A relative gradient theory for layered materials

It is possible to remedy certain difficulties with the description of short wave length phenomena and interfacial slip in standard models of a laminated material by considering the bending stiffness of the layers. If the couple or moment stresses are assumed to be proportional to the relative deformation gradient, then the bending effect disappears for vanishing interface slip, and the model correctly reduces to an isotropic standard continuum. In earlier Cosserat-type models this was not the case. Laminated materials of the kind considered here occur naturally as layered rock, or at a different scale, in synthetic layered materials and composites. Similarities to the situation in regular dislocation structures with couple stresses, also make these ideas relevant to single slip in crystalline materials. Application of the theory to a one-dimensional model for layered beams demonstrates agreement with exact results at the extremes of zero and infinite interface stiffness. Moreover, comparison with finite element calculations confirm the accuracy of the prediction for intermediate interfacial stiffness.

General strain theory, situational anger, and social networks: An assessment of conditioning influences

Using a random sample of university students to test general strain theory (GST), this study expanded on previous tests of strain theory in two ways. First, situational anger was measured, a construct that had not been used thus far in assessments of general strain. In addition, this research examined the role of social support networks as a conditioning influence on the effects of strain and anger on intentions to commit three types of criminal behavior (serious assault, shoplifting, and driving under the influence of alcohol [DUI]). The results provided mixed support for GST. While the link between anger and crime was confirmed, the nature of that relationship in some cases ran counter to the theory. Moreover, the evidence indicated that the role of social support networks was complex, and varied as a conditioning influence on intentions to engage in criminal activities. (C) 2001 Elsevier Science Ltd. All rights reserved.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Comparison of beam theory and finite-element analysis with in vivo bone strain data from the alligator cranium

The mechanical behavior of the vertebrate skull is often modeled using free-body analysis of simple geometric structures and, more recently, finite-element (FE) analysis. In this study, we compare experimentally collected in vivo bone strain orientations and magnitudes from the cranium of the American alligator with those extrapolated from a beam model and extracted from an FE model. The strain magnitudes predicted from beam and FE skull models bear little similarity to relative and absolute strain magnitudes recorded during in vivo biting experiments. However, quantitative differences between principal strain orientations extracted from the FE skull model and recorded during the in vivo experiments were smaller, and both generally matched expectations from the beam model. The differences in strain magnitude between the data sets may be attributable to the level of resolution of the models, the material properties used in the FE model, and the loading conditions (i.e., external forces and constraints). This study indicates that FE models and modeling of skulls as simple engineering structures may give a preliminary idea of how these structures are loaded, but whenever possible, modeling results should be verified with either in vitro or preferably in vivo testing, especially if precise knowledge of strain magnitudes is desired. (c) 2005 Wiley-Liss, Inc.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

The crack tip strain field of AISI 4340 - Part II - Experimental measurements

Crack tip strain maps have been measured for AISI 4340 high strength steel. No significant creep was observed. The measured values of CTOD were greater than expected from the HRR model. Crack tip branching was observed in every experiment. The direction of crack branching was in the same direction as a major ridge'' of epsilon(yy) strain, which in turn was in the same direction as predicted by the HRR model. Furthermore, the measured magnitudes of the epsilon(y)y strain in this same direction were in general greater than the values predicted by the HRR model. This indicates more plasticity in the crack tip region than expected from the HRR model. This greater plasticity could be related to the larger than expected CTOD values. The following discrepancies between the measured strain fields for AISI 4340 and the HRR predictions are noteworthy: (1) The crack branching. (2) Values of CTOD significantly higher than predicted by HRR. (3) The major ridge'' of epsilon(yy) strain an angle of about 60 degrees with the direction of overall propagation of the fatigue precrack, in which the measured magnitudes of the epsilon(yy) strain were greater than the values predicted by the HRR model. (4) Asymmetric shape of the plastic zone as measured by the epsilon(yy) strain. (5) Values of shear strain gamma(xy) significantly higher than predicted by the HRR model. (C) 1999 Kluwer Academic Publishers.

The crack tip strain field of AISI 4340 - Part III - Hydrogen influence

This paper studied the influence of hydrogen and water vapour environments on the plastic behaviour in the vicinity of the crack tip for AISI 4340. Hydrogen and water vapour (at a pressure of 15 Torr) significantly increased the crack tip opening displacement. The crack tip strain distribution in 15 Torr hydrogen was significantly different to that measured in vacuum. In the presence of sufficient hydrogen, the plastic zone was larger, was elongated in the direction of crack propagation and moreover there was significant creep. These observations support the hydrogen enhanced localised plasticity model for hydrogen embrittlement in this steel. The strain distribution in the presence of water vapour also suggests that SCC in AISI 4340 occurs via the hydrogen enhanced localised plasticity mechanism. (C) 1999 Kluwer Academic Publishers.

