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Strain wave evolution equation for nonlinear propagation in materials with mesoscopic mechanical elements.

Vitalyi Gusev1, Vladislav Aleshin

  • 1Laboratoire de Physique de l'Etat Condensé, UPRESA-CNRS 6087, Faculté des Sciences, Ecole Nationale Supérieure d'Ingénieurs du Mans, Université du Maine, 72085 Le Mans, France.

The Journal of the Acoustical Society of America
|January 2, 2003
PubMed
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This study analyzes nonlinear wave propagation in materials, revealing a transition from self-induced absorption to transparency based on wave amplitude. This finding impacts understanding of elastic wave behavior in complex material distributions.

Area of Science:

  • Materials Science
  • Solid Mechanics
  • Nonlinear Dynamics

Background:

  • Nonlinear wave propagation in materials is complex due to variations in mesoscopic element distributions.
  • The Preisach-Mayergoyz space describes hysteretic behavior in materials, with element distribution scales being critical.
  • Understanding wave behavior at high amplitudes is crucial for material diagnostics.

Purpose of the Study:

  • To analyze nonlinear wave propagation in materials with specific distribution functions.
  • To develop an evolution equation accounting for element distribution localization near the Preisach-Mayergoyz space diagonal.
  • To model elastic wave propagation with large strain amplitudes.

Main Methods:

  • Analysis of nonlinear wave propagation in materials.

Related Experiment Videos

  • Development of an evolution equation for strain waves.
  • Incorporation of element distribution localization near the Preisach-Mayergoyz space diagonal.
  • Analytical solutions to predict wave behavior.

    • Main Results:

    • A novel evolution equation for strain waves is proposed.
    • The equation models wave propagation with amplitudes exceeding characteristic localization scales.
    • Analytical solutions predict a non-monotonic dependence of wave absorption on amplitude.
    • A transition from self-induced absorption (small amplitudes) to self-induced transparency (high amplitudes) is identified.

    Conclusions:

    • The developed theory accurately models nonlinear elastic wave propagation.
    • The findings explain amplitude-dependent absorption and transparency phenomena.
    • Potential applications include seismology, high-pressure acoustics, and material diagnostics.