Electro-chemo-mechanical simulation for lithium ion batteries across the scales

In this work a phase field method is used for the solution of an electro-chemical diffusion model for a lithium-iron-phosphate particle coupled to a small-strain elasto-plasticity model. This coupling takes the mechanical dilatation of the crystal lattice during intercalation into account. The electro-chemo-mechanical coupling is derived from a Helmholtz free energy, resulting in constitutive equations for both the diffusion and the mechanical equilibrium in the electrode material. A new method for the generation of virtual microstructures is given with additional constraints to obtain smooth boundaries. This ensures valid mechanical solutions for grid refinement. The model is then discretized, linearized and solved for various microstructures. Academic results in one and two spatial dimensions are presented as well as results on spherical structures. The versatility of the numerical method is demonstrated for virtual microstructures generated by stochastic models on graphite.