Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).

Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

Liquid crystal based continuous phase retarder: From optically neutral to a quarter waveplate in 200 microseconds

Liquid crystal variable phase retarders have been incorporated into prototype devices for optical communications system applications, both as endless polarization controllers 1,2,3, and as holographic beam steerers 4. Nematic liquid crystals allow continuous control of the degree of retardation induced at relatively slow switching speeds, while ferroelectric liquid crystal based devices allow fast (sub millisecond) switching, but only between two bistable states. The flexoelectro-optic effect 5,6 in short-pitch chiral nematic liquid crystals allows both fast switching of the optic axis and continuous, electric field dependent control of the degree of rotation of the optic axis. A novel geometry for the flexoelectro-optic effect is presented here, in which the helical axis of the chiral nematic is perpendicular to the cell walls (grandjean texture) and the electric field is applied in the plane of the cell. This facilitates deflection of the optic axis of the uniaxial negatively birefringent material from lying along the direction of propagation to having some component in the polarization plane of the light. The device is therefore optically neutral at zero field for telecommunications wavelengths (1550nm), and allows a continuously variable degree of phase excursion to be induced, up to 2π/3 radians achieved so far in a 40μm thick cell. The retardation has been shown both to appear, on application of the field, and disappear on removal, at speeds of 100-500 μs. The direction of deflection of the optic axis is also dependent on the direction of the field, allowing the possibility, in a converging electrode "cartwheel cell", of endless rotation of the liquid crystal waveplate at a higher rate than achievable through dielectric coupling to plain nematic materials.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Nonlinear Analysis of m Method for Single Pile Under Lateral Loading

通过对大量模型试验结果的分析,提出了简便合理的水平荷载作用下单桩的计算方法。该方法将常用m法中单一m值与位移建立指数关系,并由b_m及K两参数来描述。将这一关系引入常用单桩m法计算中,则计算结果可考虑单桩非线性响应的影响。

Modelling nonlinear vehicle dynamics with neural networks

The nonlinear modelling ability of neural networks has been widely recognised as an effective tool to identify and control dynamic systems, with applications including nonlinear vehicle dynamics which this paper focuses on using multi-layer perceptron networks. Existing neural network literature does not detail some of the factors which effect neural network nonlinear modelling ability. This paper investigates into and concludes on required network size, structure and initial weights, considering results for networks of converged weights. The paper also presents an online training method and an error measure representing the network's parallel modelling ability over a range of operating conditions. Copyright © 2010 Inderscience Enterprises Ltd.

Continuous spectrum growth and modal instability in swirling duct flow

We present results on the stability of compressible inviscid swirling flows in an annular duct. Such flows are present in aeroengines, for example in the by-pass duct, and there are also similar flows in many aeroacoustic or aeronautical applications. The linearised Euler equations have a ('critical layer') singularity associated with pure convection of the unsteady disturbance by the mean flow, and we focus our attention on this region of the spectrum. By considering the critical layer singularity, we identify the continuous spectrum of the problem and describe how it contributes to the unsteady field. We find a very generic family of instability modes near to the continuous spectrum, whose eigenvalue wavenumbers form an infinite set and accumulate to a point in the complex plane. We study this accumulation process asymptotically, and find conditions on the flow to support such instabilities. It is also found that the continuous spectrum can cause a new type of instability, leading to algebraic growth with an exponent determined by the mean flow, given in the analysis. The exponent of algebraic growth can be arbitrarily large. Numerical demonstrations of the continuous spectrum instability, and also the modal instabilities are presented.

GSPS photonic analogue to digital conversion system using broadband continuous wave source

An 80 GSPS photonic ADC system is demonstrated, using broadband MLL and dispersive fibre to form a continuous waveform with time-wavelength mapping, and AWG to channelise. Tests are carried out for RF signals up to 10GHz. © 2005 Optical Society of America.

Organic reactions in supercritical fluids: Continuous, selective and green

Supercritical fluids (SCFs) offer a wide range of opportunities as media for chemical reactions and supercritical CO2, ScCO2, is becoming increasingly important as a benign replacement for more toxic solvents.1 High pressure reactions, however, are more capital intensive than conventional low pressure processes. Therefore, supercritical fluids will only gain widespread acceptance in those areas where the fluids give real chemical advantages as well as environmental benefits. This lecture gives a brief account of the use of flow reactors for continuous reactions in supercritical fluids, particularly those of interest for the manufacture of fine chemicals.

A Nonlinear Threshold Model Applied to Spallation Analysis

Spallation in heterogeneous media is a complex, dynamic process. Generally speaking, the spallation process is relevant to multiple scales and the diversity and coupling of physics at different scales present two fundamental difficulties for spallation modeling and simulation. More importantly, these difficulties can be greatly enhanced by the disordered heterogeneity on multi-scales. In this paper, a driven nonlinear threshold model for damage evolution in heterogeneous materials is presented and a trans-scale formulation of damage evolution is obtained. The damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that some dimensionless numbers govern the whole process of deformation and damage evolution. The effects of heterogeneity in terms of Weibull modulus on damage evolution in spallation process are also investigated.