Upscaling of chemo-mechanical properties of battery electrode material

Journal article, 2023

A variationally consistent model-based computational homogenization approach for transient chemo- mechanically coupled problems is developed based on the classical assumption of first order prolongation of the displacement and chemical potential fields within a Representative Volume Element (RVE). An upscaling procedure is introduced that is based on the assumption of micro-stationarity for the RVE problem. This is motivated by sufficient separation of time-scales. Periodic boundary conditions on the pertinent fields provide the general variational setting for the uniquely solvable RVE-problems. Due to the assumed linearity and micro-stationary, it is possible to use the pertinent sensitivity analysis for the RVE in order to derive effective macro-scale properties in closed form: the elastic stiffness, the insertion strain tensor and the mobility tensor. Statistically representative results are obtained by considering a sufficient number of RVE-realizations with varying volume fractions of the constituents. With the application to structural batteries in mind, a numerical study is conducted for a three-phase RVE microstructure representing a battery electrode material.