Frequency- and angle-dependent scattering of a finite-sized meta-structure via the relaxed micromorphic model

Aivaliotis, Alexios; Tallarico, Domenico; d’Agostino, Marco-Valerio; Daouadji, Ali; Neff, Patrizio; Madeo, Angela

doi:10.1007/s00419-019-01651-9

Cited by 29 publications

(77 citation statements)

References 37 publications

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“…Using (5), the well-posedness of (4) then only needs that C e , C micro are positive definite, while C c may be positive semi-definite (e.g., C c may be even absent) and µ L 2 c ≥ 0, see [31,59,60]. 4 Despite the name micromorphic model. 5 The situation is different when one considers homogenization towards a second gradient continuum (or micromorphic approximations thereof) where there is no independent kinematical field.…”

Section: The Static Relaxed Micromorphic Modelmentioning

confidence: 99%

Identification of Scale-Independent Material Parameters in the Relaxed Micromorphic Model Through Model-Adapted First Order Homogenization

Neff

Eidel

d’Agostino

et al. 2019

J Elast

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103

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We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is done using both classical periodic homogenization and a new procedure involving the concept of apparent material stiffness of a unit-cell under affine Dirichlet boundary conditions and Neumann's principle on the overall representation of anisotropy. We explain our idea of "maximal" stiffness of the unit-cell and use state of the art first order numerical homogenization methods to obtain the needed parameters for a given tetragonal unit-cell. These results are used in the accompanying paper [16] to describe the wave propagation including band-gaps in the same tetragonal metamaterial.

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Section: The Static Relaxed Micromorphic Modelmentioning

confidence: 99%

Identification of Scale-Independent Material Parameters in the Relaxed Micromorphic Model Through Model-Adapted First Order Homogenization

Neff

Eidel

d’Agostino

et al. 2019

J Elast

Self Cite

103

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“…where t ± c σ ± • ] ± are classical Cauchy tractions, t s (σ + σ ,tt ) • ] is the generalized traction in the relaxed micromorphic medium, with ν being the outward unit normal to the surface considered (see Aivaliotis et al, 2020) and Eq. 9 for details about the definitions of generalized tractions).…”

Section: Boundary Conditions For a Finite-size Relaxed Micromorphic Slab Embedded Between Two Cauchy Half-spacesmentioning

confidence: 99%

“…In view of the conception of meta-structures for applications in acoustic control, we consider here three tetragonal unit cells which give rise to three different metamaterials at the macroscopic scale. These metamaterials will then be characterized through the relaxed micromorphic model, thus widening the set of tetragonal microstructures that have been characterized so far with this new model (see Aivaliotis et al, 2020) for the characterization of an ultrasound microstructure). The selected microstrutures are shown in Figure 2.…”

Section: D Tetragonal Microstructures For Acoustic Controlmentioning

confidence: 99%

“…All the simulations that are reported in this section and in the next one have been carried on with the software Mathematica for what concerns the relaxed micromorphic semi-analytical solutions, and with the software Comsol for the detailed discrete numerical solutions (see (Aivaliotis et al, 2020) for more details).…”

Section: D Tetragonal Microstructures For Acoustic Controlmentioning

confidence: 99%

“…The remaining dynamic parameters L 1 , L 2 , L 3 , and L * 1 are found to have a strong effect on the dispersion curves when k → ∞ and they are determined by inverse approach to reach the best possible fitting of the Bloch-Floquet dispersion curves Aivaliotis et al, 2020).…”

Section: Dispersion Curves and Calibration Of The Relaxed Micromorphic Elastic Parametersmentioning

confidence: 99%

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Exploring Metamaterials’ Structures Through the Relaxed Micromorphic Model: Switching an Acoustic Screen Into an Acoustic Absorber

et al. 2021

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While the design of always new metamaterials with exotic static and dynamic properties is attracting deep attention in the last decades, little effort is made to explore their interactions with other materials. This prevents the conception of (meta-)structures that can enhance metamaterials’ unusual behaviors and that can be employed in real engineering applications. In this paper, we give a first answer to this challenging problem by showing that the relaxed micromorphic model with zero static characteristic length can be usefully applied to describe the refractive properties of simple meta-structures for extended frequency ranges and for any direction of propagation of the incident wave. Thanks to the simplified model’s structure, we are able to efficiently explore different configurations and to show that a given meta-structure can drastically change its overall refractive behavior when varying the elastic properties of specific meta-structural elements. In some cases, changing the stiffness of a homogeneous material which is in contact with a metamaterial’s slab, reverses the structure’s refractive behavior by switching it from an acoustic screen (total reflection) into an acoustic absorber (total transmission). The present paper clearly indicates that, while the study and enhancement of the intrinsic metamaterials’ properties is certainly of great importance, it is even more challenging to enable the conception of meta-structures that can eventually boost the use of metamaterials in real-case applications.

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A note on local higher regularity in the dynamic linear relaxed micromorphic model

Owczarek

Ghiba

Neff

2021

Math Methods in App Sciences

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We consider the regularity question of solutions for the dynamic initial-boundary value problem for the linear relaxed micromorphic model. This generalized continuum model couples a wave-type equation for the displacement with a generalized Maxwell-type wave equation for the microdistortion. Naturally, solutions are found in H 1 for the displacement u and H(Curl) for the microdistortion P. Using energy estimates for difference quotients, we improve this regularity. We show H 1 loc -regularity for the displacement field, H 1 loc -regularity for the microdistortion tensor P and that Curl P is H 1 -regular if the data are sufficiently smooth.

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Frequency- and angle-dependent scattering of a finite-sized meta-structure via the relaxed micromorphic model

Cited by 29 publications

References 37 publications

Identification of Scale-Independent Material Parameters in the Relaxed Micromorphic Model Through Model-Adapted First Order Homogenization

Identification of Scale-Independent Material Parameters in the Relaxed Micromorphic Model Through Model-Adapted First Order Homogenization

Exploring Metamaterials’ Structures Through the Relaxed Micromorphic Model: Switching an Acoustic Screen Into an Acoustic Absorber

A note on local higher regularity in the dynamic linear relaxed micromorphic model

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