FE Modelling of NiTi‐Composed Structures

The present contribution focuses on the finite element modelling of NiTi‐based shape memory alloys. For this purpose, the concept of Helm [1] has been further developed and implemented into a finite element formulation. The model is able to describe the multiaxial behaviour of SMA and therefore useful for the simulation of complex problems. Additional emphasis is put on the modelling of the shape memory effect in composites where the interaction between the alloy and other materials like e.g. polymers plays an important role. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multidimensional van der Corput and sublevel set estimates

Van der Corput's lemma gives an upper bound for one-dimensional oscillatory integrals that depends only on a lower bound for some derivative of the phase, not on any upper bound of any sort. We establish generalizations to higher dimensions, in which the only hypothesis is that a partial derivative of the phase is assumed bounded below by a positive constant. Analogous upper bounds for measures of sublevel sets are also obtained. The analysis, particularly for the sublevel set estimates, has a more combinatorial flavour than in the one-dimensional case.

     

Chemical reducing pedoenvironment in a peatland influenced by hematitic phyllite lithology in the southern Espinhaço chain,Brazil

A peatland in Pinheiro, Diamantina City, Minas Gerais State - Brazil, was sampled at different depths of two profiles with diverse vegetation coverings (grassland field and bush) in order to collect materials that might reflect changes in the chemical states of iron over the peat formation coming from original minerals such as hematitic phyllite surrounding the boggy pedon. Samples collected were chemically, structurally and magnetically characterized. The results show that both series of peats are composed of organic matter and minerals such as quartz, kaolinite, gibbsite, rutile and muscovite. Deeper layers present only quartz. Mössbauer spectroscopy shows that iron is present in both electron states, Fe²⁺ and Fe³⁺, under both vegetations, each valence appearing in the spectra in the form of a discrete doublet. No hyperfine magnetic splitting was observed in any spectrum at room temperature. The Mössbauer subspectral area of Fe²⁺ tended to increase from the upper to deeper layers. Magnetic measurements reveal that the magnetic response of the surface samples is the highest, displaying a sharp decrease below 15 cm and that the magnetic signal is a superposition of (super)paramagnetic and ferrimagnetic contributions. Samples from the grassland field also show a diamagnetic component for the deeper layers.     

The effect of signal duration on the underwater detection thresholds of a harbor porpoise (Phocoena phocoena) for single frequency-modulated tonal signals between 0.25 and 160 kHz

The underwater hearing sensitivity of a young male harbor porpoise for tonal signals of various signal durations was quantified by using a behavioral psychophysical technique. The animal was trained to respond only when it detected an acoustic signal. Fifty percent detection thresholds were obtained for tonal signals (15 frequencies between 0.25-160 kHz, durations 0.5-5000 ms depending on the frequency; 134 frequency-duration combinations in total). Detection thresholds were quantified by varying signal amplitude by the 1-up 1-down staircase method. The hearing thresholds increased when the signal duration fell below the time constant of integration. The time constants, derived from an exponential model of integration [Plomp and Bouman, J. Acoust. Soc. Am. 31, 749-758 (1959)], varied from 629 ms at 2 kHz to 39 ms at 64 kHz. The integration times of the porpoises were similar to those of other mammals including humans, even though the porpoise is a marine mammal and a hearing specialist. The results enable more accurate estimations of the distances at which porpoises can detect short-duration environmental tonal signals. The audiogram thresholds presented by Kastelein et al. [J. Acoust. Soc. Am. 112, 334-344 (2002)], after correction for the frequency bandwidth of the FM signals, are similar to the results of the present study for signals of 1500 ms duration. Harbor porpoise hearing is more sensitive between 2 and 10 kHz, and less sensitive above 10 kHz, than formerly believed.     

The hearing threshold of a harbor porpoise (Phocoena phocoena) for impulsive sounds (L)

The distance at which harbor porpoises can hear underwater detonation sounds is unknown, but depends, among other factors, on the hearing threshold of the species for impulsive sounds. Therefore, the underwater hearing threshold of a young harbor porpoise for an impulsive sound, designed to mimic a detonation pulse, was quantified by using a psychophysical technique. The synthetic exponential pulse with a 5?ms time constant was produced and transmitted by an underwater projector in a pool. The resulting underwater sound, though modified by the response of the projection system and by the pool, exhibited the characteristic features of detonation sounds: A zero to peak sound pressure level of at least 30?dB (re 1?s(-1)) higher than the sound exposure level, and a short duration (34?ms). The animal's 50% detection threshold for this impulsive sound occurred at a received unweighted broadband sound exposure level of 60?dB re 1?μPa(2)s. It is shown that the porpoise's audiogram for short-duration tonal signals [Kastelein et al., J. Acoust. Soc. Am. 128, 3211-3222 (2010)] can be used to estimate its hearing threshold for impulsive sounds.     

A finite element model for shape memory alloys considering thermomechanical couplings at large strains

In the present work we propose a new thermomechanically coupled material model for shape memory alloys (SMA) which describes two important phenomena typical for the material behaviour of shape memory alloys: pseudoelasticity as well as the shape memory effect. The constitutive equations are derived in the framework of large strains since the martensitic phase transformation involves inelastic deformations up to 8%, or even up to 20% if the plastic deformation after the phase transformation is taken into account. Therefore, we apply a multiplicative split of the deformation gradient into elastic and inelastic parts, the latter concerning the martensitic phase transformation. An extended phase transformation function has been considered to include the tension–compression asymmetry particularly typical for textured SMA samples. In order to apply the concept in the simulation of complex structures, it is implemented into a finite element code. This implementation is based on an innovative integration scheme for the existing evolution equations and a monolithic solution algorithm for the coupled mechanical and thermal fields. The coupling effect is accurately investigated in several numerical examples including pseudoelasticity as well as the free and the suppressed shape memory effect. Finally, the model is used to simulate the shape memory effect in a medical foot staple which interacts with a bone segment.     

On stereochemistry of osmium tetraoxide oxidation of allylic alcohol systems. Empirical rule

An empirical formulation is presented to predict the stereochemistry of major osmylation products of allylic alcohols and their derivatives.