Comparison of a phase-field model for intercalation induced stresses in electrode particles of lithium ion batteries for small and finite deformation theory

Lithium manganese oxide spinel, like many other electrode materials of lithium ion batteries shows phase changes during intercalation. In this paper we investigate the modeling of this phenomenon using the Cahn-Hilliard equation coupled to elasticity by means of a thermomechanical analogy. The finite and small deformation formulation of these theories are compared by means of simulations of electrode particles of lithium manganese oxide spinel. In particular, variations of the material constants are discussed. Furthermore, we investigate the identification of Gurtin's external microforce according to recent work by Anand (2012). We show that this means a significant change of the theory as compared to the classical formulation, the details of which are discussed by means of simulations.