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.