Abstract
We show that a Markov property of disturbance propagation forms the basis for study of wavefront evolution in one-dimensional piecewise constant microstructures with randomness in constitutive moduli and grain lengths. A new general method of solution to transient wave problems in such microstructures combining the method of characteristics and Markov diffusion processes is developed. In this paper we give a diffusion approximation for the case of linear elastic grains, and use it to determine rules of propagation of wavefronts in the case of bilinear elastic grains. Both, soft and hard constitutive laws are investigated.
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