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This study is concerned with modeling detrimental deformations of the binderphase within lithium-ion batteries that occur during cell assembly and usage. Atwo-dimensional poroviscoelastic model for the mechanical behavior of porouselectrodes is formulated and posed on a geometry corresponding to a thinrectangular electrode, with a regular square array of microscopic circularelectrode particles, stuck to a rigid base formed by the current collector.Deformation is forced both by (i) electrolyte absorption driven binderswelling, and; (ii) cyclic growth and shrinkage of electrode particles as thebattery is charged and discharged. The governing equations are upscaled inorder to obtain macroscopic effective-medium equations. A solution to theseequations is obtained, in the asymptotic limit that the height of therectangular electrode is much smaller than its width, that shows themacroscopic deformation is one-dimensional. The confinement of macroscopicdeformations to one dimension is used to obtain boundary conditions on themicroscopic problem for the deformations in a 'unit cell' centered on a singleelectrode particle. The resulting microscale problem is solved using numerical(finite element) techniques. The two different forcing mechanisms are found tocause distinctly different patterns of deformation within the microstructure.Swelling of the binder induces stresses that tend to lead to binderdelamination from the electrode particle surfaces in a direction parallel tothe current collector, whilst cycling causes stresses that tend to lead todelamination orthogonal to that caused by swelling. The differences between thecycling-induced damage in both: (i) anodes and cathodes, and; (ii) fast andslow cycling are discussed. Finally, the model predictions are compared tomicroscopy images of nickel manganese cobalt oxide cathodes and a qualitativeagreement is found.

A mathematical model for mechanically-induced deterioration of the binder in lithium-ion electrodes