Shock waves in random viscoelastic media

Determining the effects of material spatial randomness on the evolution of shocks is the objective of this study. Considering a linear viscoelastic-type material, a very general class of random media is modeled by a three-component random vector field: the instantaneous relaxation function (E), its derivative (E′), and the mass density (ρ). The reason for considering the randomness of the said material coefficients is the fact that a wavefront’s length scale (thickness) is most likely smaller than the Representative Volume Element, thus contradicting a “separation of scales” condition tacitly assumed in deterministic continuum mechanics, even in the context of wavefront analyses. In effect, the wavefront is an object much more appropriately analyzed as a Statistical Volume Element and therefore to be treated via a stochastic dynamical system rather than a deterministic one. Various cases of the random vector field [E, E′, ρ] _x are examined: white versus correlated noises as well as the independence versus coupling of these random fields to the shock amplitude.