Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties

The shape of irregular particles has significant influence on micro- and macro-scopic behavior of granular systems. This paper presents a combined 3D thinning and greedy set-covering algorithm to approximate realistic particles with a clump of overlapping spheres for discrete element method (DEM) simulations. First, the particle medial surface (or surface skeleton), from which all candidate (maximal inscribed) spheres can be generated, is computed by the topological 3D thinning. Then, the clump generation procedure is converted into a greedy set-covering (SCP) problem. To correct the mass distribution due to highly overlapped spheres inside the clump, linear programming (LP) is used to adjust the density of each component sphere, such that the aggregate properties mass, center of mass and inertia tensor are identical or close enough to the prototypical particle. In order to find the optimal approximation accuracy (volume coverage: ratio of clump's volume to the original particle's volume), particle flow of 3 different shapes in a rotating drum are conducted. It was observed that the dynamic angle of repose starts to converge for all particle shapes at 85% volume coverage (spheres per clump < 30), which implies the possible optimal resolution to capture the mechanical behavior of the system.Comment: 34 pages, 13 figure

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Systems Issues in Solid Freeform Fabrication

This paper is concerned with the systems aspects of the Solid Freeform Fabrication (SFF) technology, i.e., the issues that deal with getting an external geometric CAD model to automatically control the physical layering fabrication process as directly as possible, regardless ofthe source of the model. The general systems issues are described, the state of systems research is given, and open research questions are posed.Mechanical Engineerin

Finite average lengths in critical loop models

A relation between the average length of loops and their free energy is obtained for a variety of O(n)-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number) averaged loop length L stays finite for all non-zero fugacities n, and in particular it does not diverge upon entering the critical regime n -> 2+. Fully packed loop (FPL) models with n=2 seem to obey the simple relation L = 3 L_min, where L_min is the smallest loop length allowed by the underlying lattice. We demonstrate this analytically for the FPL model on the honeycomb lattice and for the 4-state Potts model on the square lattice, and based on numerical estimates obtained from a transfer matrix method we conjecture that this is also true for the two-flavour FPL model on the square lattice. We present in addition numerical results for the average loop length on the three critical branches (compact, dense and dilute) of the O(n) model on the honeycomb lattice, and discuss the limit n -> 0. Contact is made with the predictions for the distribution of loop lengths obtained by conformal invariance methods.Comment: 20 pages of LaTeX including 3 figure

Using polyhedral models to automatically sketch idealized geometry for structural analysis

Simplification of polyhedral models, which may incorporate large numbers of faces and nodes, is often required to reduce their amount of data, to allow their efficient manipulation, and to speed up computation. Such a simplification process must be adapted to the use of the resulting polyhedral model. Several applications require simplified shapes which have the same topology as the original model (e.g. reverse engineering, medical applications, etc.). Nevertheless, in the fields of structural analysis and computer visualization, for example, several adaptations and idealizations of the initial geometry are often necessary. To this end, within this paper a new approach is proposed to simplify an initial manifold or non-manifold polyhedral model with respect to bounded errors specified by the user, or set up, for example, from a preliminary F.E. analysis. The topological changes which may occur during a simplification because of the bounded error (or tolerance) values specified are performed using specific curvature and topological criteria and operators. Moreover, topological changes, whether or not they kept the manifold of the object, are managed simultaneously with the geometric operations of the simplification process

Coarse-to-fine skeleton extraction for high resolution 3D meshes

This paper presents a novel algorithm for medial surfaces extraction that is based on the density-corrected Hamiltonian analysis of Torsello and Hancock [1]. In order to cope with the exponential growth of the number of voxels, we compute a first coarse discretization of the mesh which is iteratively refined until a desired resolution is achieved. The refinement criterion relies on the analysis of the momentum field, where only the voxels with a suitable value of the divergence are exploded to a lower level of the hierarchy. In order to compensate for the discretization errors incurred at the coarser levels, a dilation procedure is added at the end of each iteration. Finally we design a simple alignment procedure to correct the displacement of the extracted skeleton with respect to the true underlying medial surface. We evaluate the proposed approach with an extensive series of qualitative and quantitative experiments