Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

doi:10.1007/s10483-018-2386-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (11): 1567-1586.doi: https://doi.org/10.1007/s10483-018-2386-6

Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

Jun YIN¹, Xianjun SHAO¹, Bo LU¹, Yicheng SONG^2,3, Junqian ZHANG^2,3,4

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. Department of Mechanics, Shanghai University, Shanghai 200444, China;
3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
4. Materials Genome Institute, Shanghai University, Shanghai 200072, China

收稿日期:2018-03-21 修回日期:2018-05-28 出版日期:2018-11-01 发布日期:2018-11-01
通讯作者: Junqian ZHANG E-mail:jqzhang2@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11332005)

Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

Jun YIN¹, Xianjun SHAO¹, Bo LU¹, Yicheng SONG^2,3, Junqian ZHANG^2,3,4

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. Department of Mechanics, Shanghai University, Shanghai 200444, China;
3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
4. Materials Genome Institute, Shanghai University, Shanghai 200072, China

Received:2018-03-21 Revised:2018-05-28 Online:2018-11-01 Published:2018-11-01
Contact: Junqian ZHANG E-mail:jqzhang2@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11332005)

摘要/Abstract

摘要： A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface (downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.

关键词: nonholonomic systems, white noises, random differential equations, bilayer electrode, lithium ion battery, finite elastoplastic bending, coupled diffusion

Abstract: A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface (downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.

Key words: bilayer electrode, finite elastoplastic bending, nonholonomic systems, white noises, random differential equations, lithium ion battery, coupled diffusion

中图分类号:

65L12

Jun YIN, Xianjun SHAO, Bo LU, Yicheng SONG, Junqian ZHANG. Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(11): 1567-1586.

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Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

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