Interaction between stress and diffusion in lithium-ion batteries: Analysis of diffusion-induced buckling of nanowires

This chapter summarizes the frameworks of the diffusion-induced stress both in the theory of linear elasticity and the theory of nonlinear elasticity, which provide the theoretical principles to investigate the coupling between stress and diffusion in analyzing the elastic deformation of materials induced by the migration/diffusion of solute atoms. The buckling behavior of an elastic core-shell nanowire induced by the migration/diffusion of lithium during lithiation is analyzed by using the theory of linear elasticity and diffusion equation. Closed-form solution is obtained for the calculation of the critical time for the onset of buckling of the nanowire. The effects of current density, length, and the radius ratio on the critical concentration and critical time for the occurrence of the buckling are studied. For an elastic-perfectly plastic core-shell nanowire, numerical analysis of the lithiation-induced buckling of the core-shell nanowire is performed, using the commercial finite element software ABAQUS. The effects of the radius ratio and yield stress of the outer shell on the critical average concentration and critical time for the occurrence of the buckling are investigated.