Stochastic dynamics of acceleration waves in random media

Martin Ostoja-Starzewski, Jerzy Trebicki

Research output: Contribution to journalArticlepeer-review


Determining the effects of material spatial randomness on the distance to form shocks from acceleration waves, x, in random media is the objective of the present study. A very general class of random media is modeled by two random fields-the dissipation (μ) and elastic nonlinearity (β). The reason for considering the randomness of said material coefficients is the fact that a wavefront's length scale is not necessarily greater than the representative volume element-a condition tacitly assumed in deterministic continuum mechanics. There are two entirely new aspects considered in the present study. One is the explicit consideration of μ and β as functions of four more fundamental material properties, and themselves random fields: the instantaneous modulus (G0), the dissipation coefficient ( G0 ), the instantaneous second-order tangent modulus ( over(E, ∼)0 ), the mass density in the reference state (ρR). The second new facet is the coupling of the four-component random field [ G0, G0, over(E, ∼)0, ρR ]x to the wavefront amplitude α, because as the amplitude grows, the wavefront gets thinner tending to a shock, and thus the material random heterogeneity shows up as a random field with ever stronger fluctuations. In effect, the wavefront is an object which is more appropriately analyzed as a statistical volume element, and therefore to be treated via a stochastic rather than a deterministic dynamical system.

Original languageEnglish (US)
Pages (from-to)840-848
Number of pages9
JournalMechanics of Materials
Issue number8-10
StatePublished - Aug 2006
Externally publishedYes


  • Random media
  • Stochastic mechanics
  • Waves in random media

ASJC Scopus subject areas

  • Materials Science(all)
  • Instrumentation
  • Mechanics of Materials


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