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Mesoscopic dynamics of microcracks

Van1, Papenfuss, Muschik

  • 1Department of Chemical Physics, Technical University of Budapest, Budafoki ut 8, 1521 Budapest, Hungary and Institut fur Mechanik, Institut fur Theoretische Physik, Technische Universitat Berlin, Strasse des 17. Juni, 10623 Berlin, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|December 2, 2000
PubMed
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This study applies mesoscopic concepts to model microcracks, deriving directional balances and macroscopic equations for cracked materials. It introduces dynamic equations for fabric tensors, enhancing our understanding of material behavior under stress.

Area of Science:

  • Continuum Mechanics
  • Materials Science
  • Solid Mechanics
  • Fracture Mechanics

Background:

  • Microcracks significantly influence material properties and failure mechanisms.
  • Existing macroscopic models often lack detailed microstructural considerations.
  • Mesoscopic approaches offer a bridge between microscopic crack behavior and macroscopic material response.

Purpose of the Study:

  • To develop a mesoscopic framework for describing microcracked continua.
  • To derive macroscopic balance equations from mesoscopic principles.
  • To establish dynamic equations for fabric tensors characterizing microcrack orientation.

Main Methods:

  • Application of mesoscopic concept to balance equations (mass, momentum, angular momentum, energy).

Related Experiment Videos

  • Averaging techniques applied to crack length and distribution functions.
  • Multipole moment expansion of orientational crack distribution for fabric tensor derivation.

    • Main Results:

    • Derivation of mesoscopic directional balances for conserved quantities.
    • Development of macroscopic balance equations for microcracked continua through successive averaging.
    • Formulation of dynamic equations for fabric tensors of varying orders, exemplified with Griffith cracks.

    Conclusions:

    • The mesoscopic approach provides a rigorous method for deriving macroscopic behavior from microcrack characteristics.
    • Fabric tensors offer a powerful tool for representing the anisotropic effects of microcracks.
    • Understanding the role of physical assumptions is crucial for accurate microcrack modeling.