1,130 research outputs found
Node-to-segment and node-to-surface interface finite elements for fracture mechanics
The topologies of existing interface elements used to discretize cohesive
cracks are such that they can be used to compute the relative displacements
(displacement discontinuities) of two opposing segments (in 2D) or of two
opposing facets (in 3D) belonging to the opposite crack faces and enforce the
cohesive traction-separation relation. In the present work we propose a novel
type of interface element for fracture mechanics sharing some analogies with
the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact
elements. The displacement gap of a node belonging to the finite element
discretization of one crack face with respect to its projected point on the
opposite face is used to determine the cohesive tractions, the residual vector
and its consistent linearization for an implicit solution scheme. The following
advantages with respect to classical interface finite elements are
demonstrated: (i) non-matching finite element discretizations of the opposite
crack faces is possible; (ii) easy modelling of cohesive cracks with
non-propagating crack tips; (iii) the internal rotational equilibrium of the
interface element is assured. Detailed examples are provided to show the
usefulness of the proposed approach in nonlinear fracture mechanics problems.Comment: 37 pages, 17 figure
Phase behavior and morphology of multicomponent liquid mixtures
Multicomponent systems are ubiquitous in nature and industry. While the
physics of few-component liquid mixtures (i.e., binary and ternary ones) is
well-understood and routinely taught in undergraduate courses, the
thermodynamic and kinetic properties of -component mixtures with have
remained relatively unexplored. An example of such a mixture is provided by the
intracellular fluid, in which protein-rich droplets phase separate into
distinct membraneless organelles. In this work, we investigate equilibrium
phase behavior and morphology of -component liquid mixtures within the
Flory-Huggins theory of regular solutions. In order to determine the number of
coexisting phases and their compositions, we developed a new algorithm for
constructing complete phase diagrams, based on numerical convexification of the
discretized free energy landscape. Together with a Cahn-Hilliard approach for
kinetics, we employ this method to study mixtures with and
components. We report on both the coarsening behavior of such systems, as well
as the resulting morphologies in three spatial dimensions. We discuss how the
number of coexisting phases and their compositions can be extracted with
Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally,
we discuss how one can reverse engineer the interaction parameters and volume
fractions of components in order to achieve a range of desired packing
structures, such as nested `Russian dolls' and encapsulated Janus droplets.Comment: 16 pages, 11 figures + hyperlinks to 7 video
On the number of tetrahedra with minimum, unit, and distinct volumes in three-space
We formulate and give partial answers to several combinatorial problems on
volumes of simplices determined by points in 3-space, and in general in
dimensions. (i) The number of tetrahedra of minimum (nonzero) volume spanned by
points in \RR^3 is at most , and there are point sets
for which this number is . We also present an time
algorithm for reporting all tetrahedra of minimum nonzero volume, and thereby
extend an algorithm of Edelsbrunner, O'Rourke, and Seidel. In general, for
every k,d\in \NN, , the maximum number of -dimensional
simplices of minimum (nonzero) volume spanned by points in \RR^d is
. (ii) The number of unit-volume tetrahedra determined by
points in \RR^3 is , and there are point sets for which this
number is . (iii) For every d\in \NN, the minimum
number of distinct volumes of all full-dimensional simplices determined by
points in \RR^d, not all on a hyperplane, is .Comment: 19 pages, 3 figures, a preliminary version has appeard in proceedings
of the ACM-SIAM Symposium on Discrete Algorithms, 200
MaterialVis: Material visualization tool using direct volume and surface rendering techniques
Cataloged from PDF version of article.Visualization of the materials is an indispensable part of their structural analysis. We developed a visualization tool for amorphous as well as crystalline structures, called Material Vis. Unlike the existing tools, Material Vis represents material structures as a volume and a surface manifold, in addition to plain atomic coordinates. Both amorphous and crystalline structures exhibit topological features as well as various defects. Material Vis provides a wide range of functionality to visualize such topological structures and crystal defects interactively. Direct volume rendering techniques are used to visualize the volumetric features of materials, such as crystal defects, which are responsible for the distinct fingerprints of a specific sample. In addition, the tool provides surface visualization to extract hidden topological features within the material. Together with the rich set of parameters and options to control the visualization, Material Vis allows users to visualize various aspects of materials very efficiently as generated by modern analytical techniques such as the Atom Probe Tomography. (C) 2014 Elsevier Inc. All rights reserved
