Description of local dilatancy and local rotation of granular assemblies by microstretch modeling

Abstract

a b s t r a c tThis study investigates the microstretch continuum modeling of granular assemblies while accounting for both the dilatant and rotational degrees of freedom of a macroelement. By introducing the solid volume fraction and the gyration radius of a granular system, the balance equations of the microstretch continuum are transformed into a new formulation of evolution equations comprising six variables: the solid volume fraction, the gyration radius, the velocity field, the averaged angular velocity, the rate of gyration radius, and the internal energy. The bulk microinertia density, the averaged angular velocity, and the microgyration tensor at a macroscopic point are obtained in terms of discrete physical quantities. The bulk part and the rotational part of the microgyration tensor are proposed as the two indices to measure the local dilatancy and local rotation of granular assemblies. It is demonstrated in the numerical simulation that the two indices can be used to identify the shear band evolution in a granular system under a biaxial compression.

Continua with partially constrained microstructure

“…In the study of the mechanics of a large number of discrete inelastic particles at relatively high concentrations and with interstices filled with a fluid of negligible mass (as it is the case of soil without cohesion, such as sand with rough surface grains, or of fluidized particulate beds), we must introduce two distinct features to describe the micro-motion: (a) the volume distribution function of the solid granular constituent ξ (firstly introduced in [45]), namely the volume fraction of the solid grains with values on the real interval (0,1) and correlated, in soil mechanics terminology, to the porosity n by the relation n = 1 − ξ (see, also, [37,44]); (b) the rotation of the rigid granules relative to each other, identified by a proper orthogonal tensor R not necessarily related to the macro-rotation R of the body itself (see, e.g., [1,21,39,51]). Point (a) is better understood if we introduce the proper mass density ρ m of a typical suspended grain in B, which corresponds to the mass density of the granule itself, and the fact that the fluid mass density is considered negligible compared to ρ m , then the bulk mass density ρ of the material element equals ρ m times the volume fraction ξ of the grains ρ = ρ m ξ.…”

Remarks on Constitutive Laws for Dry Granular Materials

“…ii) the quasi-static motion of the body admits only dilatation, or contraction, of the individual (compressible) grain and of the grains relative to one another as well as the rotation of the granule itself (see, also, [1,11]); therefore the continuum model can depict the granular material as a medium with constrained affine microstructure [17,10,5];…”

A general rotation averaging method for granular materials

“…The overall mechanical behaviors of granular materials can be reasonably well described by continuum approaches [3,9,11,22,23,29]. Since granular materials are discrete in nature, some attempts have been made to obtain the continuum properties by averaging methods [2,5,6,16,25,39], which are also referred as homogenization methods [7,19] or coarse grain methods [30,38].…”