Efficient Modeling and Simulation of Chemo-Elasto-Plastically Coupled Battery Active Particles

As an anode material for lithium-ion batteries, amorphous silicon offers a significantly higher energy density than the graphite anodes currently used. Alloying reactions of lithium and silicon, however, induce large deformation and lead to volume changes up to 300%. We formulate a thermodynamically consistent continuum model for the chemo-elasto-plastic diffusion-deformation based on finite deformations. In this paper, a plastic deformation approach with linear isotropic hardening and a viscoplastic deformation ansatz are investigated and compared to allow the evolution of plastic deformations and reduce occurring stresses. For both models, a return mapping can be derived to update the equivalent plastic strain for the next time step. Using a finite element method and an efficient space and time adaptive solution algorithm a large number of charging cycles can be examined. We derive a linearization for the global Newton scheme and compare it to an automatic differentiation technique regarding the numerical performance and physical results. Both plastic approaches lead to a stronger heterogeneous concentration distribution and to a change to tensile tangential Cauchy stresses at the particle surface at the end of one charging cycle. Different parameter studies show how an amplification of the plastic deformation is affected. Interestingly, an elliptical particle shows only plastic deformation at the smaller half axis. With the demonstrated efficiency of the applied methods, results after five charging cycles are also discussed and can provide indications for the performance of lithium-ion batteries in long term use.