H.W. Chandler

A plasticity theory without drucker's postulate, suitable for granular materials

Abstract A plasticity theory is introduced which starts with a dilatancy rule and a function of plastic strain rates which represents the energy dissipated during plastic deformation. Yield surfaces and flow rules are then derived using energy conservation and the theory of envelopes. This method allows valid plasticity theories to be derived for frictional materials, but gives results for non-frictional materials which are identical to those of the classical theories. A dissipation function which includes deformation by granule rearrangement and granule distortion is presented and used to obtain a range of yield surfaces and flow rules, which are similar to those used in the critical state theory of soil mechanics. The microstructural features which may control the governing parameters of the dissipation functions are discussed.

Homogeneous and localised deformation in granular materials: A mechanistic model

Abstract During the processing, transport or storage of granular materials it is important to be able to predict not only the bulk behaviour but also the likely damage sustained by the granules. In order to shed some light on this problem, this paper describes a mechanistic model which gives an insight into the way the granules respond when bulk granular materials are deformed. It extends the ideas of critical state soil mechanics by incorporating both local deformation at the granule contacts and rearrangement of the granules to account jointly for any bulk deformation. As illustrations, drained and undrained triaxial tests are simulated with axial symmetry and qualitative agreement with published experimental results is obtained. Some fully triaxial drained tests are also simulated in which a shear band is given the opportunity to appear. This allows the model to predict a failure surface similar to the Mohr-Coulomb criterion whilst using a yield surface with a circular cross-section on the plane of constant pressure. A maximum principle is provided for this model which can be used to obtain approximate solutions to boundary value problems.

On the elasticity and plasticity of dilatant granular materials

Abstract We present a model which simulates the response of a granular material (made up of non-plastic grains) to small cyclic shear strain. The model is based upon a dissipation function representing energy dissipated as plastic deformation and a quadratic dilatancy rule describing the volume response which produces kinematic hardening. Elastic deformation is included in the model through a function describing the rate at which it is stored as deformation occurs. Two sets of experimental data (one for a shear test, the other for a circular loading test) are used to evaluate the accuracy of the model. For the shear test, both the shear strain–shear stress curve and the shear strain–volume strain curve are reproduced well. In the circular loading test, the principal strain response and volume response are modelled realistically.

A variational principle for the compaction of granular materials

Abstract A maximum principle is introduced that enables approximate solutions to be found for boundary value problems involving plastic compaction. All that is required from the user is an adjustable stress field that obeys both equilibrium and the static boundary conditions, and an adjustable displacement field that obeys the kinematic boundary conditions. An approximate solution can then be found by adjusting the stress and displacement fields to obtain the maximum value of a volume integral by using standard optimisation methods. Two examples of its use are given: the compaction of a granular material around a cylindrical mandrel, and the compaction of granular material by its own weight in a deep parallel sided bin. The latter example demonstrates the validity of the maximum principle even when frictional boundary conditions are present.

On the Initial Stages of the Densification and Lithification of Sediments

This paper presents a model that can simulate early rock-forming processes, including the influence of the initial packing of the grains on the subsequent rearrangement that occurs as a consequence of pressure-induced grain damage. The paper is concerned with the behaviour of assemblies of loose grains and the mechanics of early lithification. Consider the concept of shear-induced negative dilatancy, where any shear deformation has a tendency to produce densification even at very low pressures. As shear deformation progresses, positive dilatancy starts to contribute and at the critical state the two effects balance. This concept is encapsulated within the mathematics of the model. The model building scheme is first outlined and demonstrated using a hard particle model. Then, the concept of ‘self cancelling shear deformations’ that contribute to the shear–volume coupling but not to the macroscopic shear deformation is explained. The structure of the hard particle model is modified to include low levels of damage at the grain contacts. A parameter that describes bonding between the grains and possible damage to those bonds is incorporated into a term that, depending on its magnitude, also accounts for frictional resistance between unbonded grains. This parameter has the potential to develop with time, increasing compressive stress, or in response to evolving chemical concentrations. Together these modifications allow densification in the short term, and the formation of sedimentary rocks in the long term, by pressure alone, to be simulated. Finally, simulations using the model are compared with experimental results on soils.