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Continuous modelling of a class of periodic elastic metamaterials with local rotation

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Abstract

In this paper, a new continuous model capable of representing a class of elastic metamaterials with strong local rotational and translational coupling is developed. This material model differs from that used in classical elasticity, as well as the micropolar continuum model. One-dimensional harmonic wave propagation is then studied based on this newly developed model, and the results are compared with those obtained from a corresponding discrete metamaterial model. It is interesting to observe that the new continuum model captures the main dynamic characteristics of the original metamaterial system and yields a dispersion relation close to that of the discrete model near the resonant frequency. This work provides a model for a class of new continuous metamaterials whose salient features cannot be captured by traditional models of continuum materials, as well as highlights the feasibility of using such continuum models to accurately predict the behaviour of discrete elastic metamaterials.

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Funding

This research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada

    Antonio Schiavone & Xiaodong Wang

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  1. Antonio Schiavone
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  2. Xiaodong Wang
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Correspondence to Xiaodong Wang.

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Schiavone, A., Wang, X. Continuous modelling of a class of periodic elastic metamaterials with local rotation. Z. Angew. Math. Phys. 73, 29 (2022). https://doi.org/10.1007/s00033-021-01656-x

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  • DOI: https://doi.org/10.1007/s00033-021-01656-x

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