SUMMARYThe discrete element method (DEM) is developed in this study as a general and robust technique for unified two-dimensional modelling of the mechanical behaviour of solid and particulate materials, including the transition from solid phase to particulate phase. Inter-element parameters (contact stiffnesses and failure criteria) are theoretically established as functions of element size and commonly accepted material parameters including Young's modulus, Poisson's ratio, ultimate tensile strength, and fracture toughness. A main feature of such an approach is that it promises to provide convergence with refinement of a DEM discretization. Regarding contact failure, an energy criterion based on the material's ultimate tensile strength and fracture toughness is developed to limit the maximum contact forces and inter-element relative displacement. This paper also addresses the issue of numerical stability in DEM computations and provides a theoretical method for the determination of a stable time-step. The method developed herein is validated by modelling several test problems having analytic solutions and results show that indeed convergence is obtained. Moreover, a very good agreement with the theoretical results is obtained in both elastic behaviour and fracture. An example application of the method to high-speed penetration of a concrete beam is also given.

SUMMARYA physically motivated constitutive law for the behaviour of geologic discontinuities with dilatancy and contact surface degradation (damage) is presented. In the formulation of the law, the paper distinguishes between macroscopic and microscopic features of the contact surface. Through macroscopic considerations, an incremental constitutive law is derived which is applicable to a large class of contact-friction problems. By idealizing the microstructure to consist of interlocking asperity surfaces, the constitutive equations are specialized for the description of rock joints including effects such as dilatancy, asperity surface degradation and bulking. Several examples are considered demonstrating the law's behaviour and agreement with experimental data. The incremental form of the equations that are derived are amenable to implementation in numerical procedures such as finite element and discrete element (rigid block) computer programs.

Chiral three‐dimensional isotropic cubic lattices with rigid cubical nodules and multiple deformable ribs are developed and analyzed via finite element analysis. The lattices exhibit geometry‐dependent Poisson's ratio that can be tuned to negative values. Poisson's ratio decreases from positive to negative values as the number of cells increases. Isotropy is obtained by adjustment of aspect ratio. The lattices exhibit significant size effects. Such a phenomenon cannot occur in a classical elastic continuum but it can occur in a Cosserat solid.

Lattices of controlled thermal expansion are presented based on planar chiral lattice structure with Poisson's ratio approaching −1. Thermal expansion values can be arbitrarily large positive or negative. A lattice was fabricated from bimetallic strips and the properties analyzed and studied experimentally. The effective thermal expansion coefficient of the lattice is about α=−3.5×10−4K−1. This is much larger in magnitude than that of constituent metals. Nodes were observed to rotate as temperature was changed corresponding to a Cosserat thermoelastic solid.

Chiral three-dimensional cubic lattices are developed with rigid cubical nodules and analyzed via finite element analysis. The lattices exhibit geometry dependent Poisson's ratio that can be tuned to negative values. Poisson's ratio tends to zero as the cubes become further apart. The lattices exhibit stretch-twist coupling. Such coupling cannot occur in a classical elastic continuum but it can occur in a chiral Cosserat solid.