Ellipsoid Packing Structures on Freeform Surfaces

Designers always get good inspirations from fascinating geometric structures gifted by the nature. In the recent years, various computational design tools have been proposed to help generate cell packing structures on freeform surfaces, which consist of a packing of simple primitives, such as polygons, spheres, etc. In this work, we aim at computationally generating novel ellipsoid packing structures on freeform surfaces. We formulate the problem as a generalization of sphere packing structures in the sense that anisotropic ellipsoids are used instead of isotropic spheres to pack a given surface. This is done by defining an anisotropic metric based on local surface anisotropy encoded by principal curvatures and the corresponding directions. We propose an optimization framework that can optimize the shapes of individual ellipsoids and the spatial relation between neighboring ellipsoids to form a quality packing structure. A tailored anisotropic remeshing method is also employed to better initialize the optimization and ensure the quality of the result. Our framework is extensively evaluated by optimizing ellipsoid packing and generating appealing geometric structures on a variety of freeform surfaces

Modeling roll compaction mechanics with multi-particle finite element methods

Roll compaction is a mechanical processing technique implemented in a wide range of industries including pharmaceutical, food production, chemical, and mining. Due to the large scale and continuous nature of the process, optimization and mechanistic understanding is of great importance. In the past, experimental procedures, continuum models, and finite element methods have been applied in order to analyze the mechanics of roll compaction, and each study has experienced its own set of limitations in regards to its predictive capacity and practical application. The difficulties have primarily included the large number of input parameters and the complex behavior of particle interactions at the local level such as friction, cohesion, segregation, and deformation. A modern technique, Multi-Particle Finite Element Methods (MPFEM), is employed to offer new insights into the roll compaction process. A two-dimensional model is developed and used to simulate the mechanical response of individual particles during deformation. The effects of parameters such as friction, feed stress, roll speed, density, and velocity fields are observed and investigated at both the macro and particulate levels. Shear banding between the rolls and particle shape behavior are investigated and determined to be crucial factors in roll compaction analysis. The implementation of MPFEM is a new sophisticated tool for evaluating roll compaction and presents significant insight into an important mechanical process.M.S., Materials Science and Engineering -- Drexel University, 201

Framework for The Generation and Design of Naturally Functionally Graded Lattice Structures

Functionally Graded Lattice (FGL) Structures have shown improved performance over uniform lattice structures in different fields. Another form of functional grading can be seen in materials in nature, where the cellular structure can vary in both cell porosity and size. To distinguish between lattice structures that vary in porosity only and lattice structures that vary in both, we will refer to the latter in this research as Naturally Functionally Graded Lattice (NFGL) structures. Research into NFGL structures' performance against FGL structures in the literature is lacking. Furthermore, the current methods in the literature to generate these structures are severely limited and suffer from multiple drawbacks. This research aims to develop a framework, namely the NFGL Framework, to generate NFGL structures without the drawbacks that exist in current methods and to improve the performance of the generated structures using the NFGL Framework against existing FGL structures. The NFGL Framework uses a novel method to generate nodes for NFGL structures from using a developed simplified sphere packing algorithm to generate conformal NFGL structures in a deterministic and computationally efficient manner. Furthermore, the NFGL Framework can perform a similarity analysis using a modified Mean Structural Similarity (MSSIM) index to improve the performance of the generated NFGL structure. The generated structures using the NFGL Framework were tested against the existing methods and showed to overcome the drawbacks of these methods with improved performance and computational time. Furthermore, the generated NFGL structures were tested against FGL structures and the results showed a performance gain from the use of NFGL structures over FGL structures with a reduced computational cost.Ph.D

DIFFUSE-INTERFACE FIELD APPROACH TO MODELING SELF-ASSEMBLY OF HETEROGENEOUS COLLOIDAL SYSTEMS AND RELATED DIPOLE-DIPOLE INTERACTION PHENOMENA

