The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Analysis of acousto-ultrasonic characteristics for contact-type transducers coupled to composite laminated plates

The acousto-ultrasonic (AU) input-output characteristics for contact-type transmitting and receiving transducers coupled to composite laminated plates are considered in this paper. Combining a multiple integral transform method, an ordinary discrete layer theory for the laminates and some simplifying assumptions for the electro-mechanical transduction behaviour of the transducers, an analytical solution is developed which can deal with all the wave processes involved in the AU measurement system, i.e, wave generation, wave propagation and wave reception. The spectral response of the normal contact pressure sensed by the receiving transducer due to an arbitrary input pulse excited by the transmitting transducer is obtained. To validate the new analytical-numerical spectral technique in the low-frequency regime, the results are compared with Mindlin plate theory solutions. Based on the analytical results, numerical calculations are carried out to investigate the influence of various external parameters such as frequency content of the input pulse, transmitter/receiver spacing and transducer aperture on the output of the measurement system. The results show that the presented analytical-numerical procedure is an effective tool for understanding the input-output characteristics of the AU technique for laminated plates. (C) 2001 Elsevier Science Ltd. All rights reserved.

Briefing: Factored material properties and limit state loads-unlikely extreme or impossible pretense

In the limit state design (LSD) method each design criterion is formally stated and assessed using a performance function. The performance function defines the relationship between the design parameters and the design criterion. In practice, LSD involves factoring up loads and factoring down calculated strengths and material parameters. This provides a convenient way to carry out routine probabilistic-based design. The factors are statistically calculated to produce a design with an acceptably low probability of failure. Hence the ultimate load and the design material properties are mathematical concepts that have no physical interpretation. They may be physically impossible. Similarly, the appropriate analysis model is also defined by the performance function and may not describe the real behaviour at the perceived physical equivalent limit condition. These points must be understood to avoid confusion in the discussion and application of partial factor LSD methods.

Pulpal heat changes with newly developed resin photopolymerisation systems

Composite resin is a widely-used direct tooth coloured restorative material. Photoactivation of the polymerisation reaction can be achieved by visible blue light from a range of light sources, including halogen lamps, metal halide lamps, plasma arc lamps, and Light Emitting Diode (LED) lights. Concerns have been raised that curing lights may induce a temperature rise that could be detrimental to the vitality of the dental pulp during the act of photoactivation. The present study examined heat changes associated with standardised class V restorations on the buccal surface of extracted premolar teeth, using a curing time of 40 seconds. The independent effects of type of light source, resin shade and remaining tooth thickness were assessed using a matrix experimental design. When a conventional halogen lamp, a metal halide lamp and two different LED lights were compared, it was found that both LED lamps elicited minimal thermal changes at the level of the dental pulp, whereas the halogen lamp induced greater changes and the metal halide lamp caused the greatest thermal insult of all the light sources. These thermal changes were influenced by resin shade, with different patterns for LED versus halogen or halide sources. Thermal stress reduced as the remaining thickness of tooth structure between the pulp and the cavity floor increased. From these results, it is concluded that LED lights produce the least thermal insult during photopolymerisation of composite resins.

The first non-turnover voltammetric response from a molybdenum enzyme: direct electroscopy of dimethylsulfoxide reductase from Rhodobacter capsulatus

The first direct voltammetric response from a molybdenum enzyme under non-turnover conditions is reported. Cyclic voltammetry of dimethylsulfoxide reductase from Rhodobacter capsulatus reveals a reversible Mo-VI/V response at + 161 mV followed by a reversible Mo-V/IV response at -102 mV versus NHE at pH 8. The higher potential couple exhibits a pH dependence consistent with protonation upon reduction to the Mo-V state and we have determined the pK(a) for this semi-reduced species to be 9.0. The lower potential couple is pH independent within the range 5 < pH < 10. The optical spectrum of the Mo chromophore has been investigated with spectroelectrochemistry. At high potential, in its resting state, the enzyme exhibits a spectrum characteristic of the Mo-VI form. This changes significantly following bulk electrolysis (-400 mV versus NHE) at an optically transparent, indium-doped tin oxide working electrode, where a single visible electronic maximum at 632 nm is observed, which is comparable with spectra reported previously for the dithionite-reduced enzyme. This two-electron process is chemically reversible by reoxidizing the enzyme at the electrode in the absence of mediators or promoters. The activity of the enzyme has been established by observation of a catalytic current in the presence of DMSO at pH 8, where a sigmoidal (steady state) voltammogram is seen. Electronic supplementary material to this paper (Fig. S 1) can be obtained by using the Springer Link server located at http://dx.doi.org/10.1007/s00775-002-0374-y.

