The construction of constitutive relations for isotropic strain-hardening elastoplastic materials of the differential type of complexity <Emphasis Type="Italic">n</Emphasis>. Part 1. Finite strains

Using approaches in rational continuum mechanics, we have developed a mathematical theory of strict construction and specialization of constitutive equations for simple (in Noll’s sense) isotropic strain-hardening elastoplastic materials of the differential type of complexity n (analogs of the Rivlin–Ericksen solids of complexity n) as the most important representatives of the materials with infinitesimal fading path shape memory (a fading path shape memory on an arbitrarily small interval of the “past”). The strains are assumed to be arbitrary. The hierarchy of the constitutive relations is constructed according to the level of complexity of the material response to deformation. Translated from Problemy Prochnosti, No. 2, pp. 27–42, March–April, 2009.     

Modelling Young’s modulus for porous bones with microstructural variation and anisotropy

A structural model with three compositional phases and two levels of hierarchical organization is proposed for predicting Young’s modulus of porous bones with microstructural variations and anisotropy based on their geometric similarity to metal foams. It has been shown that the proposed single model provides predictions of Young’s modulus with high accuracy up to ±30% for cortical and cancellous bones compared with measured data from the literature. In addition, the conversion of the solid bone shape from “Plate-like” to “Rod-like” at a porosity of 70% or higher (BV/TV 30% or lower)—verified by observations—can be predicted using the proposed model.     

Micro-mechanics based derivation of the materials constitutive relations for carbon-nanotube reinforced poly-vinyl-ester-epoxy based composites

The atomic-level computational results of the mechanical properties of Multi-Walled Carbon Nanotube (MWCNT) reinforced poly-vinyl-ester-epoxy obtained in our recent work [Grujicic M, Sun Y-P, Koudela KL (2006) Appl Surf Sci (accepted for publication, March)], have been utilized in the present work within a continuum-based micro-mechanics formulation to determine the effective macroscopic mechanical properties of these materials. Since the MWCNT reinforcements and the polymer-matrix molecules are of comparable length scales, the reinforcement/matrix interactions which control the matrix-to-reinforcement load transfer in these materials are accounted for through direct atomic-level modeling of the “effective reinforcement” mechanical properties. The term an “effective reinforcement” is used to denote a MWCNT surrounded by a layer of the polymer matrix whose thickness is comparable to the MWCNT radius and whose conformation is changed as a result of its interactions with the MWCNT. The micro-mechanics procedure yielded the effective continuum mechanical properties for the MWCNT-reinforced poly-vinyl-ester-epoxy matrix composite mats with a random in-plane orientation of the MWCNTs as a function of the following composite microstructural parameters: the volume fraction of the MWCNTs, their aspect ratio, the extent of covalent functionalization of the MWCNT outer walls as well as a function of the mechanical properties of the matrix and the reinforcements.     

Ein Mitbegründer der modernen Medizin- und Wissenschaftsethik: John Gregory (1724–1773) und seineLectures on the Duties and Qualifications of a Physician

The scottish physician and philosopher John Gregory (1724–1773) published in 1770Lectures On The Duties and Qualifications Of A Physician. Besides giving many very concrete and pragmatic rules and proposals concerning medical etiquette and decency, like most medical “codifiers” did before and after him, Gregory also develops a truely “ethical”—in the sense of (moral-) philosophically based—“system of conduct in a physician”. His concept of practicing and teaching ethics in medicine and research combines Bacon's (1561–1626) philosophy of nature and science with both, the general moral philosophy of the religious sceptic David Hume (1711–1776) and the traditional christian-occidental virtues and deontologies upheld by the movement of the so-called “Common-Sense Philosophy”. By thus combinig conservative moral traditions with the modern enlightenment philosophy of empirism, Gregory's teachings establish ethics in medicine and science on a very broad compromise. It can be proved that his very comprehensiveLectures had—particularly via the famousCode of Medical Ethics of Thomas Percival (1740–1804)—a decisive influence on our contemporary concepts of bioethics.      

Die Kopplung elliptischer Schleifen mit der Kreuzschleife und die Harmonischen der Bewegungsenergie für den allgemeinen Fall

Zusammenfassung In Erg?nzung zu einer früheren Arbeit wird gezeigt, da? auch im allgemeinen Fall der Kopplung einer elliptischen Schleife mit einer Kreuzschleife—beschr?nkt auf symmetrische Bewegungsgesetze—die Fourierkoeffizienten bei der harmonischen Analyse der kinetischen Energie sich durch relativ einfache, geschlossene Ausdrücke darstellen lassen. Dabei wird einerseits das Superpositionsprinzip für elliptische Schleifen, andererseits die Methode der Partialbruchzerlegung herangezogen. Das Superpositionsprinzip führt auf zwei zugeordnete Kurbelschleifen mit den Parameternη ₁ undη ₂, und die hierdurch gegebenen wesentlichen M?glichkeiten der elliptischen Schleife mit schwingendem und mit umlaufendem Abtrieb sowie der “flachen” und der “steilen” Ellipse wurden, soweit diese Parameter reell sind, anschaulich durch zwei Fluchtentafeln wiedergegeben.     

