Homogenization of Thin 3D Periodic Structures in the Time Domain – Effective Boundary and Jump Conditions

Maurel, Agnès; Pham, Kim; Marigo, Jean‐Jacques

doi:10.1002/9781119649182.ch4

Cited by 5 publications

(2 citation statements)

References 32 publications

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“…As the array thickness e = O ( h ) is of the same order of magnitude, it makes sense to account for its contribution too. Introduced in [23], enlarged formulations of the jump conditions has been shown to be stable, see also [24]. They are obtained by Taylor expansions of boldu0boldfalse(0+bold,x2bold,sans-seriftboldfalse) and σ0false(0+,x2,sans-seriftfalse).…”

Section: Asymptotic Analysismentioning

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: Asymptotic Analysismentioning

confidence: 99%

Revisiting imperfect interface laws for two-dimensional elastodynamics

2021

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“…The analysis of periodic metasurfaces using the homogenization theory became classical in electromagnetism [2,11,12,13,14], acoustics [15,16], elastodynamics [17,18] and water waves [19,20] and it results in effective jump (or "transition") conditions of the fields instead of their usual continuity relations (see Figure 1); the transition also involve effective parameters that may be known explicitly or given by the resolution of simple elementary static problems. In electromagnetism, the general structure of the jumps are given by the so-called Generalized Sheet Transition Conditions (GSTCs) and the effective parameters can be casted within tensors named surface susceptibility tensors.…”

Section: Introductionmentioning

confidence: 99%