Direct volume rendering of unstructured tetrahedral meshes using CUDA and OpenMP
Cataloged from PDF version of article.Direct volume visualization is an important method in many areas, including computational fluid dynamics and medicine. Achieving interactive rates for direct volume rendering of large unstructured volumetric grids is a challenging problem, but parallelizing direct volume rendering algorithms can help achieve this goal. Using Compute Unified Device Architecture (CUDA), we propose a GPU-based volume rendering algorithm that itself is based on a cell projection-based ray-casting algorithm designed for CPU implementations. We also propose a multicore parallelized version of the cell-projection algorithm using OpenMP. In both algorithms, we favor image quality over rendering speed. Our algorithm has a low memory footprint, allowing us to render large datasets. Our algorithm supports progressive rendering. We compared the GPU implementation with the serial and multicore implementations. We observed significant speed-ups that, together with progressive rendering, enables reaching interactive rates for large datasets
One-sided smoothness-increasing accuracy-conserving filtering for enhanced streamline integration through discontinuous fields
The discontinuous Galerkin (DG) method continues to maintain heightened levels
of interest within the simulation community because of the discretization flexibility it
provides. One of the fundamental properties of the DG methodology and arguably its most
powerful property is the ability to combine high-order discretizations on an inter-element
level while allowing discontinuities between elements. This flexibility, however, generates
a plethora of difficulties when one attempts to use DG fields for feature extraction and visualization,
as most post-processing schemes are not designed for handling explicitly discontinuous
fields. This work introduces a new method of applying smoothness-increasing,
accuracy-conserving filtering on discontinuous Galerkin vector fields for the purpose of enhancing
streamline integration. The filtering discussed in this paper enhances the smoothness
of the field and eliminates the discontinuity between elements, thus resulting in more
accurate streamlines. Furthermore, as a means of minimizing the computational cost of the
method, the filtering is done in a one-dimensional manner along the streamline.United States. Army Research Office (Grant no. W911NF-05-1-0395)National Science Foundation (U.S.) (Career Award NSF-CCF0347791
Fast and Exact Fiber Surfaces for Tetrahedral Meshes
Isosurfaces are fundamental geometrical objects for the analysis and visualization of volumetric scalar fields. Recent work has generalized them to bivariate volumetric fields with fiber surfaces, the pre-image of polygons in range space. However, the existing algorithm for their computation is approximate, and is limited to closed polygons. Moreover, its runtime performance does not allow instantaneous updates of the fiber surfaces upon user edits of the polygons. Overall, these limitations prevent a reliable and interactive exploration of the space of fiber surfaces. This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes. It assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends. The algorithm also allows visualization of individual fibers on the output surface, better illustrating their relationship with data features in range space. To enable truly interactive exploration sessions, we further improve the runtime performance of this algorithm. In particular, we show that it is trivially parallelizable and that it scales nearly linearly with the number of cores. Further, we study acceleration data-structures both in geometrical domain and range space and we show how to generalize interval trees used in isosurface extraction to fiber surface extraction. Experiments demonstrate the superiority of our algorithm over previous work, both in terms of accuracy and running time, with up to two orders of magnitude speedups. This improvement enables interactive edits of range polygons with instantaneous updates of the fiber surface for exploration purpose. A VTK-based reference implementation is provided as additional material to reproduce our results
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Dislocation-Radiation Obstacle Interactions: Developing Improved Mechanical Property Constitutive Models
The objective of this program was to understand the interaction of dislocations with a wide range of obstacles commonly produced in materials under irradiation (dislocation loops, voids, helium bubbles, stacking fault tetrahedra and radiation-induced precipitates). The approach employed in this program combined multi-scale modeling and dynamic in-situ and static ex-situ transmission electron microscopy experiments
Unstructured Grid Generation Techniques and Software
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop
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