A computational homogenization approach for Li-ion battery cells: Part 1 – formulation

Very large mechanical stresses and huge volume changes emerge during intercalation and
extraction of Lithium in battery electrodes. Mechanical failure is responsible for poor
cyclic behavior and quick fading of electrical performance, especially in energy storage
materials for the next generation of Li-ion batteries. A multi scale modeling of the
phenomena that lead to mechanical degradation and failure in electrodes is the concern of
the present publication. The computational homogenization technique is tailored to
model the multi physics events that coexist during batteries charging and discharging
cycles. At the macroscale, diffusion–advection equations model the coupling between
electrochemistry and mechanics in the whole cell. The multi-component porous electrode,
migration, diffusion, and intercalation of Lithium in the active particles, the swelling
of the latter are modeled at the micro-scale. A rigorous thermodynamics setting is stated
and scale transitions are formulated