Instability analysis of Li-ion battery electrode particles induced by chemomechanical growth using incremental deformation theory

Volumetric swelling due to lithiation into active battery materials is a well-known phenomenon. A chemo-mechanical framework can suitably explain the deformations of the electrode and the generation of diffusion-induced stresses (DIS). Various experimental works have shown that the effects of DIS further cause the active material to lose its structural stability. However, relatively few frameworks exist that can investigate such phenomena in a comprehensive manner. These are mainly based on the Euler–Bernoulli beam theory and the von-Karman plate theory. In the present work we present a generalized three-dimensional instability framework incorporating the theory of incremental deformation. We use this theory on a widely used chemo-mechanical framework. Notably, similar existing instability investigations on negative electrode materials are based only on incompressible material behaviour. As opposed to it, in this work we have considered a compressible material. Also, we account for the spatial and temporal nature of growth, which is a significant departure from the existing instability frameworks. Therefore, this current work brings the investigation of structural instability of electrode material closer to physical reality. In our study, we use the compound matrix method to find the critical lithiation parameter. Then we consider three sets of problems, each with a particular combination of boundary conditions applied on the inner and outer cylindrical surfaces of hollow cylindrical anode particles. These are free-free, fixed-free, and free-fixed, where each combination represents a particular type of interaction between an electrode particle and its surroundings. Most importantly, we find that the free-free and fixed-free conditions show only a pure axial and mixed mode of instability, and do not show the pure circumferential mode. The free-fixed conditions, however, shows all three modes of instability. Additionally, the presence of mode crossover makes the instability pattern of such electrode particles significant.