Colloid self-assembly under external control is a new route to fabrication of advanced materials with novel microstructures and appealing functionalities. The kinetic processes of colloidal self-assembly have attracted great interests also because they are similar to many atomic level kinetic processes of materials. In the past decades, rapid technological progresses have been achieved on producing shape-anisotropic, patchy, core-shell structured particles and particles with electric/magnetic charges/dipoles, which greatly enriched the self-assembled structures. Multi-phase carrier liquids offer new route to controlling colloidal self-assembly. Therefore, heterogeneity is the essential characteristics of colloid system, while so far there still lacks a model that is able to efficiently incorporate these possible heterogeneities. This thesis is mainly devoted to development of a model and computational study on the complex colloid system through a diffuse-interface field approach (DIFA), recently developed by Wang et al. This meso-scale model is able to describe arbitrary particle shape and arbitrary charge/dipole distribution on the surface or body of particles. Within the framework of DIFA, a Gibbs-Duhem-type formula is introduced to treat Laplace pressure in multi-liquid-phase colloidal system and it obeys Young-Laplace equation. The model is thus capable to quantitatively study important capillarity related phenomena. Extensive computer simulations are performed to study the fundamental behavior of heterogeneous colloidal system. The role of Laplace pressure is revealed in determining the mechanical equilibrium of shape-anisotropic particles at fluid interfaces. In particular, it is found that the Laplace pressure plays a critical role in maintaining the stability of capillary bridges between close particles, which sheds light on a novel route to in situ firming compact but fragile colloidal microstructures via capillary bridges. Simulation results also show that competition between like-charge repulsion, dipole-dipole interaction and Brownian motion dictates the degree of aggregation of heterogeneously charged particles. Assembly and alignment of particles with magnetic dipoles under external field is studied. Finally, extended studies on the role of dipole-dipole interaction are performed for ferromagnetic and ferroelectric domain phenomena. The results reveal that the internal field generated by dipoles competes with external field to determine the dipole-domain evolution in ferroic materials

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

Multiscale Investigation of Random Heterogenous Media in Materials and Earth Sciences

This dissertation is concerned with three major areas pertaining to the characterization and analysis of heterogeneous materials. The first is focused on the modeling of heterogeneous materials with random microstructure and understanding their thermomechanical properties as well as developing a methodology for the multiscale thermoelastic analysis of random heterogeneous materials. Realistic random microstructures are generated for computational analyses using random morphology description functions. The simulated microstructures closely resemble actual micrographs of random heterogeneous materials. The simulated random microstructures are characterized using statistical techniques and their homogenized material properties computed using the asymptotic expansion homogenization method. The failure response of random media is investigated via a direct micromechanical failure analysis which utilizes stresses at the microstructural level coupled with appropriate phase material failure models to generate initial failure envelopes. The homogenized material properties and failure envelopes are employed to perform accurate coupled macroscale and microscale analyses of random heterogeneous material components. The second area addressed in this dissertation involves the transient multiscale analysis of two-phase functionally graded materials within the framework of linearized thermoelasticity. The two-phase material microstructures, which are created using a morphology description function, have smoothly varying microstructure morphologies that depend on the volume fractions of the constituent phases. The multiscale problem is analyzed using asymptotic expansion homogenization coupled with the finite element method. Model problems are studied to illustrate the versatility of the multiscale analysis procedure which incorporates a direct micromechanical failure analysis to accurately compute the factors of safety for functionally graded components. The last area of this dissertation is concerned with determining the role of heterogeneous rock fabric features in quartz/muscovite rich rocks on seismic wave speed anisotropy. The bulk elastic properties and corresponding wave velocities are calculated for synthetic heterogeneous rock microstructures with varying material and geometric features to investigate their influence on seismic wave speed anisotropy. The asymptotic expansion homogenization method is employed to calculate precise bulk stiffness tensors for representative rock volumes and the wave speed velocities are obtained from the Christoffel equation. The obtained results are also used to assess the performance of analytic homogenization schemes currently used in the geophysics community

