Computational homogenization of locally resonant acoustic metamaterial panels towards enriched continuum beam/shell structures

Liu, Lei; Sridhar, A.; Geers, M.G.D.; Kouznetsova, V Varvara

doi:10.1016/j.cma.2021.114161

Cited by 21 publications

(9 citation statements)

References 56 publications

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“…Using the definition of the differential operator L in (31), the first integral on the left-hand side reads…”

Section: Weak Formmentioning

confidence: 99%

“…Although the resulting formulations are similar, the higher‐order inertia terms can be introduced to the equations of motion either directly through the positive‐definite kinetic energy density of Mindlin's theory, or by deriving the equations of motion based on a lattice model consisting of discrete particles with bond interactions, and stabilizing those equations by replacing the higher‐order derivatives of strain with the Laplacian of acceleration 9 . Enriching the governing partial differential equations of elastic media by the higher‐order derivatives of acceleration, or a combination of acceleration gradient and other higher‐order terms has been the topic of various studies up until now 28‐31 . Here, the equations of motion with the higher‐order inertia terms are employed for describing the size‐dependent mechanical behavior of heterogeneous solids with periodic microstructure.…”

Section: Introductionmentioning

confidence: 99%

“…9 Enriching the governing partial differential equations of elastic media by the higher-order derivatives of acceleration, or a combination of acceleration gradient and other higher-order terms has been the topic of various studies up until now. [28][29][30][31] Here, the equations of motion with the higher-order inertia terms are employed for describing the size-dependent mechanical behavior of heterogeneous solids with periodic microstructure. A common example is the additively manufactured lattice structure shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

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The scaled boundary finite element method for dispersive wave propagation in higher‐order continua

Daneshyar

Sotoudeh

Ghaemian

2022

Numerical Meth Engineering

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The classical theory of elasticity relies on the perfect structure of matter. No matter how small a medium is, it always stays homogeneous-but the reality is different. Even though the classical continuum mechanics suffices well for describing phenomena that evolve at super-microscopic scales, it ceases to reproduce reasonable responses when the size effects are pronounced. It is due to the local constitutive equations of classical continuum mechanics, which are devoid of any length scales associated with the underlying microstructure.The gradient-dependent theory of elasticity redresses this shortcoming by incorporating the kinematic quantities of the corresponding representative volume element by enriching the differential equations with higher-order spatial and temporal derivatives. In this study, the scaled boundary finite element method is formulated for the equations of motion with higher-order inertia terms. To this end, the semi-discretized scaled boundary finite element equations of the medium are derived by introducing the scaled boundary transformation of geometry to the gradient-enriched equations of motion and applying the Galerkin method of weighted residuals. It is shown that the well-established available solution methods are incapable of handling the frequency-domain representation of the derived formulation. Accordingly, a numerical solution method based on the shooting technique is proposed. The solution procedure is formulated for general numerical integration schemes via the infinite Taylor series. The evolution of the impedance-diffusion matrix and contribution of inter-subdomain forces and tractions are extracted. Four different numerical integration methods are employed to describe the solution procedure. In addition, a comparison regarding their computational efficiency is presented. For the sake of verification, the scaled boundary finite element solutions of three numerical examples are compared with reference solutions that are obtained using finite element models with extremely fine meshes. The convergence trends are also presented for both h-and p-refinement methods. The results demonstrate the capability of the proposed formulation in reproducing accurate responses.

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“…Using the definition of the differential operator L in (31), the first integral on the left-hand side reads…”

Section: Weak Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The scaled boundary finite element method for dispersive wave propagation in higher‐order continua

Daneshyar

Sotoudeh

Ghaemian

2022

Numerical Meth Engineering

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show abstract

“…The possibility of creating targeted stop bands in LR periodic structures has inspired multiple research efforts for vibration and wave propagation control of 2D structures. 14,15 Among recent studies, it is worth mentioning the application of finite element (FEM) analysis, 16,17 ad hoc analytical methods, 18,19,20 simplified models for periodic systems, 21,22 exploitation of nonlinearities for enhanced or unusual performance, 23,24,25,26,27 and experimental campaigns. 28,29,30…”

Section: Introductionmentioning

confidence: 99%

A multi-bandgap metamaterial with multi-frequency resonators

Murer

Guruva

Formica

et al. 2023

Journal of Composite Materials

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A 2D metamaterial cellular system inspired by lightweight honeycombs and spider webs is investigated. The hexagonal cells of the honeycomb act as hosting substructures for spider-web-like or cantilever resonators with added lumped masses which can vibrate, in principle, in any of the infinitely many modes. Contrary to traditional approaches utilizing discrete mass-spring resonators, here the infinite-dimensional (full spectrum) resonators are intentionally tailored to generate multiple, complete or incomplete, stop bands across which wave propagation is either totally or partially suppressed along preferential directions. The Plane Wave Expansion method is employed to obtain the dispersion curves and the bandgap sensitivity with respect to the design parameters. Experimental results based on laser scanning vibrometry corroborate the theoretical predictions and confirm the robustness of the stop band behavior with a wealth of results which pave the way towards suitable optimization strategies and a closer understanding of these formidable stop band cellular material systems.

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“…This problem can be solved by developing efficient improved numerical methods (e.g., [ 19 , 20 , 21 , 22 , 23 , 24 , 25 ]) or employing models, where the fractured zone with a distribution of cracks is substituted by an equivalent homogeneous or inhomogeneous effective media (e.g., [ 26 , 27 ]). Though some wave phenomena are not taken into account in the models incorporating homogenisation, these models are efficient and suitable for many applications [ 28 , 29 , 30 ]. If inhomogeneities or uncertainties are concentrated at the interfaces in the form of a distribution of interfacial micro-cracks or an interface roughness, the irregularities are situated randomly in the vicinity of interfaces.…”

Section: Introductionmentioning

confidence: 99%

Effective Boundary Conditions and Stochastic Crack Distribution for Modelling Guided Waves Scattering by a Partially Closed Interfacial Delamination in a Laminate

Golub

Doroshenko

2023

Materials

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Cohesive and adhesive bindings degrade during operation and maintenance even if contacting materials in a manufactured laminated structure are perfectly matched at the interfaces. Two modelling approaches for describing partially closed delaminations or imperfect contact zones, which often occurs at the interfaces, are examined and considered. To confirm the adequateness of the applicability of the effective spring boundary conditions for guided wave scattering by a finite length delamination, guided wave propagation through a damaged zone with a distribution of micro-cracks is compared with an equivalent cohesive zone model, where the spring stiffnesses for the effective boundary conditions are calculated using the properties of the considered crack distribution. Two kinds of local interfacial decohesion zones with an imperfect contact at the interfaces are considered: uniform partially closed delaminations and bridged cracks. The possibility of the employment of the effective spring boundary conditions to substitute a distribution of micro-cracks is analysed and discussed. Two algorithms of generation of a distribution of open micro-cracks providing characteristics equivalent to the effective boundary conditions are presented and examined. The influence of the characteristics of a delamination on wave characteristics (eigenfrequencies, eigenforms, transmission coefficient) is investigated for several kinds of partially closed delaminations.

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Computational homogenization of locally resonant acoustic metamaterial panels towards enriched continuum beam/shell structures

Cited by 21 publications

References 56 publications

The scaled boundary finite element method for dispersive wave propagation in higher‐order continua

The scaled boundary finite element method for dispersive wave propagation in higher‐order continua

A multi-bandgap metamaterial with multi-frequency resonators

Effective Boundary Conditions and Stochastic Crack Distribution for Modelling Guided Waves Scattering by a Partially Closed Interfacial Delamination in a Laminate

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