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

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A fully coupled model for mass and heat transport, mechanics, and chemical reactions with trapping is proposed. It is rooted in non-equilibrium rational thermodynamics and assumes that displacements and strains are small. Balance laws for mass, linear and angular momentum, energy, and entropy are stated. Thermodynamic restrictions are identified, based on an additive strain decomposition and on the definition of the Helmholtz free energy. Constitutive theory and chemical kinetics are studied in order to finally write the governing equations for the multi-physics problem. The field equations are solved numerically with the finite element method, stemming from a three-fields variational formulation. Three case-studies on vacancies redistribution in metals, hydrogen embrittlement, and the charge-discharge of active particles in Li-ion batteries demonstrate the features and the potential of the proposed model.