Drawing on ideas from Bucci et al. , we formulate a fully coupled large strain theory for ionic transport in terms of electric field, mechanical deformation and anion and cation concentrations. We derive suitable constitutive relations based on the Helmholtz energy and thermodynamic restrictions for the species fluxes of the different ionic constituents as done in the context of liquid electrolytes e.g. by Dreyer et al. . We propose a constitutive formulation that allows the calculation of the electrochemical transport in the deformed state and consistently predicts the coupling between species transport and gradients of stress and material properties based on the choice of the Helmholtz energy, similar to e.g. lithium diffusion in active particles  or the swelling of polymeric gels .
Using the framework of the newly derived transport theory, we investigate the effect of mechanics on the interfacial kinetics at the metal anode/solid electrolyte interface. Based on energetic considerations as presented in  or , we propose a modified Butler-Volmer relation that not only establishes a relation between the exchange current density and potential/concentration differences across the interface but also takes into account the mechanical state of both solid electrolyte and metal anode.
To illustrate the features of the model and to highlight cases where the electro-chemo-mechanical coupling plays an important role for ion transport and kinetics, we show numerical examples for a Lithium symmetric solid state cell with binary solid electrolyte.
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