Effective Resonant Model and Simulations in the Time-Domain of Wave Scattering from a Periodic Row of Highly-Contrasted Inclusions

Touboul, M. C.; Pham, Kim; Maurel, Agnès; Marigo, Jean‐Jacques; Lombard, Bruno; Bellis, Cédric

doi:10.1007/s10659-020-09789-2

Cited by 17 publications

(22 citation statements)

References 24 publications

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“…The case of highly contrasted inclusions able to produce internal, low-frequency, resonances is more challenging. Already considered in the scalar, antiplane, case by Pham et al [26] and Touboul et al [27], it is difficult to anticipate how the effect of these resonances translates in two-or three-dimensional elasticity. From a practical point of view, the study of guided waves by such imperfect interfaces and their link with Rayleigh, Stoneley and Love waves in realistic configurations is of interest in a geophysical context.…”

Section: Discussionmentioning

confidence: 99%

Revisiting imperfect interface laws for two-dimensional elastodynamics

2021

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We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.

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Section: Discussionmentioning

confidence: 99%

Revisiting imperfect interface laws for two-dimensional elastodynamics

2021

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“…In the case of resonant meta-interfaces, an alternative approach was to obtain effective jump conditions by applying a suitable homogenization process [33,34]. Moreover, some studies on elastic wave propagation showed that when the interphase is located between two surrounding media with microstructure, inertial properties also play a pivotal role in the modeling of the equivalent interface [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Wave propagation across a functionally graded interphase between soft and hard solids: Insight from a dynamic surface elasticity model

Aghaei¹,

Bochud²,

Rosi³

et al. 2021

Journal of the Mechanics and Physics of Solids

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Joining soft to hard materials is a challenging problem in modern engineering applications.In order to alleviate stress concentrations at the interface between materials with such a mismatch in mechanical properties, the use of functionally graded interphases is becoming more widespread in the design of the new generation of engineered composite materials.However, current macroscale models that aim at mimicking the mechanical behavior of such complex systems generally fail in incorporating the impact of microstructural details across the interphase because of computational burden. In this paper we propose to replace the thin, but yet finite, functionally graded interphase by a zero-thickness interface. This is achieved by means of an original model developed in the framework of surface elasticity, which accounts for both the elastic and inertial behavior of the actual interphase. The performance of the proposed equivalent model is evaluated in the context of elastic wave propagation, by comparing the calculated reflection coefficient to that obtained using different baseline models. Numerical results show that our dynamic surface elasticity model provides an accurate approximation of the reference interphase model over a broad frequency range. We demonstrate application of this modeling approach for the characterization of the graded tissue system at the tendon-to-bone interphase, which fulfills the challenging task of integrating soft to hard tissues over a submillimeter-wide region.

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“…In elasticity, works on interface homogenization focused first on rows of non-resonant inclusions [9,28,8,27], and then on resonant inclusions [31,29,41]. In [31,41], two-scale asymptotic method has been combined with matched-asymptotic expansions to yield effective jump conditions, both in the frequency domain [31] and in the time domain [41]; in the latter case, the jump conditions turn out to be non-local. Second-order accuracy in terms of the small ratio k m h has been reached, where k m is the wavenumber in the background medium and h is the typical size of the inclusions.…”

Section: Introductionmentioning

confidence: 99%

“…As is usual in structural dynamics, a phenomenological model is therefore considered. In this framework, the results presented in [41,40] are modified and need to be re-examined on their main features: (i) effective jump conditions, (ii) energy balance, (iii) auxiliary fields, and (iv) discretization of the interfaces. These four points are addressed here.…”

Section: Introductionmentioning

confidence: 99%

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Damping in a row of locally-resonant inclusions: Dynamic homogenization and scattering of transient shear waves

2021

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The scattering of scalar waves by a periodic row of inclusions is theoretically and numerically investigated. The wavelength in the background medium is assumed to be much larger than the typical sizes of the inclusions. The latter are also much softer than the matrix, yielding localized resonances within the microstructure. Previous works in the inviscid case have concerned: (i) the derivation of effective resonant jump conditions, that are non local in time (Touboul et al., J. Elasticity, 2020); (ii) the introduction of auxiliary fields along the interface, providing a time-domain formulation of the scattering problem (Touboul et al., J. Comput. Phys., 2020). The present contribution extends the analysis to dissipative cases, which allows to be closer from real devices. The effective jump conditions with damping are obtained, both in the frequency domain and in the time domain. An exact plane-wave solution is proposed. A balance of energy is written, and new auxiliary fields are introduced. Practical implementation of the simulation methods is discussed. Then, numerical experiments are proposed to validate the auxiliary-field approach. The effect of dissipation is examined, and the relevance of the homogenized simulations in comparison with full-field simulations of transient waves is assessed. As an application, a numerical experiment of Coherent Perfect Absorption is finally proposed: at critical values of the attenuation parameter and close to the resonant frequencies, the waves impacting the dissipative resonant interface are fully absorbed.

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Effective Resonant Model and Simulations in the Time-Domain of Wave Scattering from a Periodic Row of Highly-Contrasted Inclusions

Cited by 17 publications

References 24 publications

Revisiting imperfect interface laws for two-dimensional elastodynamics

Revisiting imperfect interface laws for two-dimensional elastodynamics

Wave propagation across a functionally graded interphase between soft and hard solids: Insight from a dynamic surface elasticity model

Damping in a row of locally-resonant inclusions: Dynamic homogenization and scattering of transient shear waves

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