Deformation-dependent effective mobility in Structural Battery Electrolytes

This paper considers chemical diffusion in a Structural Battery Electrolyte (SBE) under the influence of finite deformation, which serves as a first step towards the more rigorous electro-chemically coupled modeling of deformation-dependent ionic transport in SBEs. The SBE is a porous (bicontinuous) microstructure consisting of a solid (polymer) skeleton, and pores filled with a liquid electrolyte. We present a variationally consistent computational homogenization scheme and exploit 3D-representation of the microstructure to compute the deformation-dependent effective mobility via direct upscaling in a two-step procedure (sequentially coupled approach). The pertinent RVE problem is established for the mechanical (equilibrium) problem under macro-scale deformation control, while adopting Neo-Hooke hyperelasticity for the fine-scale modeling of the solid skeleton. Thereby, the elastic moduli are calibrated based on experimental data for the effective response. Subsequently, Fickian diffusion, with a constant mobility in the liquid electrolyte is considered in the deformed pore space. Exploiting a pull-back to the reference configuration, we avoid remeshing while still incorporating the necessary pore space deformation. By adopting a suitable constitutive model for the fictitious solid in the pore space, we also prevent self-penetration of the solid skeleton during deformation, which mimics contact behavior without explicitly solving a computationally expensive contact problem involving contact search. Upon homogenizing the local ionic flux, we obtain the effective mobility pertaining to the macro-scale chemical potential gradient, while noting that the RVE-problem is linear in the chemical potential for a given macro-scale deformation gradient. The numerical results show that when the macro-scale loading is of compressive type, the pore volume is reduced and, as a direct consequence, the effective mobility becomes smaller. In essence, the framework can track the geometrically induced anisotropy of the RVE under mechanical loading, corresponding to a change in the computational domain for the transport problem, thereby influencing the ionic flux. E.g. for a bicontinuous SBE with 37% initial porosity and an externally applied macroscopic compression of 20% strain, we could observe up to 26% reduction in the effective mobility components.