Variationally consistent homogenization of electrochemical ion transport in a porous structural battery electrolyte

In this paper, we develop a multi-scale modeling framework for a multiphysics problem characterized by electro-chemically coupled ion transport in a Structural Battery Electrolyte (SBE). The governing equations of the problem are established by coupling Gauss law with mass conservation for each mobile species. By utilizing variationally consistent homogenization, we are able to establish a two-scale model where both the macro-scale and sub-scale equations are deduced from a single-scale problem. Investigations of the sub-scale RVE problem show that the transient effects are negligible for the length scales relevant to the studied application, which motivates the assumption of micro-stationarity. In the special case of linear constitutive response, we get a numerically efficient solution scheme for the macro-scale problem that is based on a priori upscaling. As a final step, we demonstrate the numerically efficient solution scheme by solving a 2D macro-scale problem using upscaled constitutive quantities based on a 3D RVE.