  In battery modeling, the electrode is discretized at the macroscopic scale
with a single representative particle in each volume. This lacks the accurate
physics to describe interparticle interactions in electrodes. To remedy this,
we formulate a model that describes the evolution of degradation of a
population of battery active material particles using ideas in population
genetics of fitness evolution, where the state of a system depends on the
health of each particle that contributes to the system. With the fitness
formulation, the model incorporates effects of particle size and heterogeneous
degradation effects which accumulate in the particles as the battery is cycled,
accounting for different active material degradation mechanisms. At the
particle scale, degradation progresses nonuniformly across the population of
active particles, observed from the autocatalytic relationship between fitness
and degradation. Electrode-level degradation is formed from various
contributions of the particle-level degradation, especially from smaller
particles. It is shown that specific mechanisms of particle-level degradation
can be associated with characteristic signatures in the capacity-loss and
voltage profiles. Conversely, certain features in the electrode-level phenomena
can also provide insight into the relative importance of different
particle-level degradation mechanisms.
