A computational multiscale homogenization framework accounting for inertial effects: Application to acoustic metamaterials modelling Article Swipe
D. Roca
,
O. Lloberas‐Valls
,
J. Cante
,
J. Oliver
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1016/j.cma.2017.10.025
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1016/j.cma.2017.10.025
A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuations and their gradients are then accounted for in a saddle-point formulation of that variational principle in terms of Lagrange functionals. A physical interpretation of the involved Lagrange multipliers can then be readily obtained. The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuation
Related Topics
Concepts
Homogenization (climate)
Metamaterial
Virtual work
Inertial frame of reference
Discretization
Finite element method
Microscale chemistry
Lagrange multiplier
Computer science
Classical mechanics
Statistical physics
Physics
Mathematical analysis
Mathematics
Mathematical optimization
Optics
Biodiversity
Ecology
Thermodynamics
Mathematics education
Biology
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.cma.2017.10.025
- OA Status
- hybrid
- Cited By
- 53
- References
- 31
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2768499567
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2768499567Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1016/j.cma.2017.10.025Digital Object Identifier
- Title
-
A computational multiscale homogenization framework accounting for inertial effects: Application to acoustic metamaterials modellingWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2017Year of publication
- Publication date
-
2017-11-14Full publication date if available
- Authors
-
D. Roca, O. Lloberas‐Valls, J. Cante, J. OliverList of authors in order
- Landing page
-
https://doi.org/10.1016/j.cma.2017.10.025Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
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https://doi.org/10.1016/j.cma.2017.10.025Direct OA link when available
- Concepts
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Homogenization (climate), Metamaterial, Virtual work, Inertial frame of reference, Discretization, Finite element method, Microscale chemistry, Lagrange multiplier, Computer science, Classical mechanics, Statistical physics, Physics, Mathematical analysis, Mathematics, Mathematical optimization, Optics, Biodiversity, Ecology, Thermodynamics, Mathematics education, BiologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
53Total citation count in OpenAlex
- Citations by year (recent)
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2025: 6, 2024: 10, 2023: 3, 2022: 7, 2021: 11Per-year citation counts (last 5 years)
- References (count)
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31Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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