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The dynamic problem of the symmetric expansion of a cylindrical or spherical cavity in a granular medium is considered. The constitutive behaviour of the material is governed by a hypoplasticity relation for granular soils capable of describing both monotonic and cyclic deformation. The problem is solved numerically by a finite-difference technique. A nonreflecting boundary condition used at the outer boundary of the computational domain makes it possible to model a continuous multi-cycle loading on the cavity wall. The solution is illustrated by numerical examples. Possible geomechanical applications to the modelling of the vibratory compaction and penetration in granular soils are discussed.

Engineering materials are generally non-homogeneous, yet standard continuum descriptions of such materials are admissible, provided that the size of the non-homogeneities is much smaller than the characteristic length of the deformation pattern. If this is not the case, either the individual non-homogeneities have to be described explicitly or the range of applicability of the continuum concept is extended by including additional variables or degrees of freedom. In the paper the discrete nature of granular materials is modelled in the simplest possible way by means of finite-difference equations. The difference equations may be homogenised in two ways: the simplest approach is to replace the finite differences by the corresponding Taylor expansions. This leads to a Cosserat continuum theory. A more sophisticated strategy is to homogenise the equations by means of a discrete Fourier transformation. The result is a Kunin-type non-local theory. In the following these theories are analysed by considering a model consisting of independent periodic 1D chauns of solid spheres connected by shear translational and rotational springs. It is found that the Cosserat theory offers a healthy balance between accuracy and simplicity. Kunin’s integral homogenisation theory leads to a non-local Cosserat continuum description that yields an exact solution, but does not offer any real simplification in the solution of the model equations as compared to the original discrete system. The rotational degree of freedom affects the phenomenology of wave propagation considerably. When the rotation is suppressed, only one type of wave, a shear wave, exists. When the restriction on particle rotation is relaxed, the velocity of this wave decreases and another, high velocity wave arises.

The central problem of devising mathematical models of granular materials is how to define a granular medium as a continuum. This paper outlines the elements of a theory that could be incorporated in discrete models such as the Discrete-Element Method, without recourse to a continuum description. It is shown that familiar concepts from continuum mechanics such as stress and strain can be defined for interacting discrete quantities. Established concepts for constitutive equations can likewise be applied to discrete quantities. The key problem is how to define the constitutive response in terms of truncated strain measures that are a practical necessity for analysis of large granular systems.

A classical problem in metal plasticity is the compression of a block of material between rigid platens. The corresponding problem for a layer of granular material that conforms to the Coulomb-Mohr yield condition and the double-shearing theory for the velocity field has also been solved. A layer of granular material between rough rigid plates that is subjected to both compression and shearing forces is considered. Analytical solutions are obtained for the stress and velocity fields in the layer. The known solutions for steady simple shear and pure compression are recovered as special cases. Yield loads are determined for combined compression and shear in the case of Coulomb friction boundary conditions. Numerical results which describe the stress and velocity fields in terms of the normal and shear forces on the layer at yield are presented for the case in which the surfaces of the platens are perfectly rough. Post-yield behaviour is briefly considered.

The objective of this paper is to assess the predictive capability of different classes of extended plasticity theories (bounding surface plasticity, generalized plasticity and generalized tangential plasticity) in the modeling of incremental nonlinearity, which is one of the most striking features of the mechanical behavior of granular soils, occurring as a natural consequence of the particular nature of grain interactions at the microscale. To this end, the predictions of the various constitutive models considered are compared to the results of a series of Distinct Element simulations performed . In the comparison, extensive use is made of the concept of incremental strain-response envelope in order to assess the directional properties of the material response for a given initial state and stress history.

The incompressible plastic flow equations for a Drucker-Prager yield law and a flow rule are shown not to allow a steady single radial velocity component, for flows from a wedge-shaped hopper. The corresponding equations for two components of velocity are considered, using a series expansion of Kaza and Jackson, which connects asymptotically to Jenike’s radial solution. This asymptotic solution gives a poor model of mass flows about the orifice, and an improvement is obtained by considering the pressure variation along the axis of the wedge, but using the angular variations determined by the power-series method. Numerical difficulties occurred for certain parameter values, when solving the two-point boundary-value problem resulting from the asymptotic series method. The region of this parametric sensitivity is associated with an internal maximum in the pressure field, whose appearance tends to offer a conservative estimate for the mass-funnel flow transition.

This paper presents a numerical study of the micro-and macro-dynamic behavior of the unsteady-state granular flow in a cylindrical hopper with flat bottom by means of a modifed discrete-element method (DEM) and an averaging method. The results show that the trends of the distributions of the microscopic properties such as the velocity and forces, and the macroscopic properties such as the velocity, mass density, stress and couple stress of the unsteady-state hopper flow are similar to those of steady-state hopper flow, and do not change much with the discharge of particles. However, the magnitudes of the macroscopic properties in different regions have different rates of variation. In particular, the magnitudes of the two normal stresses vary little with time in the orifice region, but decrease in other regions. The magnitude of the shear stress decreases with time when far from the bottom wall and central axis of the hopper. The results also indicate that DEM can capture the key features of the granular flow, and facilitated with a proper averaging method, can also generate information helpful to the test and development of an appropriate continuum model for granular flow.