On hysteresis in elasto-plasticity and in ferromagnetism

We define hysteresis as rate-independent memory, illustrate some of its properties, and review some scalar models of elasto-plasticity: the stop, the play, the Prandtl–Ishlinski models. In particular we study the Prager model of linear kinematic hardening, which encompasses stops and plays. We then couple the latter model with the dynamic equation for a one-dimensional system, show existence of a weak solution, and deal with its homogenization. We also discuss the extension to tensors and to three-dimensional systems.

We then deal with ferromagnetic hysteresis. We review the classic Preisach model and a vector extension. Finally, we formulate a model of vector ferromagnetic hysteresis, couple it with the magnetostatic equations, and discuss its homogenization. The latter consists in a two-length-scale model, and corresponds to a variant of the vector Preisach model.     

Extreme Poisson's ratios and related elastic crystal properties

With the aim of understanding anisotropic crystals that possess a negative Poisson's ratio and to lay a foundation for investigating molecular mechanisms, we discuss the definition of the ratio and establish conditions on the compliance that govern its sign. We derive results on orientation averaging that are useful in the context of anisotropy and helpful in the investigation of isotropic polycrystals. We discuss α-cristobalite, a polymorph of silicon dioxide that possesses interesting negative ratio properties in single crystals and hypothetical polycrystals. In this connection, we draw attention to the transverse compliance as an alternative and simpler metric for gaging the ratio and for orientation averaging. For α-cristobalite, we arrive at new results for the directions that yield the most negative Poisson's ratio. This result should be of value in divining the underlying molecular mechanism that explains the negative values of Poisson's ratio in α-cristobalite, a crystal of tetragonal symmetry that possesses six independent elastic constants.     

Modeling of the oscillating field effects on the Heβ line emission in short pulse laser-produced plasmas

Strong oscillating fields may induce strong modifications of the emission spectra of ions. We discuss here the possibility of observing such effects in actual laser experiments where space- and time-integration effects can easily mask their existence. Focusing on the Al He_β transition, we first discuss the calculation of its spectral broadening in the presence of a strong laser field. Then, starting from 1D hydro-simulations of short, intense, laser pulse-produced plasmas that provide the density, temperature and laser intensity profiles as a function of time, full integrated collisional-radiative calculations of the laser field-dependent emissivity of the Al He_β line, are presented.     

On the equilibrium configurations of flexible fibers in a flow

We discuss the equilibrium configurations of a fiber clamped to a spherical body and immersed in a flow ranging between 0 and 50 cm/s. Experimental and numerical results are presented and the effects of flow speed and positioning of the fiber upon the equilibrium configuration are investigated. Our investigations reveal that the orientation of the fiber and its length has a significant impact upon its bending and drag experienced by the sphere-fiber system. We note that the longer fibers (i) bend significantly more than the shorter ones and (ii) display oscillatory or flapping motion at much lower flow speeds than their shorter counterparts. The simulations also reveal that the drag on the fiber is noticeably effected by the size of the basal body. Drag exponents (or Vogel exponents) are also computed and seen to deviate slightly from previous results.     

Numerical stability of the method of Brownian configuration fields

We investigate numerical aspects of the Brownian configuration fields method, and in particular its numerical stability as the Weissenberg number increases. Our results show the method to be immune to the type of instability leading to numerical blowup in the simulation of macroscopic models. We discuss this finding in the light of the stability criterion proposed in Fattal et al. [R. Fattal, R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg using the log-conformation representation, J. Non Newtonian Fluid Mech. 126 (2005) 23–37].     

A Comment on Governing Equations of Envelope Surface Created by a Two-Dimensional Directional Wavepacket Centered around a Propagation Direction on an Elastic Plate

Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this paper, we consider natural vibrations of an elastic plate and the propagation of a wavepacket on it. We derive the two-dimensional equations that govern the spatial and temporal evolution of the amplitude of a wavepacket and discuss its features. We especially consider a directional wavepacket on an elastic plate, which propagation direction is centered around a main direction, but which wavenumber and frequency are fixed by a certain value. The fact that its envelope becomes time-invariant and is governed by the Schrödinger–Nohara type equation is shown.     

Existence of entropy as a consequence of asymptotic stability

For a class of physical systems whose temporal evolution is governed by ordinary differential equations, the consequences of an assumption of asymptotic stability for equilibrium states in isolation remarkably resemble various forms of the second law of thermodynamics. Here we apply a known converse to Lyapunov's stability theorem to motivate both Gibbs' theory of thermostatics and the use of the Clausius-Duhem inequality for systems which are out of equilibrium and exchanging heat with their surroundings. We also discuss conditions under which the entropy of a system can be expressed as a sum of the entropies of its material points.     

Nonlinear Dynamics of an Electrically Driven Impact Microactuator

We study the dynamics of an electrostatically driven impact microactuator. Impact between moving elements of the microactuator is modeled using the coefficient of restitution. Friction between the microactuator and its supporting substrate is modeled using the Amonton–Coulomb law. We consider the bifurcations under changes in the driving voltage and frequency. Grazing bifurcations introduce discontinuous transitions between different motions. It is also found that impacts dramatically change the characteristics of the frequency-response curve. Finally, we discuss the evolution of incomplete chatter to complete chatter, that is, sticking.Contributed by Prof. G. Rega.     

