Mechanism of Deformation of Particulate Materials as Markov Process

Abstract

In this paper, the micrometric approach which can establish the constitutive relations of particulate materials such as sands is described. In this approach the motion of particles in particulate materials is assumed to be a Markov Process which is one of the well-known stochastic processes. This assumption is reasonable because the irregularities of the particles in both size and shape, and the complicated fabric of particulate materials are considered to prohibit the deterministic approach to the motion of individual particles in the particulate materials.First, the Markov Process is explained briefly and the basic equation of the Markov Process is derived. Secondly, the Markov Process is applied to the mechanical behaviors of particulate materials, and the concepts of potential berrier and potential slip plane are introduced in order to determine the coefficients in the basic equation of the Markov Process. Thirdly, the strain of particulate materials is derived by averaging the motion of particles. Finally, the stress-strain relationship obtained from the micrometric approach is compared with the result of the drained triaxial compression test on Toyoura Sand. It is shown that this approach is very valuable in order to analyse the various mechanical behaviors of particulate materials comprehensively.