Isostaticity in Cosserat continuum

Under conditions of isostaticity in granular media, the contact forces for all particles are statically determinate and forces can be computed without recourse to deformation equations or constitutive relationships. Given that stresses represent spatial averages of inter-particle forces, the stress-equilibrium equations for the isostatic state form a hyperbolic system of partial differential equations that describe the internal stress state using only boundary tractions. In this paper, we consider a Cosserat medium and propose closure relationships in terms of stresses and couple stresses from observations of stress variations in the critical state regime from discrete element simulations and experiments on sand, even though the isostatic condition is only satisfied in an average sense. It is shown that the governing equations are hyperbolic, which can be solved using the method of characteristics. Examples of both analytic and numerical solutions are presented. These examples clearly demonstrate that stress chains (characteristic lines) form oblique angles with the assumed direction of the force chains.     

Percolating contact subnetworks on the edge of isostaticity

We search for a percolating, strong subnetwork of contacts in a quasi-statically deforming, frictional granular material. Of specific interest in this study is that subnetwork which contributes to the majority of the total deviator stress and is, or is on the edge of being, isostatic. We argue that a subnetwork derived from the minimal spanning trees of a graph—optimized to include as many elastic contacts as possible and which bear normal contact forces above a given threshold delivers such a network. Moreover adding the strong 3-force-cycles to the spanning tree introduces a level of redundancy required to achieve a network that is almost if not isostatic. Results are shown for assemblies of non-uniformly sized circular particles under biaxial compression, in two-dimensions: a discrete element (DEM) simulation of monotonic loading under constant confining pressure, and cyclic loading of photoelastic disks under constant volume.     

A comparison of the mediational properties of four adolescent smoking expectancy measures.

This prospective study compared the ability of 4 smoking expectancy measures to mediate the influence of peer, parent, and current smoking on adolescents' cigarette use 3 months later. No evidence for mediation was found when expectancies were operationalized as unidimensional subjective expected utility (SEU). multidimensional SEU, or unidimensional SEU decomposed into probability and desirability main effects and their interaction. Evidence for partial mediation was found for the decomposed multidimensional SEU measure. The results suggest that (a) peer and current cigarette use may influence future smoking indirectly through adolescents' probability estimates that smoking will control negative emotions and (b) the relationship between current and future smoking also may be mediated by adolescents' beliefs about the desirability of weight control. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Stabilized finite element method for viscoplastic flow: formulation with state variable evolution

A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady‐state metal‐forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well‐known instabilities, one due to the incompressibility constraint and one due to the convection‐type state variable equation. Both of these instabilities are handled by adding mesh‐dependent stabilization terms, which are functions of the Euler–Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton–Raphson implementation into an object‐oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non‐linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal‐forming problems show that the stabilized finite element method is effective and efficient for non‐linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd.     

Development of micromechanical models for granular media

Micromechanical analysis has the potential to resolve many of the deficiencies of constitutive equations of granular continua by incorporating information obtained from particle-scale measurements. The outstanding problem in applying micromechanics to granular media is the projection scheme to relate continuum variables to particle-scale variables. Within the confines of a projection scheme that assumes affine motion, contact laws based on binary interactions do not fully capture important instabilities. Specifically, these contact laws do not consider mesoscale mechanics related to particle group behaviour such as force chains commonly seen in granular media. The implications of this are discussed in this paper by comparison of two micromechanical constitutive models to particle data observed in computer simulations using the discrete element method (DEM). The first model, in which relative deformations between isolated particle pairs are projected from continuum strain, fails to deliver the observed behaviour. The second model accounts for the contact mechanics at the mesoscale (i.e. particle group behaviour) and, accordingly, involves a nonaffine projection scheme. In contrast with the first, the second model is shown to display strain softening behaviour related to dilatancy and produce realistic shear bands in finite element simulations of a biaxial test. Importantly, the evolution of microscale variables is correctly replicated. This paper is dedicated to Professor Ching S. Chang on the occasion of his 60th birthday.     

