Applied Mathematics and Mechanics

, Volume 39, Issue 11, pp 1567–1586 | Cite as

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

  • Jun Yin
  • Xianjun Shao
  • Bo Lu
  • Yicheng Song
  • Junqian ZhangEmail author


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

lithium ion battery bilayer electrode coupled diffusion finite elastoplastic bending 



lithium molar concentration in the reference state


saturation concentration at the stoichiometric limit


partial molar volume


initial thickness of the active layer


thickness of the deformed active layer


initial thickness of the current collector


thickness of the deformed current collector


in-plane stretch ratio


transverse stretch ratio


chemical volumetric eigen-strain


Young’s modulus


Poisson’s ratio


in-plane Cauchy stress


transverse Cauchy stress


von Mises stress


yield stress


Faraday’s constant


gas constant




electrical current density in the reference state


diffusion coefficient


in-plane logarithmic stress


transverse logarithmic stresses


state of charge (SOC)

Chinese Library Classification

O33 O29 

2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jun Yin
    • 1
  • Xianjun Shao
    • 1
  • Bo Lu
    • 1
  • Yicheng Song
    • 2
    • 3
  • Junqian Zhang
    • 2
    • 3
    • 4
    Email author
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of MechanicsShanghai UniversityShanghaiChina
  3. 3.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiChina
  4. 4.Materials Genome InstituteShanghai UniversityShanghaiChina

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