Asymptotic analysis of wave propagation in a finite viscoplastic bar

Summary Axially symmetric wave propagation in a finite extent cylindrical sample, whose viscoplastic behaviour is described by the Bodner-Partom model, involves variables which can be scaled so as to bring out a small parameter characteristic of the problem at hand. Asymptotic solutions can be derived from power series expansions of the variables with respect to the small parameter.In the one-dimensional case, a finite difference solution is shown to agree with the zero order term of the asymptotic expansion which is closely related to the Hopkinson pressure bar simplified theory.Then it is shown in a special case that retaining the sole first term of each asymptotic expansion amounts to eliminating the needlessly intricate fluctuations of the exact solution due to successive wave reflections at the specimen's both ends, while keeping the essentials of the response and simplifying the numerical work.Afterwards, the relative orders of magnitude of the various stress components with respect to the small parameter are estimated in the more general framework of the two-dimensional problem, with a view to re-deriving the so-called inertia correction; the latter relies on an appropriate definition of the mean stress experienced by the sample and uses the first two terms of the asymptotic expansions.This study suggests the applicability of the method in a more general scope, taking into account in a consistent way other phenomena (friction and lateral motion of the adjacent bars, for instance) or more refined constitutive equations.Notation a=h/R aspect ratio of specimen - A specimen cross-section area - A ₁ bar cross-section area - c elastic wave speed in specimen - c ₁ elastic wave speed in bars - E specimen Young's modulus - E ₁ bar Young's modulus - h specimen length - H Z/E - r radial coordinate - R specimen radius - s _ij stress deviator - t time - T incident signal duration - u _i physical displacement in specimen - U _i dimensionless displacement in specimen - V ₀,V ₁ dimensionless velocities on end faces - w _p plastic work - W _p dimensionless plastic work - x axial coordinate - Z Bodner-Partom hardening parameter - small parameter - zero order longitudinal extension rate - strain rate tensor - dimensionless axial coordinate - dimensionless axial coordinate - polar angle - Poisson's ratio - specimen density - _ij stress tensor - _ij dimensionless stress tensor - equivalent stress - dimensionless time - dimensionless viscoplastic strain rate in axial direction     

THERMAL STRESSES IN ASYMMETRICALLY HEATED THICK CYLINDRICAL SHELLS

A new thick shell theory is proposed that accounts for shear and normal stress in the radial direction on one hand, expansion and warping of fibers normal to the mean surface on the other; it accurately describes the stress distribution in thick piping structures subjected to severe through-the-wall thermal gradients, e.g., in solar boiler tubes.     

An integrated on chip organic optical source based on electrochemiluminescence

We report here on an original “glass-PDMS-glass” electrochemiluminescence optofluidic device that integrates 32 electrodes on a large surface. This organic electrically powered light source has been integrated on chip using an alternative process based on a photopatternable silicone resist. Under a continuous flow rate, this device allows electrogenerated chemiluminescence for several minutes which would be very useful for future μTAS systems.     

Generalized Kirchhoff-Love assumptions for thick shells: Application to thermal stresses in rectilinear tubes

Summary Asymptotic expansions of displacements in powers of a small parameter related to the shell thickness are re-derived with a view to investigating the way in which the leading terms depend on the thickness coordinate. The outcome of this preliminary study gives a hint concerning possible kinematic assumptions to be used as starting points for constructing thick shell theories. Then the problem of reducing the number of independent generalized displacements by enforcing all or part of the traction boundary conditions on the shell outer and inner surfaces is studied. Several thick shell theories are proposed and compared; the superiority of a certain generalized Kirchhoff-Love assumption is brought out in the particular case of circular cylindrical shells subjected to several types of thermal loadings.With 3 Figures     

Nanowires network for biomolecular detection using contactless impedance tomoscopy technique

Here we present the detection of ultralow concentrations of biomolecules in a device made from a polycarbonate membrane containing a network of gold nanowires and using a "contactless" impedance tomoscopy technique. The sensor comprises a thin dielectric layer with two parallel band electrodes on the one side and a microchannel containing gold nanowires onto which the adsorption of antibodies occurs. Upon applying a high-frequency ac voltage between the two electrodes, the adsorption process occurring at the surface of the gold nanowires can be followed through contactless impedance measurements. The configuration allows the real-time detection of biomolecules with a bulk concentration in the picomolar range.     