Apparent strain localization and shear wave dispersion in elastic fault gouge with microrotations

Shear deformation of fault gouge or other particulate materials often results in observed strain localization, or more precisely, the localization of measured deformation gradients. In conventional elastic materials the strain localization cannot take place therefore this phenomenon is attributed to special types of non-elastic constitutive behaviour. For particulate materials however the Cosserat continuum which takes care of microrotations independent of displacements is a more appropriate model. In elastic Cosserat continuum the localization in displacement gradients is possible under some combinations of the generalized Cosserat elastic moduli. The same combinations of parameters also correspond to a considerable dispersion in shear wave propagation which can be used for independent experimental verification of the proposed mechanism of apparent strain localization in fault gouge.

A social identity theory of leadership

A social identity theory of leadership is described that views leadership as a group process generated by social categorization and prototype-based depersonalization processes associated with social identity. Group identification, as self-categorization, constructs an intragroup prototypicality gradient that invests the most prototypical member with the appearance of having influence; the appearance arises because members cognitively and behaviorally conform to the prototype. The appearance of influence becomes a reality through depersonalized social attraction processes that make followers agree and comply with the leader's ideas and suggestions. Consensual social attraction also imbues the leader with apparent status and creates a status-based structural differentiation within the group into leader(s) and followers, which has characteristics of unequal status intergroup relations. In addition, a fundamental attribution process constructs a charismatic leadership personality for the leader, which further empowers the leader and sharpens the leader-follower status differential. Empirical support for the theory is reviewed and a range of implications discussed, including intergroup dimensions, uncertainty reduction and extremism, power, and pitfalls of prototype-based leadership.

Multilayer transverse gradient coil design

In small, cylindrical gradient coils consisting of a single layer of wires, the limiting factor in achieving large magnetic field gradients is the rapid increase in coil resistance with efficiency. This behavior results from the decrease in the maximum usable wire diameter as the number of turns is increased. By adopting a multilayer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favorable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. By extending the theory used to design standard cylindrical gradient coils, mathematical expressions have been developed that allow the design of multilayer coils. These expressions have previously been applied to the design of a four-layer z-gradient coil. As a further development, the equations have now been modified to allow the design of multilayer transverse gradient coils. The variation in coil performance with the number of layers employed has been investigated for coils of a size suitable for use in NMR microscopy, and the effect of constructing the coil using wires or cuts in a continuous conducting surface has also been assessed. We find that at fixed resistance a small wire-wound two-layer coil offers an increase in efficiency of a factor of about 1.5 compared with a single-layer coil. In addition, a two-layer coil of 10-mm inner diameter has been designed and built. This coil had an efficiency of 0.41 Tm-1 A(-1), a resistance of 0.96 +/- 0.01 Omega, and an inductance of 22.3 +/- 0.2 muH. The coil produces a gradient that deviates from linearity by less than 5% over a central cylindrical region of interest of height and length 6.2 mm. (C) 2003 Wiley Periodicals, Inc.

Martensite Crystallography - the apparent controversy between the infinitesimal deformation approach and the phenomenological theory of martensitic transformations

The aim of this article is to demonstrate that the apparent controversy between the infinitesimal deformation (ID) approach and the phenomenological theory of martensitic transformations (PTMTs) in predicting the crystallographic characteristics of a martensitic transformation is entirely based on unjustified approximations associated with the way in which the ID calculations are performed. When applied correctly, the ID approach is shown to be absolutely identical to the PTMT. Nevertheless, there may be some advantages in using the ID approach. In particular, it is somewhat simpler than the PTMT; it is based on a physical concept that is easier to understand and, most important, it may provide a tool for investigating some of the features of martensitic transformations that have eluded explanation via the PTMT.

Altitudinal variation in behavioural thermoregulation: Local adaptation vs. plasticity in California grasshoppers

We investigated the adaptive significance of behavioural thermoregulation in univoltine populations of the grasshopper Melanoplus sanguinipes along an altitudinal gradient in California using laboratory tests of animals raised under different temperatures. Trials consisted of continuous body temperature measurements with semi-implanted microprobes in a test arena, and observation and simultaneous recording of behavioural responses. These responses included mobility, basking and orientation of the body axes (aspect angle) towards a radiation source. Mobility and basking are determined by the altitudinal origin of the parental generation and not by the temperature treatments. With increasing altitude, individuals tend increasingly to raise body temperatures via mobility and increased basking. In contrast, body orientation towards the radiation source is influenced by the temperature treatments but not by the altitude of origin. Individuals experiencing higher temperatures during rearing show a lower tendency to lateral flanking. We conclude that body orientation responses are not adapted locally. In contrast other components of the behavioural syndrome that increase body temperature, such as mobility and basking, are adaptive in response to local selection pressure. The thermoregulatory syndrome of these grasshoppers is an important contribution to life-history adaptations that appropriately match season lengths.

Convergence analysis of a discrete-time single-unit gradient ICA algorithm

We revisit the one-unit gradient ICA algorithm derived from the kurtosis function. By carefully studying properties of the stationary points of the discrete-time one-unit gradient ICA algorithm, with suitable condition on the learning rate, convergence can be proved. The condition on the learning rate helps alleviate the guesswork that accompanies the problem of choosing suitable learning rate in practical computation. These results may be useful to extract independent source signals on-line.

The displacement and strain field of three-dimensional rheologic model of earthquake preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.