Composites with piezoelectric thin fibers – first evidence of piezoelectric behavior

 The integration of functional components into composite materials is still a challenge for materials science. The integrated components themselves acting as sensor and/or as actuator should not interfere with the excellent mechanical properties of fiber-reinforced composite materials. Using this approach the implementation of ”one-dimensional”geometries – like fibers with small diameters – is recommended. Thin fibers consisting of piezoelectric materials like PZT are among the promising candidates offering the sensor/actuator coupling. Sol-gel processing is useful for fabricating PZT fibers thin enough to behave flexibly. Therefore, they offer the opportunity to make composite materials adaptive while maintaining the structural conformity. Sol-gel derived high-quality PZT fibers with diameters smaller than 30 μm have been successfully integrated into planar fiber architectures. Within them the fibers are oriented uni-directionally. These architectures are embedded with interdigital electrodes. After embedding the fiber/electrode architectures within glass fiber-reinforced polymers the fibers can be poled and become piezoelectric. The resulting structures were suitable to be tested as adaptive components. It has been demonstrated that such structures can detect impacts and tensions. They can also be driven actively leading to a vibration of the structure. Received: 21 July 1998 / Reviewed and accepted: 22 October 1998     

A Theory for the High-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> Cuprates: Anomalous Normal-State and Spectroscopic Properties,Phase Diagram,and Pairing

A theory of highly correlated layered superconducting materials is applied for the cuprates. Differently from an independent-electron approximation, their low-energy excitations are approached in terms of auxiliary particles representing combinations of atomic-like electron configurations, where the introduction of a Lagrange Bose field enables treating them as bosons or fermions. The energy spectrum of this field accounts for the tendency of hole-doped cuprates to form stripe-like inhomogeneities. Consequently, it induces a different analytical behavior for auxiliary particles corresponding to “antinodal” and “nodal” electrons, enabling the existence of different pairing temperatures at T ^∗ and T _c . This theory correctly describes the observed phase diagram of the cuprates, including the non-Fermi-liquid to FL crossover in the normal state, the existence of Fermi arcs below T ^∗ and of a “marginal-FL” critical behavior above it. The qualitative anomalous behavior of numerous physical quantities is accounted for, including kink- and waterfall-like spectral features, the drop in the scattering rates below T ^∗ and more radically below T _c , and an effective increase in the density of carriers with T and ω, reflected in transport, optical and other properties. Also is explained the correspondence between T _c , the resonance-mode energy, and the “nodal gap”.     

Fibre reinforced concrete: new design perspectives

Although the use of Fibre Reinforced Concrete (FRC) for structural applications is continuously increasing, it is still limited with respect to its potentials, mainly due to the lack of International Building Codes for FRC structural elements. Within fib (Féderation Internationale du Béton), the Special Activity Group 5 is preparing a New fib Model Code that aims to update the previous CEB-FIP Model Code 90, published in 1993, that can be considered as the reference document for Eurocode 2. The New Model Code includes several innovations and addresses among other topics, new materials for structural design. In this respect, FRC will be introduced. The Technical Groups fib TG 8.3 “Fibre reinforced concrete” and fib TG 8.6 “Ultra high performance FRC” are preparing some sections of the New Model Code, including regular and high performance FRC. This paper aims to briefly explain the main concepts behind the structural rules for FRC structural design.     

Multi-scale computational method for elastic bodies with global and local heterogeneity

A multi-scale computational method using the homogenization theory and the finite element mesh superposition technique is presented for the stress analysis of composite materials and structures from both micro- and macroscopic standpoints. The proposed method is based on the continuum mechanics, and the micro–macro coupling effects are considered for a variety of composites with very complex microstructures. To bridge the gap of the length scale between the microscale and the macroscale, the homogenized material model is basically used. The classical homogenized model can be applied to the case that the microstructures are periodically arrayed in the structure and that the macroscopic strain field is uniform within the microscopic unit cell domain. When these two conditions are satisfied, the homogenization theory provides the most reliable homogenized properties rigorously to the continuum mechanics. This theory can also calculate the microscopic stresses as well as the macroscopic stresses, which is the most attractive advantage of this theory over other homogenizing techniques such as the rule of mixture. The most notable feature of this paper is to utilize the finite element mesh superposition technique along with the homogenization theory in order to analyze cases where non-periodic local heterogeneity exists and the macroscopic field is non-uniform. The accuracy of the analysis using the finite element mesh superposition technique is verified through a simple example. Then, two numerical examples of knitted fabric composite materials and particulate reinforced composite material are shown. In the latter example, a shell-solid connection is also adopted for the cost-effective multi-scale modeling and analysis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Superconductivity and Structure