Small Molecule Inhibitors of AI-2 Signaling in Bacteria: State-of-the-Art and Future Perspectives for Anti-Quorum Sensing Agents

Bacteria respond to different small molecules that are produced by other neighboring bacteria. These molecules, called autoinducers, are classified as intraspecies (i.e., molecules produced and perceived by the same bacterial species) or interspecies (molecules that are produced and sensed between different bacterial species). AI-2 has been proposed as an interspecies autoinducer and has been shown to regulate different bacterial physiology as well as affect virulence factor production and biofilm formation in some bacteria, including bacteria of clinical relevance. Several groups have embarked on the development of small molecules that could be used to perturb AI-2 signaling in bacteria, with the ultimate goal that these molecules could be used to inhibit bacterial virulence and biofilm formation. Additionally, these molecules have the potential to be used in synthetic biology applications whereby these small molecules are used as inputs to switch on and off AI-2 receptors. In this review, we highlight the state-of-the-art in the development of small molecules that perturb AI-2 signaling in bacteria and offer our perspective on the future development and applications of these classes of molecules.     

Numerical implementation of the ‘summed progressing wave’ formalism. computation of short-time and long-time transients

A mixed initial-boundary value problem associated with a hyperbolic integro-differential system is solved by means of the ‘summed progressing wave’ formalism. Once the numerical problem has been set, the pertaining solution methods are described. A simple approximate solution is also proposed. Attenuation functions are calculated through a novel method using the semi-group property exhibited by the exponential of an integro-differential operator. The long-time solution of the problem at hand can be brought out owing to this procedure.     

Steady-State Crack Velocity in a Viscoelastic Composite Material

The velocity of a semi-infinite crack slowly propagating in aninfinitely long strip made of a viscoelastic composite material isdetermined according to Christensen's fracture criterion. The edges ofthe strip are subjected to uniform opposite displacements normal to thecrack plane. The crack velocity is obtained from an energy balanceequation involving the energy dissipated in the whole strip; the latteris evaluated using an approximate, but sufficiently accurate, expressionof the stress field in the structure obtained by taking into account thestrong anisotropy of the long fibre composite material of interest. Thisnew version of Christensen's criterion compares favourably with theoriginal one and gives crack velocity predictions very close to thoseprovided by Schapery's criterion.     

Rotating disk electrodes to assess river biofilm thickness and elasticity

The present study examined the relevance of an electrochemical method based on a rotating disk electrode (RDE) to assess river biofilm thickness and elasticity. An in situ colonisation experiment in the River Garonne (France) in August 2009 sought to obtain natural river biofilms exhibiting differentiated architecture. A constricted pipe providing two contrasted flow conditions (about 0.1 and 0.45 m s⁻¹ in inflow and constricted sections respectively) and containing 24 RDE was immersed in the river for 21 days. Biofilm thickness and elasticity were quantified using an electrochemical assay on 7 and 21 days old RDE-grown biofilms (t₇ and t₂₁, respectively). Biofilm thickness was affected by colonisation length and flow conditions and ranged from 36 ± 15 μm (mean ± standard deviation, n = 6) in the fast flow section at t₇ to 340 ± 140 μm (n = 3) in the slow flow section at t₂₁. Comparing the electrochemical signal to stereomicroscopic estimates of biofilms thickness indicated that the method consistently allowed (i) to detect early biofilm colonisation in the river and (ii) to measure biofilm thickness of up to a few hundred μm. Biofilm elasticity, i.e. biofilm squeeze by hydrodynamic constraint, was significantly higher in the slow (1300 ± 480 μm rpm^1/2, n = 8) than in the fast flow sections (790 ± 350 μm rpm^1/2, n = 11). Diatom and bacterial density, and biofilm-covered RDE surface analyses (i) confirmed that microbial accrual resulted in biofilm formation on the RDE surface, and (ii) indicated that thickness and elasticity represent useful integrative parameters of biofilm architecture that could be measured on natural river assemblages using the proposed electrochemical method.     

Predicting fatigue transverse crack growth in cross-ply carbon–epoxy laminates from quasi static strength tests by using iso-damage curves

Cross-ply laminates made of carbon/epoxy IM7/977-2 system are investigated. The fatigue study is confined to ambient temperature conditions and zero loading ratio. Damage is characterized by the transverse crack density ρ in the central 90°-layer. The family of experimental fatigue cracking curves (ρ versus N, where N is the number of cycles, for each tensile test maximum stress amplitude) can be replaced with a set of “iso-damage curves”, i.e. contour curves of constant ρ in the σ–log (N) plane. The iso-damage curves approximately constitute a fan of straight lines that intersect at a common point (σ_e, log (N_s)), where N_s is a very large number of cycles beyond which no more crack appears, and σ_e is some fatigue limit.Our aim is to propose a simple method to predict fatigue cracking at an arbitrary maximum stress level loading by using data stemming from a constant strain rate test. This method essentially rests upon the construction of the above “iso-damage” curves, using very simple assumptions.