Wavefront propagation in a class of random microstructures—II. Non-Linear elastic grains

The propagation of stress pulses is studied in one-dimensional piecewise constant microstructures of grains with power-law elastic response, having randomness present in constitutive moduli and grain lengths. Materials of two types are being considered: all grains of either a soft or a hard type. First, a Markov process is established for evolution of forward propagating disturbances, with the main feature being the progressive curving and random diffusion of the characteristics. Next, a study is conducted of the sensitivity of loading and unloading shock waves, as well as of washing out of pulses, to the randomness in the medium. It is found that the curving of characteristics shifts the formation of a shock with respect to the classical homogeneous medium solutions, but the strength is always decreased due to the presence of backscattered waves.