Governing equations for a two-scale analysis of Li-ion battery cells

This contribution describes a computational homogenization approach to model the multi-physics processes in Li-ion batteries in a multi-scale view. The adopted approach originates from the fundamental balance laws (of mass, momentum, charge) at both scales and the multi scale analysis roots itself on an energy-based weak formulation of the balance laws, which allows to extend the Hill-Mandel energy averaging theorem to the problem at hand. Electroneutrality assumption has been taken into account. Maxwell's equations are considered in a quasi-static sense in a rigorous setting. Time dependent scale transitions are formulated, as required by the length/time scales involved in Li-ion batteries processes, while scale separation in time is argued. Constitutive assumptions, computational procedures and simulations will be collected in a companion paper.