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Revisiting imperfect interface laws for two-dimensional elastodynamics.

Kim Pham1, Agnès Maurel2, Jean-Jacques Marigo3

  • 1IMSIA, CNRS, EDF, CEA, ENSTA Paris, Institut Polytechnique de Paris, 828 Bd des Maréchaux, 91732 Palaiseau, France.

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Summary
This summary is machine-generated.

This study models elastic wave interactions with imperfect interfaces using advanced asymptotic analysis. The derived effective model accurately predicts wave behavior, outperforming simplified spring models in most scenarios.

Keywords:
asymptotic analysiselastodynamicshigh-order homogenizationimperfect interfaceperiodic defectsvoid/crack

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Area of Science:

  • Solid Mechanics
  • Wave Propagation
  • Materials Science

Background:

  • Interaction of elastic waves with interfaces is crucial in materials science.
  • Imperfect interfaces, like those with periodic voids or cracks, significantly alter wave behavior.
  • Existing models often oversimplify interface complexities.

Purpose of the Study:

  • To develop an effective model for in-plane elastic wave interaction with imperfect interfaces.
  • To analyze the limitations of simplified spring models for such interactions.
  • To provide a robust framework for understanding wave phenomena at complex interfaces.

Main Methods:

  • High-order asymptotic analysis.
  • Two-scale homogenization and matched asymptotic techniques.
  • Derivation of jump conditions for displacements and stresses in 2D elasticity.

Main Results:

  • An effective model with novel jump conditions was derived.
  • Model stability is ensured by positive effective interfacial energy.
  • Massless-spring models are recovered in specific limits (small voids, collinear cracks).
  • Mass-spring models are validated only at normal incidence.

Conclusions:

  • The developed model offers a more accurate representation of elastic wave interaction with imperfect interfaces.
  • The study clarifies the applicability and limitations of various spring models.
  • This work provides a foundation for analyzing wave propagation in complex engineered materials.