Generalized Theory for DISes in a Large Deformed Solid

Analysis of diffusion-induced stress in the electrode materials of metal-ion batteries, especially in silicon-anode lithium-ion battery with large deformation, involves an in-depth understanding of the interaction between atomic migration and matrix volume expansion. Under large migration velocity of solute atoms in a host matrix, such chemo-mechanical coupling can result in the damage or structural degradation of the matrix (electrode), leading to capacity fading. Incorporating the effects of concentration changing rate on strain energy in Helmholtz free energy and the finite deformation framework, a generalized theory has been established to solve stresses in an elasto-plastic electrode induced by lithiation. Numerical calculations of lithiation-induced stresses are performed in an amorphous nano-spherical silicon electrode by using the free-volume-based constitutive relation of amorphous materials and the generalized theory. We analyze the effects of the volumetric expansion coefficient associate with solute atoms and the volumetric expansion coefficient associate with the concentration changing rate of solute atoms on the stress evolution. The results reveal that the concentration changing rate of solute atoms likely accelerates surface cracking of electrode materials during lithiation.