Chemo-mechanical modelling of the breathing effect during lithiation and delithiation in Li-Si batteries

  • Dittmann, Jan (Kiel University)
  • Stern, Jan-Ole (Kiel University)
  • Beiranvand, Hamzeh (Kiel University)
  • Wulfinghoff, Stephan (Kiel University)

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Due to their high energy density and high cell voltage, lithium-ion batteries have become the most prominent battery type used in electronic devices today. However, research still aims to reduce costs, increase sustainability and improve battery performance by new combinations of electrode and electrolyte materials. One promising candidate for a superior anode material is silicon due to its ability to form an alloy with lithium, which leads to a much higher theoretical capacity in comparison to commonly used electrodes that store lithium-ions by intercalation. However, the main disadvantage of silicon is the large volume change (breathing) during lithia- tion and delithiation, which results in high mechanical stresses, cracking and ultimately failure of the battery. Structuring the anode is a possible solution to minimize these stresses but requires tools to better understand and predict the material behavior. Here, we present a chemo-mechanical FEM model for the breathing effect of the silicon anode during lithiation and delithiation. The model is based on the framework for gradient extended standard dissipative solids [1]. It couples diffusion of lithium ions, phase transformation with a moving phase boundary and the related volume changes which lead to mechanical stresses in the material. The driving force for diffusion is given by the gradient of the electrochemical potential. Phase transformation and phase boundary movement is described by a phase field with a double obstacle potential [2], which is implemented using a micromorphic approach [3] to shift the constraint of the order parameter ξ ∈ [0, 1] from the nodes to the Gauss points. Fur- ther, the model is implemented for finite strains and discriminates between elastic deformations and chemical volume expansion by splitting the deformation gradient multiplicatively into two respective parts.