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

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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.

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Abbreviations

c :

lithium molar concentration in the reference state

c max :

saturation concentration at the stoichiometric limit

Ω:

partial molar volume

h 1 :

initial thickness of the active layer

H 1 :

thickness of the deformed active layer

h c :

initial thickness of the current collector

H c :

thickness of the deformed current collector

λθ :

in-plane stretch ratio

λr :

transverse stretch ratio

εs :

chemical volumetric eigen-strain

E :

Young’s modulus

v :

Poisson’s ratio

σ θ :

in-plane Cauchy stress

σ r :

transverse Cauchy stress

σ eq :

von Mises stress

σY:

yield stress

F :

Faraday’s constant

R :

gas constant

T :

temperature

i n :

electrical current density in the reference state

D :

diffusion coefficient

L θ :

in-plane logarithmic stress

L r :

transverse logarithmic stresses

Q :

state of charge (SOC)

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Author information

Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Jun Yin, Xianjun Shao & Bo Lu

  2. Department of Mechanics, Shanghai University, Shanghai, 200444, China

    Yicheng Song & Junqian Zhang

  3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China

    Yicheng Song & Junqian Zhang

  4. Materials Genome Institute, Shanghai University, Shanghai, 200072, China

    Junqian Zhang

Authors
  1. Jun Yin
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  2. Xianjun Shao
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  3. Bo Lu
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Correspondence to Junqian Zhang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11332005)

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Yin, J., Shao, X., Lu, B. et al. Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries. Appl. Math. Mech.-Engl. Ed. 39, 1567–1586 (2018). https://doi.org/10.1007/s10483-018-2386-6

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  • DOI: https://doi.org/10.1007/s10483-018-2386-6

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