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Nonlinear waves in solids with slow dynamics: an internal-variable model.

H Berjamin1, N Favrie2, B Lombard1

  • 1Aix-Marseille Université, CNRS, Centrale Marseille, LMA, 13284 Marseille, France.

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|June 8, 2017
PubMed
Summary

This study introduces a new 3D model for slow dynamics in heterogeneous solids, capturing sound speed reduction and hysteresis under dynamic loading. The thermodynamically admissible model accurately reflects experimental observations in materials like rocks and concrete.

Keywords:
dynamic acoustoelasticityhysteresisnon-destructive evaluationsoftening

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Area of Science:

  • Continuum mechanics
  • Solid mechanics
  • Materials science

Background:

  • Heterogeneous solids like rocks and concrete exhibit 'slow dynamics', where sound speed decreases with strain amplitude during dynamic loading.
  • Existing one-dimensional models for this phenomenon are not thermodynamically admissible.
  • Hysteresis is observed in the steady-state response of these materials.

Purpose of the Study:

  • To develop a three-dimensional, thermodynamically admissible model for slow dynamics in heterogeneous solids.
  • To incorporate an internal variable describing material softening and an expression for specific internal energy.
  • To derive a constitutive law from the Clausius-Duhem inequality and propose evolution equations for the internal variable.

Main Methods:

  • Derivation of a three-dimensional continuum model within the finite-strain theory.
  • Introduction of an internal variable for material softening and a specific internal energy function.
  • Application of the Clausius-Duhem inequality to deduce a mechanical constitutive law.
  • Proposal and selection of an evolution equation for the internal variable with one relaxation time.

Main Results:

  • A new, thermodynamically admissible, and dissipative (inelastic) continuum model for slow dynamics.
  • The model qualitatively reproduces key features of real experimental data for small uniaxial deformations.
  • The model successfully captures sound speed reduction and hysteresis phenomena.

Conclusions:

  • The developed 3D model provides a thermodynamically consistent framework for understanding slow dynamics in heterogeneous solids.
  • The model's ability to reproduce experimental results highlights its potential for analyzing materials like rocks and concrete.
  • This work advances the theoretical understanding of inelastic behavior and wave propagation in complex materials.