A free volume-based analytical model for plastic flow in thin-walled silicon structures of lithium-ion batteries

Realizing that physically based constitutive models can provide insight into the plastic deformation of amorphous silicon during lithiation, we establish a physically based constitutive model with the free volume theory and investigate the plastic flow in thin-walled silicon anodes, including silicon thin film, thin-walled hollow nanoparticle and nanotube. Analytical solutions of stress fields in the three thin-walled anode structures are obtained, and the analytical result of the in-plane stress in a silicon thin film is in good accord with the experimental data reported in the literature, suggesting the applicability of this model in the analysis of lithiation-induced stress in silicon-based anodes. Further analyses show that for all the three thin-walled structures the stress and free volume decrease with the increase in the state of charge (SOC). The spatiotemporal variations of the stresses in the hollow nanoparticle and nanotube are very similar to each other. The three components of the stress field in both structures are nearly uniform due to thin-walled structures. The stress along the hoop direction is larger than the other two, which indicates that circumferential surface cracks are likely to occur first. At the quasi-static state, the stresses and free volume increase with increasing the charging rate, indicating that the resistance to plastic flow fades with the increase in the C-rate.