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Title: Plane wave propagation in random granular media
Authors: Ostoja-Starzewski, Martin.
Keywords: Granular materials
Markov processes
Random media
Stochastic analysis
Wave propagation
Diffusion processes
Elastic solids
Publisher: Structures Laboratory (U.S.)
Series/Report no.: Contract Report;SL-92-2
Abstract: Abstract: We show that a Markov property of disturbance propagation forms the basis for a study of wavefronts in graph representable microstructures. Stochastic Huygens' minor principle is developed to analyze wavefront propagation in 1-D, 2-D, and 3-D models of material microstructures. A diffusion approximation is obtained for microstructures with grains described by piecewise linear constitutive laws. A new general method of solution to transient wave problems in such microstructures is developed: The method uses solutions from deterministic problems as a reference basis for an analysis of field fluctuations and scatter in stochastic media. The wavefront is modeled as a random field in space-time governed by a Markovian propagator. Explicit formulas for random arrivals in space-time and random modulation of pulses are obtained from this diffusion approximation. The key coefficients appearing in these formulas are calculated in the dimensionless setting of a 1-D linear elastic setting for a wide range of statistics of material properties. Finally, a local averaging process is proposed to obtain various smoothing approximations of this random field.
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