Homogenization of locally resonant interface for wave propagation Kim Pham ([email protected]) IMSIA, ENSTA ParisTech - CNRS - EDF - CEA, Universit Paris-Saclay, 828 Bd des Marchaux, 91732 Palaiseau, France

We present a homogenization model for a single row of locally resonant inclusions. The resonances, of the Mie type, result from a high contrast in the shear modulus between the inclusions and the elastic matrix. The presented homogenization model is based on a matched asymptotic expansion technique; it slightly differs from the classical homogenization, which applies for thick arrays with many rows of inclusions (and thick means large compared to the wavelength in the matrix). Instead of the effective bulk parameters found in the classical homogenization, we end up with interface parameters entering in jump conditions for the displacement and for the normal stress; among these parameters, one is frequency dependent and encapsulates the resonant behavior of the inclusions. Our homogenized model is validated by comparison with results of full wave calculations, see Fig. 1. It is shown to be efficient in the low frequency domain and accurately describes the effects of the losses in the soft inclusions. U num

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Figure 1: Scattering of an oblique plane incidental wave on the microstructural interface (Direct Numerical Simulation and Homogenized interface are separated by vertical dotted line). Depending on the frequency, a perfect transmission (Left) or a perfect reflection (Right) can be achieved.

Short Bio Kim Pham is assistant professor at ENSTA ParisTech in Mechanical Department. His research interest include Damage, Phase Transformation, Wave propagation in complex media, Variational formulation and Homogenization techniques.

References [1] K. Pham, A. Maurel, J.-J. Marigo, Two scale homogenization of a row of locally resonant inclusions - the case of anti-plane shear waves, JMPS, Volume 106, 2017, Pages 80-94.

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