, whereby linear transient diffusion driven by a chemical potential is used as a model problem. Due to the models linearity, it is beneficial to assume micro-stationarity in order to provide direct upscaling and avoid excessive computational cost. First order homogenization with a single macroscale chemical potential is taken as the most basic approach; however, the accuracy is negatively affected whenever relevant micro-transient effects can not be captured using the stationary sub-scale problem. To improve the accuracy while still upscaling from a stationary sub-scale problem, different formulations based on dual macroscale potentials, one for each phase, are proposed and investigated in this paper. As to the prolongation order within the particles and matrix phase, respectively, two types are considered: constant-linear and linear-linear. Most importantly, for the case of linear prolongation, different ways of defining the macroscale variables (acting as loading on the RVE-problem) in terms of suitable measures of the chemical potential can be envisioned: (1) averaging of