A computational multiscale homogenization framework accounting for inertial effects: Application to acoustic metamaterials modelling

Roca, D.; Lloberas-Valls, Oriol; Cante, Juan; Oliver, J.

doi:10.1016/j.cma.2017.10.025

Cited by 45 publications

(49 citation statements)

References 28 publications

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“…The ensuing microbalance and macrobalance of momentum were solved as coupled equations of motion at the macroscale. A similar outcome was achieved in the work of Roca et al, 24 albeit with their homogenized stress and rate of change of momentum derived via Lagrange multipliers-based approach. Within the domain of linear elastic acoustic metamaterials, Sridhar et al 25 adopted an analytical plane wave expansion to simplify their earlier macroscale problem involving both microbalance and macrobalance of momentum.…”

Section: Introductionsupporting

confidence: 71%

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Homogenized enriched model for blast wave propagation in metaconcrete with viscoelastic compliant layer

Tan

Poh

Tkalich

2019

Numerical Meth Engineering

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Summary In this contribution, a reduced‐order homogenization approach is adopted and extended to incorporate the linear viscoelasticity effect. A homogenized enriched model emerges from the homogenization framework, which is utilized here for the analysis of blast wave propagation in metaconcrete with linear viscoelastic compliant layer(s). A semidiscrete equation of motion for the unit cell is first extracted for micro‐macro transition, through a series of transformations to effect the periodic boundary conditions and model reduction, respectively. The ensuing microbalance and macrobalance of momenta are next subjected to spatial and temporal discretizations toward a system of equations to be solved numerically. The predictive capability of the proposed model is demonstrated through a series of benchmark examples involving several metaconcrete variants. It is observed that the dual resonator configuration achieves a greater extent of wave attenuation than the single resonator counterpart.

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Section: Introductionsupporting

confidence: 71%

“…As a result of orthogonal diagonalization, the following two equations of motion can be obtained from (23a) in terms of the relevant submatrices ofm,d,k, andf after utilizing (24) m rrp r +k rrp r +d rr…”

Section: Microbalance Of Momentummentioning

confidence: 99%

Homogenized enriched model for blast wave propagation in metaconcrete with viscoelastic compliant layer

Tan

Poh

Tkalich

2019

Numerical Meth Engineering

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“…This is the case, for example, of the one proposed in [103] for meta poro-elastic laminates with thin coatings, that couples the FEM, which simulates the response in the poro-elastic medium with inclusions, and the Bloch expansion, which simulates the surrounding media using a technique similar to the transfer matrix method to account for the coatings. Multiscale and homogenization modeling techniques are also attractive ways of addressing the issue when different scales are involved, such as microporous materials where one is interested in the macroscopic effect due to the microstructure of the system [104], and they can be adopted in a metamaterial design process [105,106].…”

Section: Challengesmentioning

confidence: 99%

Acoustic Metamaterials in Aeronautics

et al. 2018

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Metamaterials, man-made composites that are scaled smaller than the wavelength, have demonstrated a huge potential for application in acoustics, allowing the production of sub-wavelength acoustic absorbers, acoustic invisibility, perfect acoustic mirrors and acoustic lenses for hyper focusing, and acoustic illusions and enabling new degrees of freedom in the control of the acoustic field. The zero, or even negative, refractive sound index of metamaterials offers possibilities for the control of acoustic patterns and sound at sub-wavelength scales. Despite the tremendous growth in research on acoustic metamaterials during the last decade, the potential of metamaterial-based technologies in aeronautics has still not been fully explored, and its utilization is still in its infancy. Thus, the principal concepts mentioned above could very well provide a means to develop devices that allow the mitigation of the impact of civil aviation noise on the community. This paper gives a review of the most relevant works on acoustic metamaterials, analyzing them for their potential applicability in aeronautics, and, in this process, identifying possible implementation areas and interesting metabehaviors. It also identifies some technical challenges and possible future directions for research with the goal of unveiling the potential of metamaterials technology in aeronautics.

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“…This is the case, for example, of the one proposed in [101] for meta poro-elastic laminates with thin coatings, that couples the Finite Element Method simulating the response in the poro-elastic medium with inclusions, and the Bloch expansion simulating the surrounding media using a technique similar to the transfer matrix method to account for the coatings. Multiscale and homogenization modeling techniques are also attractive ways to address the issue when different scales are involved, such as microporous materials in which one is interested in the macroscopic effect due to the microstructure of the system [102] and can be adopted in a metamaterial design process [103,104].…”

Section: Challengesmentioning

confidence: 99%

Acoustic Metamaterials in Aeronautics

Palma¹,

Mao²,

Burghignoli³

et al. 2018

Preprint

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Metamaterials, man-made composites scaled smaller than the wavelength, have demonstrated a huge potential in their applications in acoustics, opening up for sub--wavelength acoustic absorbers, acoustic invisibility, perfect acoustic mirrors and acoustic lenses for hyper focusing, acoustic illusions and enabling new degrees of freedom in the control of the acoustic field. The zero, or even negative, refractive sound index of metamaterials offers possibilities in control of the acoustic pattern and sound at sub--wavelength scales. Despite the tremendous growth of the research on acoustic metamaterials during the last decade, the potential of metamaterial-based technologies in aeronautics is still not fully explored and its utilization is still in its infancy. Thus the principal concepts mentioned above could very well provide means to develop devices that would allow the mitigation of the impact of the civil aviation noise on the community. This paper gives a review of the state of the art of the most relevant works on acoustic metamaterials, analyzing them against their potential applicability in aeronautics, and in this process identifying possible implementation areas and interesting metabehaviors. It also identifies some technical challenges and possible future directions for research with the goal of unveiling the potential of metamaterials technologies in aeronautics.

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A computational multiscale homogenization framework accounting for inertial effects: Application to acoustic metamaterials modelling

Cited by 45 publications

References 28 publications

Homogenized enriched model for blast wave propagation in metaconcrete with viscoelastic compliant layer

Homogenized enriched model for blast wave propagation in metaconcrete with viscoelastic compliant layer

Acoustic Metamaterials in Aeronautics

Acoustic Metamaterials in Aeronautics

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