The performance and prediction ability of advanced approach to ductile fracture

The present paper deals with the modelling of ductile fracture which is the result of severe plastic deformation under monotonic loading. It can be the result of a crash or accident or introduced intentionally. There is a need of increasing the safety in many fields of industrial sector or transportation. The aluminium alloy 2024-T351 is widely used for studies of ductile fracture. The material was supplied as a cold-rolled plate for this study and examined within a broad range of stress states. First of all, the flow curve was determined using the standard tensile test of smooth cylindrical bar. Then, the tensile tests of variously notched cylindrical bars were conducted to show the pressure dependence. The tensile and torsion tests of notched tube were added in order to document the dependency on the deviatoric stress state. Finally, the compression test of smooth cylinder was executed. Then, deviatoric stress state dependent plasticity and the original ductile fracture hyperbolic criterion were calibrated. The damage accumulation nonlinearity was examined through loading–unloading experiments. The double damage curve approach, inspired by the fatigue life prediction, was revisited and calibrated using the semi-cyclic testing. Finally, the softening effect was studied aiming to couple the damage with plasticity. The performance and prediction ability was verified after the model was completely calibrated and implemented into the Abaqus finite element software. Three different cases of tension were chosen for this comparative purpose. The tension of notched cylindrical and tubular specimens and flat specimen. The ductile fracture criterion coupled with plasticity should provide the slant fracture in the conditions of plane strain due to localization. Nevertheless, it is shown that the proposed approach has still some drawbacks in prediction of the crack propagation

Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators

We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled -contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators -and, in particular, micromechanical oscillators- provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phase-shift control oscillations are stable over the whole resonance curve. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices

The Bosma effect revisited - I. HI and stellar disc scaling models

The observed proportionality between the centripetal contribution of the dynamically insignificant HI gas in the discs of spiral galaxies and the dominant contribution of DM - the "Bosma effect" - has been repeatedly mentioned in the literature but largely ignored. We have re-examined the evidence for the Bosma effect by fitting Bosma effect models for 17 galaxies in the THINGS data set, either by scaling the contribution of the HI gas alone or by using both the observed stellar disc and HI gas as proxies. The results are compared with two models for exotic cold DM: internally consistent cosmological NFW models with constrained compactness parameters, and URC models using fully unconstrained Burkert density profiles. The Bosma models that use the stellar discs as additional proxies are statistically nearly as good as the URC models and clearly better than the NFW ones. We thus confirm the correlation between the centripetal effects of DM and that of the interstellar medium of spiral galaxies. The edificacy of "maximal disc" models is explained as the natural consequence of "classic" Bosma models which include the stellar disc as a proxy in regions of reduced atomic gas. The standard explanation - that the effect reflects a statistical correlation between the visible and exotic DM - seems highly unlikely, given that the geometric forms and hence centripetal signatures of spherical halo and disc components are so different. A literal interpretation of the Bosma effect as being due to the presence of significant amounts of disc DM requires a median visible baryon to disc DM ratio of about 40%.Comment: Accepted by A&A (Paper I

Generalised Mersenne Numbers Revisited

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked. Asymptotically, using a cyclic rather than a linear convolution, residue multiplication modulo a Mersenne number is twice as fast as integer multiplication; this property does not hold for prime GMNs, unless they are of Mersenne's form. In this work we exploit an alternative generalisation of Mersenne numbers for which an analogue of the above property --- and hence the same efficiency ratio --- holds, even at bitlengths for which schoolbook multiplication is optimal, while also maintaining very efficient reduction. Moreover, our proposed primes are abundant at any bitlength, whereas GMNs are extremely rare. Our multiplication and reduction algorithms can also be easily parallelised, making our arithmetic particularly suitable for hardware implementation. Furthermore, the field representation we propose also naturally protects against side-channel attacks, including timing attacks, simple power analysis and differential power analysis, which is essential in many cryptographic scenarios, in constrast to GMNs.Comment: 32 pages. Accepted to Mathematics of Computatio

Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model

Monte Carlo results for the moments of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary conditions in d=5 dimensions, are analyzed in the critical region and compared to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod. Phys. C (1998)]. We show that this finite-size scaling theory (formulated in terms of two scaling variables) can account for the longstanding discrepancies between Monte Carlo results and the so-called ``lowest-mode'' theory, which uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature distance from the critical temperature, only to a very limited extent. While the CD theory gives a somewhat improved description of corrections to the ``lowest-mode'' results (to which the CD theory can easily be reduced in the limit t \to 0, L \to \infty, tL^{d/2} fixed) for the fourth-order cumulant, discrepancies are found for the susceptibility (L^d ). Reasons for these problems are briefly discussed.Comment: 9 pages, 13 Encapsulated PostScript figures. To appear in Eur. Phys. J. B. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

Carbon Leakage Revisited: Unilateral Climate Policy with Directed Technical Change

A common critique to the Kyoto Protocol is that the reduction in emissions of CO2 by countries who comply with it will be (partly) offset by the increase in emissions on the part of other countries (carbon leakage). This paper analyzes the effect of technical change on carbon leakage in a two-country model where only one of the countries enforces an exogenous cap on emissions. Climate policy induces changes in relative prices, which cause carbon leakage through a terms-of-trade effect. However, these changes in relative prices in addition affect the incentives to innovate in different sectors. We allow entrepreneurs to choose the sector for which they innovate (directed technical change). This leads to a counterbalancing induced-technology effect, which always reduces carbon leakage. We therefore conclude that the leakage rates reported in the literature so far may be too high, as these estimates neglect the effect of relative price changes on the incentives to innovate.Climate Policy, Carbon Leakage, Directed Technical Change, International Trade

Innovating for Learning: Designing for the Future of Education

Teaching has moved online as the world has moved online and learning is losing its sense of physical location with the availability of many different options from mobile to MOOC (Massive Open Online Course). The impact of online learning is not confined to distance learning; when a student attends a campus university they are now as likely to meet with their fellow learners virtually as face to face. The education sector has yet to fully adapt to what this means, and indeed there strong signs of a built in resilience from providers, employers and students themselves which may mean an apparent evolution is more likely than a revolution. At the same time, there are some quiet changes underway that mean we should be preparing to innovate for the revolution to come. Some of those changes are considered in work undertaken at The Open University that has been disseminated in a series of Innovating Pedagogy reports. These reports allow the academic authors to be more speculative than is usual practice and engage in considering the future, while remaining based on a view of what is happening in the sector. In particular they adopt a position focused on pedagogy that balances technology-based futurology that can dominate yet fail to resonate with those actually involved in the teaching process. The annual Innovating Pedagogy reports cover 10 topics each, with some deliberate overlap from year to year and development of themes that show innovations moving into teaching practice. This is illustrated by two cases, the impact of MOOCs and the application of learning design and analytics. The development of MOOCs demonstrates the value of reviewing pedagogy that aligns with technology. While the use of learning design and learning analytics demonstrates how improvements in the way we describe our learning processes and the way we understand learner behaviour is helping determine how choices in pedagogy impact on student satisfaction, progression and success

The role of different sliding resistances in limit analysis of hemispherical masonry domes

A limit analysis method for masonry domes composed of interlocking blocks with non-isotropic sliding resistance is under development. This paper reports the first two steps of that work. It first introduces a revision to an existing limit analysis approach using the membrane theory with finite hoop stresses to find the minimum thickness of a hemispherical dome under its own weight and composed of conventional blocks with finite isotropic friction. The coordinates of an initial axisymmetric membrane surface are the optimization variables. During the optimization, the membrane satisfies the equilibrium conditions and meets the sliding constraints where intersects the block interfaces. The results of the revised procedure are compared to those obtained by other approaches finding the thinnest dome. A heuristic method using convex contact model is then introduced to find the sliding resistance of the corrugated interlocking interfaces. Sliding of such interfaces is constrained by the Coulomb’s friction law and by the shear resistance of the locks keeping the blocks together along two orthogonal directions. The role of these two different sliding resistances is discussed and the heuristic method is applied to the revised limit analysis method