The degree of the isolation of the CuO₂ planes (e.g. distance or bond valence to the apical coordination) has been shown by quantitative algorithms to be the major factor in determining aspects of the doping curves. They include the magnitude of the optimal number of doped holes (h_op) and the corresponding T _cop. It is shown that the roots of these phenomenological laws lie in a related structural dependence of super-exchange. The latter is expressed in the pseudo-gap or Neel temperature of the undoped parent compound. A fruitful language can be developed which deals with a buildup of complex quantum chemical features by bringing two holes into vicinity of a super-exchange O, forming a “local” Cu₂O₇ pair. Structural considerations also dictate that stress is relieved by alternate orthogonal pair orientation. This leads to plaid patterns with primary and secondary channels of charge. The presence of these two types of charge channels is involved in the mechanism of superconducting charge transport. Similar structuring of doped charge into plaid patterns of “local” pairs has been proposed for “all” high T _c superconductivity. STM now gives pictorial representation of the remnants of such an electronic crystal structure. The response of these bond-ordering motifs to structural details is further discussed. These ideas supply organization to the manifold experimental situation and provide opportunities for a unifying theory for high T _c superconductivity in terms of real space structuring of “local” pairs, largely on crystal-chemical principles.     

Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations

We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of coercive elliptic partial differential equations with affine (input) parameter dependence. The critical ingredients are: reduced-basis approximation to effect significant reduction in state-space dimensionality; a posteriori error bounds to provide rigorous error estimation and control; “offline/online” computational decompositions to permit rapid evaluation of output bounds, output bound gradients, and output bound Hessians in the limit of many queries; and reformulation of the approximate optimization statement to ensure (true) feasibility and control of suboptimality. To illustrate the method we consider the design of a three-dimensional thermal fin: Given volume and power objective-function weights, and root temperature “not-to-exceed” limits, the optimal geometry and heat transfer coefficient can be determined—with guaranteed feasibility—in only 2.3 seconds on a 500 MHz Pentium machine; note the latter includes only the online component of the calculations. Our method permits not only interactive optimal design at conception and manufacturing, but also real-time reliable adaptive optimal design in operation.     

Time dependent behavior of elements combining ultra-high performance fiber reinforced concretes (UHPFRC) and reinforced concrete

Structural elements combining Ultra-High Performance Fiber Reinforced Concretes (UHPFRC) and concrete offer a high potential in view of rehabilitation and modification of existing structures. The investigation of the time-dependent behavior of composite “UHPFRC-concrete” elements is a fundamental step in the determination of durability and serviceability. For this, an experimental program was conducted on large composite “UHPFRC-concrete” beams and a numerical model was validated with the test results. The experimental results and a parametric study performed with the numerical model showed that UHPFRC and normal strength reinforced concrete are compatible in the long-term and that the critical period of composite “UHPFRC-concrete” elements are the first 90 days after the casting of the UHPFRC layer. Thus, the high potential of such composite elements can be exploited also in the long term.     

Evolution of a Network of Vortex Loops in the Turbulent Superfluid Helium; Derivation of the Vinen Equation

The evolution a network of vortex loops due to the fusion and breakdown in the turbulent superfluid helium is studied. We perform investigation on the base of the “rate equation” for the distribution function n(l) of number of loops in space of their length l. There are two mechanisms for change of quantity n(l). Firstly, the function changes due to deterministic process of mutual friction, when the length grows or decreases depending on orientation. Secondly, the change of n(l) occurs due to random events when the loop crosses itself breaking down into two daughter or two loops collide merging into one larger loop. Accordingly the “rate equation” includes the “collision” term collecting random processes of fusion and breakdown and the deterministic term. Assuming, further, that processes of random colliding are fastest we are in position to study more slow processes related to deterministic term. In this way we study the evolution of full length of vortex loops per unit volume—so-called vortex line density ℒ(t). It is shown this evolution to obey the famous Vinen equation. In conclusion we discuss properties of the Vinen equation from the point of view of the developed approach.     

Nonequilibrium Casimir force on a particle in cold vacuum background near a heated plate

General expressions for a nonequilibrium Casimir force in a stationary situation for the “small particle-plate” system with arbitrary local dielectric properties of materials are obtained for the given particle (T ₁) and plate (T ₂) temperatures and a “cold” (T ₃ = 0) vacuum background over the plate.     

