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- W2023341363 abstract "We study the effects of material spatial randomness on the growth to shock or decay of acceleration waves. In the deterministic formulation, such waves are governed by a Bernoulli equation dα/dx =−μ (x)α+β(x)α2 in which the material coefficientsμ andβ represent the dissipation and elastic nonlinearity, respectively. In the case of a random microstructure, the wavefront sees the local details: it is a mesoscale window travelling through a random continuum. Upon a stochastic generalization of the Bernoulli equation, both coefficients become stationary random processes, and thecritical amplitudeαc as well as thedistance to form a shockx∞ become random variables. We study the character of these variables, especially as compared to the deterministic setting, for various cases of the random process: (i) one white noise; (ii) two independent white noises; (iii) two correlated Gaussian noises; and (iv) an Ornstein–Uhlenbeck process. Situations of fully positively, negatively or zero correlated noises in μ and β are investigated in detail. Particular attention is given to the determination of the average critical amplitude〈αc〉, equations for the evolution of the moments ofα, the probability of formation of a shock wave within a given distancex, and the average distance to form a shock wave. Specific comparisons of these quantities are made with reference to a homogeneous medium defined by the mean values of theμ,βx process." @default.
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- W2023341363 date "1999-07-08" @default.
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- W2023341363 title "On the growth and decay of acceleration waves in random media" @default.
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- W2023341363 doi "https://doi.org/10.1098/rspa.1999.0418" @default.
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