Upscaling of chemo-mechanical properties of battery electrode material

A variationally consistent model-based computational homogenization approach for transient chemomechanically 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.

Automated summary

A variationally consistent model-based computational homogenization approach is developed for transient chemomechanically coupled problems using the classical assumption of first order prolongation of displacement and chemical potential fields. An upscaling procedure based on micro-stationarity assumption is introduced, allowing for unique solvability of the RVE-problems with periodic boundary conditions. The effective macro-scale properties such as elastic stiffness, insertion strain tensor, and mobility tensor are derived through sensitivity analysis of the RVE.