Assessing the mechanical microstructure of shale by nanoindentation : the link between mineral composition and mechanical properties

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2008.Includes bibliographical references (leaves 335-351).Shale is a multi-phase, multi-scale sedimentary rock that makes up 75% of the earth's sedimentary basins and is especially critical in petroleum engineering applications. At macroscopic scales, shales possess a diverse set of possible compositions, resulting in a diverse set of mechanical properties. This thesis assesses microstructure and material invariant properties of shale as the link between engineering performance and composition. A comprehensive experimental microporomechanics approach, employing advanced experimental and analytical nanoindentation techniques, provides the basis for assessment of microstructure and material invariant properties. Nanoindentation experiments and analysis tools are designed to probe and infer the elastic and strength properties of the porous clay composite in shale. The results of this investigation show that properties of the porous clay composite scale with the clay packing density in the material, but otherwise do not depend on mineral composition. These scaling relationships are representative of a granular composite of spherical particles, and lead to identification of intrinsically anisotropic material invariant elastic properties and intrinsically isotropic material invariant hardness properties. The material invariant hardness represents a combination of cohesive and frictional behavior that is seen to scale with the average clay packing density in the sample. Nanoindentation results also provide evidence of packing density distributions that are analogous to pore size distributions.(cont.) These observations are combined to define a model of the elementary building block of shale. Exploring the physical origin of this building block suggests that it represents an agglomerated polycrystal group of individual clay minerals. Particles in the porous clay composite exhibit fractal packings, which suggest a quantitative link between contemporary theories about the origin of friction and the experimental scaling of friction in shale. The new understanding provided by this thesis represents a leap forward for predictive models of shale behavior. The model of the elementary building block can be used as a basis for micromechanical homogenization models which predict poroelastic properties and strength behavior of shale at the lab-bench scale based on only two volume fraction parameters. The success of these models validates the elementary building block model and illustrates its engineering significance.by Christoper P. Bobko.Ph.D

Aspects of mathematical biology : from self-organisation of the cytoskeleton to transport of migratory species

This thesis spans scales of mathematical biology, from single molecules to groups of organisms. We explore questions regarding the self-organisation of the cytoskeleton and the long distance migration of animals. Though disparate at first glance, both topics revolve around transport and self-organisation of biological particles. We first model the microtubule cytoskeleton: a self-organising dynamic scaffolding along which cellular components, e.g. proteins, are transported. Its organisation is crucial for correct cellular functions; for example, maintaining the correct distribution of E-cadherin (the epithelial cell adhesion protein) along the cell boundary to ensure tissue integrity. Using stochastic simulations, genetic manipulations of the Drosophila epithelial cells and a probabilistic model we show that microtubule cytoskeleton selforganisation principally depends on cell geometry and microtubule seed density and is robust at the tissue scale. We then extend this work. Specifically, we build and explore an analytical model and perform stochastic simulations to explain microtubule self-organisation in crowded cytoplasm, i.e. containing various highly anisotropic barriers. We consider Drosophila follicular epithelium cells, which contain actin cables throughout. We find that anisotropy in the cell interior leads to a significant increase in the number of microtubules pointing in the direction of the anisotropy. This allows us to deduce the type of interaction between microtubules and actin cables. We introduce a new measure of self-organisation of microtubules, the bundling factor, and use it to explore the persistent direction of transport created by microtubule bundles. A second research topic is subsequently discussed. Many animals navigate long distances for purposes including foraging or nesting. While often mysterious, various lines of research support the idea that navigation is aided by a combination of cues whose magnitudes change with distance from the target. Motivated by agent-based simulations from a study of green sea turtle migration, we construct an abstract model for taxis-based animal navigation. We investigate the key properties of various navigating cues and their impact on animal migration, and discuss how the starting location can affect the mean first passage time of a migratory journey