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Finite element modeling of the indentation behavior of two-dimensional materials

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Abstract

The finite element method is used to investigate the indentation behavior of two-dimensional (2D) materials mounted on a substrate. The overall indentation response of the composite structure of 2D-material/substrate is highly sensitive to the elastic modulus ratio of the 2D-material to its substrate (\(\lambda \)). When \(\lambda \) is small (e.g., \(\lambda < 100\)), the overall indentation load–displacement relationship agrees with the classic indentation model (e.g., the Hertz model), whereas with a large \(\lambda \) (e.g., \(\lambda \ge 10^{3}\)), the indentation behavior of the composite structure will deviate from the manner predicted by the classic indentation model. In addition, with a small \(\lambda \), the overall indentation modulus of the composite structure is very close to that of the pure substrate (i.e., the 2D-material has a very weak contribution to the overall indentation modulus), and thus, the elastic modulus of the 2D-material cannot be effectively determined from the overall indentation modulus. The contribution of the 2D-material rapidly increases with \(\lambda \), and when \(\lambda > 10^{4}\), it is possible to accurately determine the elastic modulus of the 2D-material from the overall indentation response by the inverse analysis.

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Guoxin Cao

  2. HEDPS, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing, 100871, China

    Guoxin Cao & Tianxiao Niu

  3. IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai, 200240, China

    Guoxin Cao & Tianxiao Niu

Authors
  1. Guoxin Cao
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  2. Tianxiao Niu
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Correspondence to Guoxin Cao.

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Cao, G., Niu, T. Finite element modeling of the indentation behavior of two-dimensional materials. Acta Mech 230, 1367–1376 (2019). https://doi.org/10.1007/s00707-017-2020-3

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  • DOI: https://doi.org/10.1007/s00707-017-2020-3

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