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A theory of mechanobiological sensation: strain amplification/attenuation of coated liquid inclusion with surface tension

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Abstract

Cells are compressible and can be regarded as a kind of coated liquid inclusion embedded in a three-dimensional elastic matrix. In the presence of far-field loading, how the coating influences the mechanical response (e.g., volume change) of the liquid inclusion remains elusive, especially when surface tension effects become significant at cell size level. We developed a theoretical model to characterize the mechanical amplification or attenuation role of coating on spherical liquid inclusions, with surface tension and liquid compressibility accounted for. We found that surface tension could increase the volumetric strain of the inclusion through decreasing its effective bulk modulus. We further found that, when there is a monotonic stiffness variation (either decreasing or increasing) from matrix via coating to inclusion, the presence of coating amplified the volumetric strain compared with the case without coating; in the opposite, when there is a non-monotonic stiffness change from matrix via coating to inclusion, the volumetric strain is attenuated by the coating. The results are useful for understanding and exploring the mechanobiological sensation of certain types of cell, e.g., osteocytes and cancer cells.

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grants 12032010, 11532009, and 11902155), the Natural Science Foundation of Jiangsu Province (Grant BK20190382), the foundation of “Jiangsu Provincial Key Laboratory of Bionic Functional Materials”, the Foundation for the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Fei Ti, Shaobao Liu & Tian Jian Lu

  2. Xi’an Modern Chemistry Research Institute, Xi’an, 710065, China

    Xin Chen

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

    Xin Chen & Tian Jian Lu

  4. Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an, 710049, China

    Xin Chen, Haiqian Yang & Tian Jian Lu

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  1. Fei Ti
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  2. Xin Chen
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  3. Haiqian Yang
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  4. Shaobao Liu
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Correspondence to Shaobao Liu or Tian Jian Lu.

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Ti, F., Chen, X., Yang, H. et al. A theory of mechanobiological sensation: strain amplification/attenuation of coated liquid inclusion with surface tension. Acta Mech. Sin. 37, 145–155 (2021). https://doi.org/10.1007/s10409-020-01017-3

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