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Title: Stochastic models of wavefront propagation in random granular media
Authors: Ostoja-Starzewski, Martin
Keywords: Granular materials
Markov processes
Diffusion processes
Random media
Stochastic analysis
Wave propagation
Publisher: Structures Laboratory (U.S.)
Series/Report no.: Contract Report;SL-92-5
Abstract: Abstract: Determination of the effects of material microscale randomness on wavefront propagation is the focus of this report. The study is set in the context of one-dimensional microstructures with material randomness, of high signal-to-noise ratio, being present in constitutive moduli and grain lengths. Two different, but related, categories of problems - transient waves in granular microstructures and acceleration wavefronts in nonlinear elastic/dissipative continua - are discussed. In the first category, special focus is placed on microstructures with nonlinear elastic grains and an extension to two- and three-dimensional wave propagation. In the second category, particular attention is given to the phenomenon of stochastic competition between dissipation and elastic nonlinearity in formation of a shock from an acceleration wave. Explicit formulas for critical inverse amplitudes are obtained and illustrated graphically for different cases of correlatedness between dissipation and elastic nonlinearity. Additionally. the problem of determination of random time to form a shock is discussed. The common thread of both problem categories studied here is the use of Markov diffusion processes in description of wave evolutions in one as well as two and three dimensions.
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