Incorporating multiscale mechanics in lithium-ion battery models

Abstract

Lithiation-induced swelling in lithium-ion batteries generates stresses not only within active particles, but also across the surrounding non-active matrix, electrodes, and cell stack. These stresses can modify the chemical potential of lithium and therefore influence transport, reaction kinetics, and terminal voltage. We derive a reduced-order electro-chemo-mechanical model that captures this multiscale coupling while retaining a complexity comparable to standard Doyle--Fuller--Newman models. The electrode is modelled as a periodic array of spherical active particles embedded in a homogenised elastic non-active matrix. Exploiting the small stiffness of the non-active matrix relative to the active material, together with scale separation between particles, electrodes, and the full cell, we obtain an effective mechanical correction to the active-particle chemical potential and overpotential. This correction depends on particle swelling, electrode-scale strain, and macroscopic boundary conditions such as clamping or applied pressure. The resulting formulation can be incorporated directly into DFN, SPMe, and SPM frameworks, providing a computationally efficient route to include battery-scale mechanical effects in electrochemical simulations.