Micro-mechanical approximation to the stress field around an inclined fiber of FRCC

Matrix spalling or crushing is one of the important mechanisms of fiber-matrix interaction of fiber reinforced cementitious composites (FRCC). The fiber pullout mechanisms have been extensively studied for an aligned fiber but matrix failure is rarely investigated since it is thought not to be a major affect. However, for an inclined fiber, the matrix failure should not be neglected. Due to the complex process of matrix spalling, experimental investigation and analytical study of this mechanism are rarely found in literature. In this paper, it is assumed that the load transfer is concentrated within the short length of the inclined fiber from the exit point towards anchored end and follows the exponential law. The Mindlin formulation is employed to calculate the 3D stress field. The simulation gives much information about this field. The 3D approximation of the stress state around an inclined fiber helps to qualitatively understand the mechanism of matrix failure. Finally, a spalling criterion is proposed by which matrix spalling occurs only when the stress in a certain volume, rather than the stress at a small point, exceeds the material strength. This implies some local stress redistribution after first yield. The stress redistribution results in more energy input and higher load bearing capacity of the matrix. In accordance with this hypothesis, the evolution of matrix spalling is demonstrated. The accurate prediction of matrix spalling needs the careful determination of the parameters in this model. This is the work of further study. (C) 2002 Elsevier Science Ltd. All rights reserved.

Single mode Lamb waves in composite laminated plates generated by piezoelectric transducers

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Beneficial effects of air inclusions on the performance of ethylene vinyl acetate (EVA) mouthguard material

Objective: To investigate the impact characteristics of an ethylene vinyl acetate (EVA) mouthguard material with regulated air inclusions, which included various air cell volumes and wall thickness between air cells. In particular, the aim was to identify the magnitude and direction of forces within the impacts. Method: EVA mouthguard material, A mm thick and with and without air inclusions, was impacted with a constant force impact pendulum with an energy of 4.4 J and a velocity of 3 m/s. Transmitted forces through the EVA material were measured using an accelerometer, which also allowed the determination of force direction and magnitude within the impacts. Results: Statistically significant reductions in the transmitted forces were observed with all the air inclusion materials when compared with EVA without air inclusions. Maximum transmitted force through one air inclusion material was reduced by 32%. Force rebound was eliminated in one material, and reduced second force impulses were observed in all the air inclusion materials. Conclusion: The regulated air inclusions improved the impact characteristics of the EVA mouthguard material, the material most commonly used in mouthguards world wide.

Effect of ethylene vinyl acetate (EVA) closed cell foam on transmitted forces in mouthguard material

Objectives: To compare transmitted forces through ethylene vinyl acetate (EVA) mouthguard material and the same EVA material with gas inclusions in the form of a closed cell foam. Method: EVA mouthguard materials with and without foam gas inclusions and 4 mm thick were impacted with a constant force from an impact pendulum. Various porosity levels in the foam materials were produced by 1%, 5%, and 10% by weight foaming agent. The forces transmitted through the EVA after energy absorption by the test materials were measured with a force sensor and compared. Results: Only minor non-significant differences in transmitted forces through the EVA with and without foam were shown. Conclusions: The inclusion of gas in the form of a closed cell foam in 4 mm thick EVA mouthguard materials did not improve the impact performance of the EVA mouthguard material.

A design method for superconducting MRI magnets with ferromagnetic material

The emphasis of this work is on the optimal design of MRI magnets with both superconducting coils and ferromagnetic rings. The work is directed to the automated design of MRI magnet systems containing superconducting wire and both `cold' and `warm' iron. Details of the optimization procedure are given and the results show combined superconducting and iron material MRI magnets with excellent field characteristics. Strong, homogeneous central magnetic fields are produced with little stray or external field leakage. The field calculations are performed using a semi-analytical method for both current coil and iron material sources. Design examples for symmetric, open and asymmetric clinical MRI magnets containing both superconducting coils and ferromagnetic material are presented.