Random fields and processes in mechanics of granular materials

This paper gives a review of newly developed stochastic methods for analysis of the effects of granular materials' geometric and physical randomness at the microscale on their response at the macroscale. Two problem areas are discussed: (i) determination of stochastic and deterministic constitutive laws for a wide class of granular materials; and (ii) wavefront propagation in random continuous and heterogeneous media. Techniques in both areas take advantage of results in mechanics of microstructures and methods of random processes and fields. Focus in the first area is on scale-dependence of stochastic constitutive laws of random microstructures and the relation of mechanics of granular materials to the mechanics of matrix-inclusion systems, homogenization and the stochastic finite element method. Focus in the second area is on modelling wavefronts' evolutions in one-dimensional media modelled by random processes with piecewise-constant and continuous realizations.