Isogeometric analysis of mechanically coupled Cahn–Hilliard phase segregation in hyperelastic electrodes of Li-ion batteries

In this work, a Cahn–Hilliard phase-field model coupled with mechanics is proposed and implemented with the isogeometric finite element method in 3D. Thereby, phase-dependent elastic properties are taken into account. The model is derived from the variational theorem in the line of the original Cahn–Hilliard model and is in agreement with that derived using a microforce balance. Isogeometric analysis is employed to treat the fourth-order Cahn–Hilliard equation and the third-order drifting term in a straightforward fashion. The additional boundary condition ∇c⋅n=0, arising from the Cahn–Hilliard equation, is enforced weakly using a Lagrange multiplier. The calculated phase segregation behavior in a bar is validated by analytical results. In particular, the influence of the phase-dependent elastic properties on phase segregation and the thickness of the phase interface is demonstrated. Finally, the phase segregation and the mechanical stress state in particles with different geometries are studied.