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

Kai Zhang, Yong Li, Bailin Zheng, Fuqian Yang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)561-578
Number of pages18
JournalActa Mechanica
Issue number2
StatePublished - Feb 2022

Bibliographical note

Funding Information:
The authors are grateful for the support from the National Natural Science Foundation of China under Grant Numbers 11902222 and 11902073. This work is sponsored by “Chenguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission under Grant No. 19CG23 and “the Fundamental Research Funds for the Central Universities” supported by Jiangsu Key Laboratory of Engineering Mechanics, Southeast University under Grant No. LEM2001.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering


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