Effects of the microstructure and density profiles on wave propagation across an interface with material properties

  • I. Scala
  • G. RosiEmail author
  • L. Placidi
  • V.-H. Nguyen
  • S. Naili
Original Article


The characterization of the interphase condition between two materials is current in mechanics. In general, its modeling is achieved by considering an interface with only purely elastic properties. In this paper, following previous works, also inertial interface properties are taken into account. For sufficiently low-frequency regime, we investigate two density profiles (affine and quadratic), for the interphase. Moreover, the interface and the interphase are placed between two solids with different characteristics. The first one is non-dispersive, while for the second one three cases are considered: (a) solid without microstructure, i.e., a Cauchy continuum, (b) solid with microstructure characterized by normal dispersion, i.e., a strain gradient continuum, and (c) by anomalous dispersion. The reflection coefficients are plotted for each case. These results are evaluated with respect to a benchmark finite elements simulation of the finite heterogeneous interphase, and the error is discussed. It is shown that the effects of microstructure can be appreciated at higher frequencies and that the proposed model results to be accurate.


Density profiles Interface Interphase Reflection coefficient Strain gradient Wave propagation 


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The authors thank the Laboratoire International Associé Coss&Vita for the financial support via “Fédération Francilienne de Mécanique, CNRS FR2609.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS 61Université Paris-EstCréteil CedexFrance
  2. 2.Faculty of EngineeringInternational Telematic University UninettunoRomeItaly

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