Discrete dislocation plasticity analysis of size effects in single crystals

The effect of size and slip system configuration on the tensile stress-strain response of micron-sized planar crystals as obtained from discrete dislocation plasticity simulations is presented. The crystals are oriented for either single or symmetric double slip. With the rotation of the tensile axis unconstrained, there is a strong size dependence, with the flow strength increasing with decreasing specimen size. Below a certain specimen size, the flow strength of the crystals is set by the nucleation strength of the initially present Frank-Read sources. The main features of the size dependence are the same for both the single and symmetric double slip configurations.

Discrete element calculations of the impact of a sand column against rigid structures

Discrete particle simulations of column of an aggregate of identical particles impacting a rigid, fixed target and a rigid, movable target are presented with the aim to understand the interaction of an aggregate of particles upon a structure. In most cases the column of particles is constrained against lateral expansion. The pressure exerted by the particles upon the fixed target (and the momentum transferred) is independent of the co-efficient of restitution and friction co-efficient between the particles but are strongly dependent upon the relative density of the particles in the column. There is a mild dependence on the contact stiffness between the particles which controls the elastic deformation of the densified aggregate of particles. In contrast, the momentum transfer to a movable target is strongly sensitive to the mass ratio of column to target. The impact event can be viewed as an inelastic collision between the sand column and the target with an effective co-efficient of restitution between 0 and 0.35 depending upon the relative density of the column. We present a foam analogy where impact of the aggregate of particles can be modelled by the impact of an equivalent foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally and yet give predictions to within 5% of the full discrete particle calculations. They also suggest that "model" materials can be used to simulate the loading by an aggregate of particles within a laboratory setting. © 2012 Elsevier Ltd. All rights reserved.

Stress-strain response of hydrate-bearing sands: Numerical study using discrete element method simulations

Gas hydrate is a crystalline solid found within marine and subpermafrost sediments. While the presence of hydrates can have a profound effect on sediment properties, the stress-strain behavior of hydrate-bearing sediments is poorly understood due to inherent limitations in laboratory testing. In this study, we use numerical simulations to improve our understanding of the mechanical behavior of hydrate-bearing sands. The hydrate mass is simulated as either small randomly distributed bonded grains or as "ripened hydrate" forming patchy saturation, whereby sediment clusters with 100% pore-filled hydrate saturation are distributed within a hydrate-free sediment. Simulation results reveal that reduced sand porosity and higher hydrate saturation cause an increase in stiffness, strength, and dilative tendency, and the critical state line shifts toward higher void ratio and higher shear strength. In particular, the critical state friction angle increases in sands with patchy saturation, while the apparent cohesion is affected the most when the hydrate mass is distributed in pores. Sediments with patchy hydrate distribution exhibit a slightly lower strength than sediments with randomly distributed hydrate. Finally, hydrate dissociation under drained conditions leads to volume contraction and/or stress relaxation, and pronounced shear strains can develop if the hydrate-bearing sand is subjected to deviatoric loading during dissociation.

Centrifuge and discrete element modelling of tunnelling effects on pipelines

The paper presents centrifuge test data of the problem of tunnelling effects on buried pipelines and compares them to predictions made using DEM simulations. The paper focuses on the examination of pipeline bending moments, their distribution along the pipe, and their development with tunnel volume loss. Centrifuge results are obtained by PIV analysis and compared to results obtained using the DEM model. The DEM model was built to replicate the centrifuge model as closely as possible and included numerical features formulated specially for this task, such as structural elements to replicate the tunnel and pipeline. Results are extremely encouraging, with deviations between DEM and centrifuge test bending moment results being very small. © 2010 Taylor & Francis Group, London.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Modeling fatigue crack growth in crystalline solids with discrete dislocation plasticity

Analyses of crack growth under cyclic loading conditions are discussed where plastic flow arises from the motion of large numbers of discrete dislocations and the fracture properties are embedded in a cohesive surface constitutive relation. The formulation is the same as used to analyse crack growth under monotonic loading conditions, differing only in the remote loading being a cyclic function of time. Fatigue, i.e. crack growth in cyclic loading at a driving force for which the crack would have arrested under monotonic loading, emerges in the simulations as a consequence of the evolution of internal stresses associated with the irreversibility of the dislocation motion. A fatigue threshold, Paris law behaviour, striations, the accelerated growth of short cracks and the scaling with material properties are outcomes of the calculations. Results for single crystals and polycrystals will be discussed.

Continuous dynamical systems that realize discrete optimization on the hypercube

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0,1}n. The search is achieved by a gradient-like system in [0,1]n with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0,1}n. Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. © 2004 Elsevier B.V. All rights reserved.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.