Geometric structures in cellular solids span the spectrum from perfectly periodic to strictly random. Depending on the degree of disorder at the cellular-scale, the corresponding continuum-scale mechanical response ca...
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Geometric structures in cellular solids span the spectrum from perfectly periodic to strictly random. Depending on the degree of disorder at the cellular-scale, the corresponding continuum-scale mechanical response can admit instabilities or can remain stable for the entire range of compressive deformations. In the present work, the response of cellular materials to quasi-static uni-axial compression is investigated. The underlying geometric structures in these materials are allowed to range from highly ordered to highly disordered, and the corresponding transition from unstable to stable mechanical response is explored. A stochastic constitutive model is developed and used for this purpose. Model development begins with an established cellular-scale mechanical response description, but this cellular-scale model is generalized to accommodate finite strain. A continuum-scale constitutive model is established by averaging the cellular-scale model over an ensemble of foam cells, and stochastic variation in cellular-scale geometric structure and material properties is considered through the use of probability density functions for the associated model parameters. Results show that dispersity in geometric structure has little to no effect on the initial elastic properties of the cellular materials under investigation. For deformations occurring prior to any occurrence of instability, however, increasing dispersity is accompanied by decreasing stiffness, an increase in critical strain, and a decrease in the extent of localized deformation. Most notably, materials with the highest degrees of dispersity in their cellular structures exhibit mechanical response that remains stable for the entire range of compressive deformations, demonstrating a general stabilizing effect of dispersity in geometric structure on the continuum-scale mechanical response of cellular solids. (c) 2006 Elsevier Ltd. All rights reserved.
Grain crushing is one of the micromechanisms that governs the stress-strain behaviour of a granular material, and also its permeability by altering the grain size distribution. It is therefore advantageous to be able ...
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Grain crushing is one of the micromechanisms that governs the stress-strain behaviour of a granular material, and also its permeability by altering the grain size distribution. It is therefore advantageous to be able to predict the point of onset of crushing and to quantify the subsequent evolution of crushing. This paper uses the data of Discrete Element Method (DEM) simulations to inform a statistical model of granular crushing. Distributions of normalised contact forces are first obtained. If the statistical distribution of the crushing strength of the grains is then known, the onset of crushing within an assembly of grains should be predictable. Two different cases, one in which grain strength was statistically independent of grain size and one showing an arbitrary trend, were used to compare with DEM results and so confirm the validity of the statistical method. (c) 2007 Elsevier Ltd. All rights reserved.
A Bayesian probability density for an interpolating function is developed, and its desirable properties and practical potential are demonstrated. This density has an often needed but previously unachieved property, he...
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A Bayesian probability density for an interpolating function is developed, and its desirable properties and practical potential are demonstrated. This density has an often needed but previously unachieved property, here called cardinal interpolation, which ensures extrapolation to the density of the least-squares linear model. In particular, the mean of the cardinal interpolation density is a smooth function that intersects given (x, y) points and which extrapolates to their least-squares line, and the variance of this density is a smooth function that is zero at the point x values, that increases with distance from the nearest point x value, and that extrapolates to the well-known quadratic variance function for the least-squares line. The new cardinal interpolation density is developed for Gaussian radial basis interpolators using fully Bayesian methods that optimize interpolator smoothness. This optimization determines the basis function widths and yields an interpolating density that is non-Gaussian except for large magnitude x and which is therefore not the outcome of a Gaussian process. Further, new development shows that the salient property of extrapolation to the density of the least-squares linear model can be achieved for more general approximating (not just interpolating) functions.
We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be...
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We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes;1 day]. This observation is confirmed using eight distinct experimental data sets. It is at odds with the exponential decay implied by the most commonly used mobility models. In this paper, we study how this newly uncovered characteristic of human mobility impacts one class of forwarding algorithms previously proposed. We use a simplified model based on the renewal theory to study how the parameters of the distribution impact the performance in terms of the delivery delay of these algorithms. We make recommendations for the design of well-founded opportunistic forwarding algorithms in the context of human-carried devices.
We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be...
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We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes;1 day]. This observation is confirmed using eight distinct experimental data sets. It is at odds with the exponential decay implied by the most commonly used mobility models. In this paper, we study how this newly uncovered characteristic of human mobility impacts one class of forwarding algorithms previously proposed. We use a simplified model based on the renewal theory to study how the parameters of the distribution impact the performance in terms of the delivery delay of these algorithms. We make recommendations for the design of well-founded opportunistic forwarding algorithms in the context of human-carried devices.
An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length ...
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An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics is described by a universal (i.e., material independent) distribution. The latter directly derives from results obtained when modeling crack propagation as a depinning phenomenon. Crack arrest (or effective toughness) statistics appears to be fully characterized by two parameters.. namely, an asymptotic crack length (or macroscopic toughness) value and a power law size-dependent width. The experimental knowledge of the crack arrest statistics at one given scale thus gives access to its knowledge at all scales.
Stress evolution in a dense granular material is closely related to interactions of contacting particles. We investigate statistics related to particle interactions and the relationship between the averaged local rela...
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Stress evolution in a dense granular material is closely related to interactions of contacting particles. We investigate statistics related to particle interactions and the relationship between the averaged local relative motion and the macroscopic motion. The validity of the Voigt and Reuss assumptions is examined, and extensions to these assumptions are proposed. Effects of history in the dense granular material are investigated. Statistical samples used in this paper are obtained using three-dimensional numerical simulations of dense granular media under uniaxial cyclical compression. The results show that stresses arise mostly from normal forces between particles, and direct contributions from frictional tangential forces between particles are small. Tangential friction, however, significantly increases the particle contact time, and thus reduces the rate of contact breakage. The contact breakage rate is demonstrated to be a stress relaxation rate. Therefore, stress increases significantly with friction between particles as a result of prolonged relaxation time. (c) 2006 Elsevier Ltd. All rights reserved.
We presented two integrated solution schemes, sectional feature based strategy and surface feature based strategy, for modeling industrial components from point cloud to surfaces without using triangulation. For the s...
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We presented two integrated solution schemes, sectional feature based strategy and surface feature based strategy, for modeling industrial components from point cloud to surfaces without using triangulation. For the sectional feature based strategy, slicing, curve feature recognition and constrained fitting are introduced. This strategy emphasizes the advanced feature architecture patterns from 2D to 3D in reverse engineering. The surface feature based strategy relies on differential geometric attributes estimation and diverse feature extraction techniques. The methods and algorithms such as attributes estimation based on 4D Shepard surface, symmetry plane extraction, quadric surface recognition and optimization, extruded and rotational surface extraction, and blend feature extraction with probability and statistic theory are proposed. The reliable three-dimensional feature fabricated the valid substratum of B-rep model faultlessly. All the algorithms are implemented in RE-SOFT, a reverse engineering software developed by Zhejiang University. The proposed strategies can be used to capture the original design intention accurately and to complete the reverse modeling process conveniently. Typical industrial components are used to illustrate the validation of our feature-based strategies. (C) 2006 Elsevier Ltd. All rights reserved.
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