The main result is a model prediction: when mechanics is carried from the particle level through the electrode and across the cell, the calculated charging voltage includes a positive contribution that reaches approximately 15 mV at full charge. The isolated-particle version contributes only a few millivolts and changes sign during charging.
That comparison comes from deterministic PyBaMM simulations of three DFN-type configurations: a standard DFN without mechanics, a version with isolated-particle stress-assisted diffusion, and a full multiscale mechanics version. The reported values therefore describe the behavior of model configurations under the selected parameterization.
A mechanics correction for familiar battery models
The preprint’s aim is to develop a reduced-order model that links particle-, electrode- and cell-scale mechanics to lithium transport and reaction behavior while keeping complexity comparable to a standard DFN model. In practical terms, it tries to add the effects of swelling and mechanical constraint without replacing the broader battery-modeling framework.
Here, mechanics refers to the push and pull created when active particles swell inside the surrounding material. Each electrode is represented as a periodic array of spherical active particles embedded in a homogenized elastic non-active matrix. The formulation separates the particle, electrode and cell scales so that information can pass between them.
The derivation begins with a small stiffness ratio between the non-active matrix and the active particles. At leading order, the particle problem is mechanically isolated from the surrounding matrix; the multiscale mechanical coupling appears at first order as a correction.
Turning local swelling into whole-cell stress
The researchers use homogenization, a way of translating fine-scale behavior into larger-scale material properties, to introduce mechanical cell functions. These functions represent how the non-active matrix responds to electrode-scale strain and to the swelling of the particles, providing the quantities needed to calculate effective stress.
The resulting homogenized electrode properties are cubic-symmetric and generally anisotropic, meaning their effective mechanical response need not be the same in every direction. That detail allows the model to retain directional information produced by the underlying electrode structure.
At the cell scale, the reduced mechanical problem retains through-cell displacements. Under thin-electrode and stiff-current-collector assumptions, it links the size of the strain to electrode swelling and to the boundary conditions imposed on the whole cell, such as whether the cell is allowed to move or is held in place.
A simplification that keeps the voltage calculation manageable
Surface averaging converts the angularly heterogeneous first-order particle problem into a radial mechanical and transport problem. The reduced problem is sufficient to determine the exchange current, the modeled rate of charge-transfer reaction at the particle surface.
In that radial first-order problem, the homogeneous stress created by the matrix is independent of radius. The model therefore represents it as a shift in chemical potential and interfacial overpotential—the voltage correction associated with the particle interface—rather than as an additional radial-diffusion contribution.
The result is a mechanically corrected DFN model. The same correction can also be reduced to single-particle models, including SPM and SPMe, in slow-charging limits.
The simulated voltage effect grows at high charge
The PyBaMM comparison puts the three model versions on the same footing: standard DFN without mechanics, isolated-particle stress-assisted diffusion, and full multiscale mechanics. This design separates the contribution from particle-level stress effects from the additional coupling supplied by the matrix and cell-scale mechanics.
The full multiscale voltage contribution grows almost monotonically during charging and reaches approximately 15 mV at full charge. By contrast, the isolated-particle contribution remains only a few millivolts and changes sign during the charge process.
The comparison gives the reduced formulation a measurable model-level effect: mechanical information from outside an individual particle changes the electrochemical potential predicted by the simulation, particularly near high state of charge. It does not turn the result into a universal voltage adjustment, since the value comes from the stated model and parameterization.
How the cell is held matters
The simulations also compare different mechanical boundary conditions. Load-controlled cases at 0, 200 and 400 kPa have only weakly different voltage corrections, while the clamped case produces the largest correction: about 16 mV at full charge, accompanied by growing compressive through-cell stress.
For the model, the way the cell is constrained is therefore part of the voltage calculation, not a detail that can always be separated from the electrochemistry. The result follows from the link between electrode swelling, through-cell strain and whole-cell boundary conditions.
A useful prediction, still tied to idealized assumptions
The mechanics is intentionally idealized. The model assumes spherical active particles, a linearly elastic homogenized matrix and separator, and perfectly bonded particle–matrix interfaces. Those choices define the effective mechanical response used in the voltage correction.
The reported 15 mV and 16 mV values are approximate simulation results. The supplied analysis reports no inferential statistical tests, confidence intervals or formal uncertainty analysis, and the size of the correction is scenario- and parameter-specific.
The study’s evidence does not establish that the simulated millivolt shifts occur in measured cells. Nor does the formulation, as presented, provide a universal correction across different particle arrangements, contact states, material assumptions or cell designs.
That distinction matters because the paper addresses how mechanics can be incorporated into electrochemical models, not whether the same correction has already been demonstrated across operating cells. The contribution is a reduced formulation and a set of simulation predictions that can be tested against mechanical and voltage measurements.
The next test is realism
Several questions remain open. More realistic particle arrangements, particle contacts and binder bridges could alter the effective cell functions and the resulting voltage correction. The influence of nonlinear porous-matrix behavior, fluid pressure, viscoelastic response and finite housing stiffness also remains to be assessed.
Further work would also need to examine fast charging, repeated cycling and experimentally measured fixed-displacement or applied-pressure conditions. Those tests would show how well the reduced correction transfers beyond the selected deterministic simulations.
For now, the preprint offers battery modelers a way to include mechanics from the particle to the cell scale while retaining a DFN-based structure. Its central numerical message is narrower: under the stated assumptions, the added mechanics can produce a voltage contribution of roughly 15 mV at full charge, rising to about 16 mV in the clamped scenario.
The supplied document is an arXiv version-one preprint dated 20 Aug 2026. The work was supported by the EPSRC Faraday Institution Multi-Scale Modelling project, EP/S003053/1, grant FIRG059.
Paper data and sources
Original title: Incorporating multiscale mechanics in lithium-ion battery models
Authors: Andrea Giudici, Andres F. Galvis, Smita Sahu et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text