Electrodynamics and Thermomechanics of Material Bodies

We consider a material body emersed in space and, relative to an aether frame, the balance laws which govern its interaction with an electromagnetic, thermal and mechanical environment. A detailed formulation of a non-relativistic theory for studying thermomechanical–electromagnetic processes in deformable media is presented and certain invariance issues are discussed. The idea of an isolated process in a given aether frame is introduced and we identify a related non-increasing Lyapunov function for such processes. This function suggests the structure of a class of minimization problems within the statical theory and we discuss a typical problem within the area of elastic dielectrics.      

Quasistatic Evolution of Sessile Drops and Contact Angle Hysteresis

We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of solutions with prescribed initial configuration for the corresponding quasistatic evolution.We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.     

Volume Visualizing High-Resolution Turbulence Computations

Using several volume-visualization packages including a new package we developed called Volsh, we investigate a 25-Gbyte dataset from a 256³ computation of decaying quasi-geostrophic turbulence. We compare surface fitting and direct volume rendering approaches, as well as a number of techniques for producing feature-revealing spatial cues. We also study the pros and cons of using batch and interactive tools for visualizing the data and discuss the relative merits of using each approach. We find that each tool has its own advantages and disadvantages, and a combination of tools is most effective at exploring large four-dimensional scalar datasets. The resulting visualizations show several new phenomena in the dynamics of coherent vortices. Received 30 April 1997 and accepted 27 August 1997     

Optimization of the nonlinear convergence rate of the SIMPLER Picard algorithm for steady incompressible internal flows through enforcement of continuity projections

We discuss the performance optimization of the Semi‐Implicit Method for Pressure‐Linked Equations—Revised (SIMPLER) Picard algorithm for steady incompressible internal flows. We discuss the nonlinear convergence of the Picard iteration as a function of the pressure and scalar potential continuity projections stemming from the SIMPLER algorithm, for three example problems. In particular, we discuss the choice of under‐relaxation method, and choice of under‐relaxation factors; the choice of the projection algorithm; and the required tolerance for the linear solve of the generalized Poisson equations for the pressure and scalar potential equations that arise from the projection operations. We conclude that the convergence of the nonlinear Picard iteration can be effectively controlled by the optimal enforcement of the continuity projections. Copyright © 2005 John Wiley & Sons, Ltd.     

二维纳米材料异质结构的原子间相互作用模型

近些年二维纳米材料得到了大量的研究,其中一个热点研究方向是将不同的二维纳米材料堆垛成纳米异质结构,从而实现多功能的纳米器件.这些二维纳米材料可以从面外和面内两个方向上进行堆垛从而形成两类不同的异质结构.在关于这类二维纳米材料及其异质结构的理论研究中,原子间的相互作用起到类似于连续介质力学中本构关系的作用.因此学者提出了多种方案用于描写原子间相互作用,主要包括第一性原理计算和经验势能模型等.本文主要是对比和分析各种描写二维纳米材料及其异质结构的常见经验势能模型,从而为研究人员选择相互作用模型提供一些参考.      

Two-dimensional model of a plate made of an anisotropic inhomogeneous material

We present an asymptotic derivation of the two-dimensional equations of equilibrium of a thin elastic inhomogeneous plate manufactured of an anisotropic material of general form with 21 moduli of elasticity. We also consider simplified models obtained under special assumptions on the moduli. We use test examples to illustrate the error estimate of the proposed model and discuss its scope. The model is compared with the classical Kirchhoff–Love and Timoshenko–Reissner models.     

Two-phase theory for the superplastic flow

We discuss a theoretical approach to the stress induced motion of vacancies in a polycrystalline material and its connection with superplastic flow, put forward recently by us. After introducing an alternate formulation, the theory is applied to explain the temperature dependent stress-strain rate curves exhibited by some representative alloys. The agreement with experiment is remarkable. We also employ it to study the rate of cavity growth in two superplastic copper alloys that exhibit particularly strong cavitation.     

A free rectangular plate on elastic foundation

This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations. We talk over the two cases, that is, the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively. We select a fiexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces. We apply the variational method meanwhile and then obtain better approximate solutions.     

Strain induced shape formation in fibred cylindrical tubes

The aim of the paper is to solve and discuss the representation problem of a special class of integrable distortion fields in fibred cylindrical bodies and to analyze the corresponding induced shape changes. We find and discuss the compatibility conditions, i.e. the conditions to be satisfied to get a pair compatible distortion/shape change, when different fields of fibers are assigned on the cylindrical body, through the specification of the fields of fiber angles.     

Dynamics of pulsatile flows through microtubes from nonlocality

In this paper we introduce a new notion of complexified nonlocal-in-time-space material derivative operator and we discuss its implications in fluid mechanics. After deriving the complexified fluid equations, we investigate the problem of laminar flow of a particle fluid in a microtube. We demonstrate the occurrence of pulsatile flows through microtubes in agreement with recent findings.     

Thermodynamics applied to gradient theories involving the accumulated plastic strain: The theories of Aifantis and Fleck and Hutchinson and their generalization

We discuss the physical nature of flow rules for rate-independent (gradient) plasticity laid down by Aifantis and by Fleck and Hutchinson. As a central result we show that:

•

the flow rule of Fleck and Hutchinson is incompatible with thermodynamics unless its nonlocal term is dropped. If the underlying theory is augmented by a general defect energy dependent on γ^p and ∇γ^p, then compatibility with thermodynamics requires that its flow rule reduce to that of Aifantis.

We establish this result (and others) within a general framework obtained by combining a virtual-power principle of Fleck and Hutchinson with the first two laws of thermodynamics—balance of energy and the Clausius-Duhem inequality—under isothermal conditions.