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Interaction Between Stress and Diffusion in Lithium-Ion Batteries: Analysis of Diffusion-Induced Buckling of Nanowires

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Handbook of Mechanics of Materials

Abstract

This chapter summarizes the frameworks of the diffusion-induced stress both in the theory of linear elasticity and the theory of nonlinear elasticity, which provide the theoretical principles to investigate the coupling between stress and diffusion in analyzing the elastic deformation of materials induced by the migration/diffusion of solute atoms. The buckling behavior of an elastic core-shell nanowire induced by the migration/diffusion of lithium during lithiation is analyzed by using the theory of linear elasticity and diffusion equation. Closed-form solution is obtained for the calculation of the critical time for the onset of buckling of the nanowire. The effects of current density, length, and the radius ratio on the critical concentration and critical time for the occurrence of the buckling are studied. For an elastic-perfectly plastic core-shell nanowire, numerical analysis of the lithiation-induced buckling of the core-shell nanowire is performed, using the commercial finite element software ABAQUS. The effects of the radius ratio and yield stress of the outer shell on the critical average concentration and critical time for the occurrence of the buckling are investigated.

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Author information

Authors and Affiliations

  1. Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY, USA

    F. Q. Yang

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China

    Y. Li & B. L. Zheng

  3. Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

    K. Zhang

Authors
  1. F. Q. Yang
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  2. Y. Li
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  3. B. L. Zheng
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  4. K. Zhang
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Corresponding author

Correspondence to F. Q. Yang .

Editor information

Editors and Affiliations

  1. Materials Science and Strength of Materials, University of Stuttgart Institute for Materials Testing, Stuttgart, Germany

    Siegfried Schmauder

  2. Department of Civil Engineering, National Taiwan University Department of Civil Engineering, Taipei, T´ai-pei, Taiwan

    Chuin-Shan Chen

  3. BEC 254, University of Alabama at Birmingham, Birmingham, Alabama, USA

    Krishan K. Chawla

  4. Fulton School of Engineering, Arizona State University, Tempe, Arizona, USA

    Nikhilesh Chawla

  5. Engineering Mechanics, Zhejiang University Engineering Mechanics, Hangzhou, China

    Weiqiu Chen

  6. Katayanagi Advanced Research Laboratorie, Tokyo University of Technology Katayanagi Advanced Research Laboratorie, Tokyo, Japan

    Yutaka Kagawa

Appendix: Postbuckling Analysis of an Elastic Rod

Appendix: Postbuckling Analysis of an Elastic Rod

A pin-end column with a radius of 10 nm and a length of 500 nm was created to validate the imperfection method used in the finite element analysis. The elastic modulus and Poisson’s ratio of the column are 200 GPa and 0.3, respectively. The first-order buckling mode was used to analyze the post buckling of the column, which was obtained from the buckle step in the finite element analysis. Figure 7 shows the relationship between the reaction force at the boundary and the arc length, in which the maximum reaction force is found to be 608 × 10−10 N. The critical buckling load calculated from Eq. 48 is 620.126 × 10−10 N. There is only ~1.9% difference. Such a result validates the finite element model used in the analysis of the lithiation-induced post buckling of the nanowire.

Fig. 7
figure 7

Reaction force versus arc length for the post buckling of a pin-end column

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Yang, F.Q., Li, Y., Zheng, B.L., Zhang, K. (2018). Interaction Between Stress and Diffusion in Lithium-Ion Batteries: Analysis of Diffusion-Induced Buckling of Nanowires. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6855-3_59-1

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  • DOI: https://doi.org/10.1007/978-981-10-6855-3_59-1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6855-3

  • Online ISBN: 978-981-10-6855-3

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