Evidence has accumulated recently that a high-capacity electrode of a lithium-ion battery may not recover its initial shape after a cycle of charge and discharge.  Such a plastic behavior is studied here by formulating a theory that couples large amounts of lithiation and deformation.  The homogeneous lithiation and deformation in a small element of an electrode under stresses is analyzed within nonequilibrium thermodynamics, permitting a discussion of equilibrium with respect to some processes, but not others.  The element is assumed to undergo plastic deformation when the stresses reach a yield condition.  The theory is combined with a diffusion equation to analyze a spherical particle of an electrode being charged and discharged at a constant rate.  When the charging rate is low, the distribution of lithium in the particle is nearly homogeneous, the stress in the particle is low, and no plastic deformation occurs.  When the charging rate is high, the distribution of lithium in the particle is inhomogeneous, and the stress in the particle is high, possibly leading to fracture and cavitation. 

Silicon can host a large amount of lithium, making it a promising electrode for high-capacity lithium-ion batteries.  Upon absorbing lithium, silicon swells several times its volume; the deformation often induces large stresses and pulverizes silicon.

During charging or discharging of a lithium-ion battery, lithium is extracted from one electrode and inserted into the other.  This extraction-insertion reaction causes the electrodes to deform.  An electrode is often composed of small active particles in a matrix.  If the battery is charged at a rate faster than lithium can homogenize in an active particle by diffusion, the inhomogeneous distribution of lithium results in stresses that may cause the particle to fracture.  The distributions of lithium and stress in a LiCoO2 particle are calculated.  The energy release rates are then calculated for the particle containing

In a lithium-ion battery, both electrodes are atomic frameworks that host mobile lithium ions. When the battery is being charged or discharged, lithium ions diffuse from one electrode to the other. Such an insertion reaction deforms the electrodes, and may cause the electrodes to crack. This paper uses fracture mechanics to determine the critical conditions to avert cracking. The method is applied to cracks induced by the mismatch between phases in crystalline particles of LiFePO4