The AC Conductivity of Liquid-Phase-Sintered Silicon Carbide

Analysis of the AC conductivity, complex dielectric constant, and the resulting immittance spectra of liquid-phase-sintered silicon carbide (SiC) ceramics showed that for this system, the dominant experimental observations are due to a multicomponent grain-boundary phase and not due to SiC grains. This is confirmed by noting that the temperature dependence of the conductivity of the components, derived from the impedance spectra, is proportional to exp[−( T ₀/ T )^1/4] and not to exp[− C / T ]. The electrical properties of some of the grain boundaries are also found to be excitation voltage dependent. Combining the electrical results, which are also found to depend on the method of preparation and heat treatment, with a Rietveld analysis allows the composition of the grain boundaries of the models to be deduced.     

A characteristic length scale in confined elastic buckling of a force chain

We examine the confined elastic buckling of a single N-particle force chain. For a given set of material parameters, a characteristic load-carrying capacity is attained for a clearly defined range of force chain lengths N ≥ L*. The rotation and translation of particles along periodically located segments of the critical buckling mode, each of length L*, are on average consistent with those for particles inside the shear band. Preliminary results from postbuckling analysis show that the critical buckling mode is unstable and that buckling culminates in a localized response over one of these segments where observed shear band kinematics prevail. Thus, the localized buckling response is characterized by the rotation of a finite number of particles with a clearly defined length L*. For a wide range of material properties, L* is around eight particle diameters—the observed shear band thickness for many granular materials, most notably sand.     

Relation of family subsystems to adolescent depression: Implementing a new family assessment strategy.

A multitrait-multimethod (or more precisely, a multidyad-multiperspective) approach to family assessment is used to investigate the relation of conflict, cohesion, and expressiveness in family subsystems to depression in a sample of 107 high school students. Confirmatory factor analysis and structural equation modeling revealed that (1) mothers' reports tended to be more reliable and adolescents' reports tended to be less reliable than others; (2) substantial differences existed between family dyads, thus calling into question the utility of global family constructs; (3) effects of marital conflict and cohesion on adolescent depression were entirely mediated by the parent–adolescent relationships; (4) father–adolescent conflict and cohesion were more strongly related to adolescent depression than were mother–adolescent conflict and cohesion; and (5) expressiveness was unrelated to adolescent depression. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Peer-model attributes and children's achievement behaviors.

In two experiments, we investigated how attributes of peer models influenced achievement behaviors among children who had experienced difficulties learning mathematical skills in school. In Experiment 1, children (M?=?10.6 years) observed either a same- or opposite-sex peer model demonstrating rapid (mastery model) or gradual (coping model) acquisition of fraction skills. Observing a coping model led to higher self-efficacy, skill, and training performance. In Experiment 2, children (M?=?10.9 years) observed either one or three same-sex peer models demonstrating mastery or coping behaviors while solving fractions. Children in the single-coping-model, multiple-coping-model, and multiple-mastery-model conditions demonstrated higher self-efficacy, skill, and training performance, compared with subjects who observed a single mastery model. In both studies, children who observed coping models judged themselves more similar in competence to the models than did subjects who observed mastery models. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Attempted Synthesis of Bowl-Shaped Polycyclic Aromatic Hydrocarbons via Oxidative Electrocyclization. Products from the Dications of Dibenzo [g,p] chrysene,Tetrabenzo[5.5]fulvalene,and Diphenylmethylidenefluorene

Synthesis of diindeno[1,2,3,4-defg: 1′,2′,3′,4′-mnop]chrysene (1), a portion of the C₆₀ surface, was attempted through oxidative cyclization of tetrabenzo[5.5]fulvalene (2), dibenzo[gp]chrysene (3), and diphenylmethylidenefluorene (4) by SbF₅/SO₂CIF. Compounds 2 and 3 were oxidized to dications which then underwent a single cyclization to give precursors to 1. Compound 4 underwent two oxidative cyclizations to give a precursor to 1. AM1 calculations of the possible products from cyclization were consistent with preferential formation of the cyclized product with the lower ΔHf. Oxidative cyclization may offer a one-pot synthetic alternative for the preparation of unusual polycyclic aromatic hydrocarbons.