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Fractional-order non-Fick mechanical-diffusion coupling model based on new fractional derivatives and structural transient dynamic responses of multilayered composite laminates

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Abstract

Nano-batteries have been widely used in electric vehicles, new energy, and aerospace engineering since their high energy density, low manufacturing cost, and long cycle life. In recent years, there have been many papers that contributed to investigate the diffusion-mechanical coupling problems under non-uniform molar concentration environments (e.g., rapid charging, etc.). Nevertheless, the memory dependence of strain relaxation and mass transfer has not been considered yet. This paper aims to construct a unified fractional-order non-Fick mechanical-diffusion coupling model by introducing the fractional derivatives of the Caputo (C), Caputo–Fabrizio (CF), Atangana–Baleanu (AB), and Tempered-Caputo (TC) types. The proposed theoretical model is applied to investigate structural transient dynamic responses of multilayered composite laminates with imperfect interfacial conditions by Laplace transformation approach. The influences of different fractional derivatives, imperfect interfacial conditions, and materials constants ratios on the wave propagations and dynamic mechanical-diffusion responses are evaluated and discussed in detail.

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Acknowledgements

This work is supported by the Special Funds for Guiding Local Scientific and Technological Development by the Central Government (22ZY1QA005), National Natural Science Foundation of China (11972176, 12362014), Young Science and Technology Talents Lift Project of Gansu Province, Natural Science Foundation of Gansu Province (21JR1RA241), Young Doctoral Fund Project of Higher Education Institutions of Gansu Province (2022QB-066), Basic Research Innovation Group Project of Gansu Province (21JR7RA347), Opening Project from the State Key Laboratory for Strength and Vibration of Mechanical Structures (SV2019-KF-30, SV2021-KF-20), Basic Research Top-notch Talent Project of Lanzhou Jiaotong University, Tianyou Youth Talent Lift Program of Lanzhou Jiaotong University.

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Authors and Affiliations

  1. School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu, People’s Republic of China

    Yaning Lu & Chenlin Li

  2. State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Yaning Lu

  3. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Chenlin Li

  4. School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, People’s Republic of China

    Tianhu He

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Correspondence to Chenlin Li.

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Lu, Y., Li, C. & He, T. Fractional-order non-Fick mechanical-diffusion coupling model based on new fractional derivatives and structural transient dynamic responses of multilayered composite laminates. Arch Appl Mech 94, 239–259 (2024). https://doi.org/10.1007/s00419-023-02518-w

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