A general multiscale framework for the emergent effective elastodynamics of metamaterials
| Autor: | V Varvara Kouznetsova, Mgd Marc Geers, A. Sridhar |
|---|---|
| Přispěvatelé: | Mechanics of Materials, Group Kouznetsova, Group Geers |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Physics
Homogenization Micromorphic continua Acoustic metamaterials Continuum (measurement) Mechanical Engineering Computation Floquet–Bloch transform Metamaterial Cauchy distribution Bragg's law 02 engineering and technology 021001 nanoscience & nanotechnology Condensed Matter Physics Homogenization (chemistry) Computational multiscale analysis 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials Scale separation Phononic crystals Floquet-Bloch transform Statistical physics 0210 nano-technology Eigenvalues and eigenvectors |
| Zdroj: | Journal of the Mechanics and Physics of Solids, 111, 414-433. Elsevier |
| ISSN: | 0022-5096 |
| DOI: | 10.1016/j.jmps.2017.11.017 |
| Popis: | This paper presents a general multiscale framework towards the computation of the emergent effective elastodynamics of heterogeneous materials, to be applied for the analysis of acoustic metamaterials and phononic crystals. The generality of the framework is exemplified by two key characteristics. First, the underlying formalism relies on the Floquet–Bloch theorem to derive a robust definition of scales and scale separation. Second, unlike most homogenization approaches that rely on a classical volume average, a generalized homogenization operator is defined with respect to a family of particular projection functions. This yields a generalized macro-scale continuum, instead of the classical Cauchy continuum. This enables (in a micromorphic sense) to homogenize the rich dispersive behavior resulting from both Bragg scattering and local resonance. For an arbitrary unit cell, the homogenization projection functions are constructed using the Floquet–Bloch eigenvectors obtained in the desired frequency regime at select high symmetry points, which effectively resolves the emergent phenomena dominating that regime. Furthermore, a generalized Hill–Mandel condition is proposed that ensures power consistency between the homogenized and full-scale model. A high-order spatio-temporal gradient expansion is used to localize the multiscale problem leading to a series of recursive unit cell problems giving the appropriate micro-mechanical corrections. The developed multiscale method is validated against standard numerical Bloch analysis of the dispersion spectra of example unit cells encompassing multiple high-order branches generated by local resonance and/or Bragg scattering. |
| Databáze: | OpenAIRE |
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