New composite sorbents of water and ammonia for chemical and adsorption heat pumps

New sorbents of water and ammonia — “salt in porous matrix” composites and “salt on fiber” composites — have been reviewed. The possibility of “constructing” the sorption properties of the composites at the nanophase level by varying their composition, the size of the host-matrix pores, and synthesis conditions has been shown. The application of the new materials in adsorption refrigerating devices has been considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 6, pp. 160–175, November–December, 2006.     

Framework flexibility of sodium zirconium phosphate: role of disorder, and polyhedral distortions from Monte Carlo investigation

A detailed Monte Carlo investigation of the structural changes of the framework of sodium zirconium phosphate, [Zr₂P₃O₁₂]⁻,—NASICON (acronym for Na-SuperIonic CONductor)—accommodating alkali ions of varying sizes (Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺) is carried out over a range of temperatures. Simulation results are critically compared with the structural models proposed earlier and available experimental results. Anisotropic changes of the rhombohedral cell parameters—a contracts while c expands with the size of the alkali ion substituted—is observed in good agreement with previous experimental results. The mechanism of anisotropic variation of lattice parameters involves dominantly, coupled rotations of the polyhedra as proposed by Alamo and co-workers. It is, however, observed that the distortions of the PO₄ tetrahedra and ZrO₆ octahedra are significant, and accounts for nearly one-third of the total change in a and c—parameters as the size of the alkali ion increases. This suggests that ‘rigid’ polyhedral models, permitting only angular distortions of the polyhedra, are of limited quantitative applicability in these solids. The same mechanism is found to be responsible for the low/anisotropic thermal expansion of these solids. Evidence that the polyhedral rotations are dynamic, opposed to a static-frozen-in disorder, is provided.     

Multiscale finite element method for a locally nonperiodic heterogeneous medium

A generalization of the mathematical homogenization theory to account for locally nonperiodic solutions is presented. Such nonperiodicity may arise either due to the rapidly varying microstructure (e.g.: graded materials, microcracks) or because the macroscopic solution is not smooth and may have significant variation within a microstructure. In the portion of the problem domain where the material is formed by a spatial repetition of the base cell and the macroscopic solution is smooth, a double scale asymptotic expansion and solution periodicity are assumed, and consequently, mathematical homogenization theory is employed to uncouple the microscopic problem from the global solution. For the rest of the problem domain it is assumed that the periodic solution does not exist (cutouts, cracks, free edges in composites, etc.) and the approximation space is decomposed into macroscopic and microscopic fields. Compatibility between the two regions is explicitly enforced. The proposed method is applied to resolve the structure of the microscopic fields in the single ply composite plates with a centered hole and with a centered crack and in the [0/90] _s laminated plate. Numerical results are compared to the reference solution, an engineering global-local approach, and the direct extraction from the mathematical homogenization method.     

The study of lifetime of polymer and composite bone joint screws under cyclical loads and <Emphasis Type="Italic">in vitro</Emphasis> conditions

The “strain-life time” method has been adapted for life-time prediction of polymer and composite bone joint screws. Mechanical and fatigue properties of screws made of biostable (polysulfone), biosorbable (poly(lactide-co-glycolide) and short carbon fibre reinforced polymer composite materials have been examined in this study. The lifetime predictions under in vitro conditions were calculated for polymer and composite implants. The forecasting of joint screws stability under conditions close to natural body environment is shown to be feasible based on equations describing lifetime of the examined joint screws.     

Possible Implications of the Principle of the ‘<Emphasis Type="Italic">Mise en Pratique</Emphasis>’ in its Application to the Kelvin

In 2005, the CIPM, in accepting CCT Recommendation T3, made a substantial change in the definition of the quantity ‘temperature’ by transforming the written standards for temperature (the “temperature scales”) into implementations of the mise en pratique of the kelvin. Having considered “that the creation of a formal mise en pratique of the definition of the kelvin would considerably simplify and clarify statements and recommendations of the CCT concerning the realization of the definition of the kelvin and the implementation of practical temperature scales,” the CIPM decision transformed the present ITS-90 and PLTS-2000 into two ways to implement the mise en pratique, with the possibility to further define “in due course” in the mise en pratique “recommendations concerning the direct determination of thermodynamic temperature.” The paper presents the author’s views regarding possible implications for the concept of a mise en pratique when applied to the kelvin beyond the present implementation. One possibility is to promote the formal use and status of realizations of the thermodynamic scale that, in practice, today only represents the physical basis of an empirical scale like the ITS-90. Another path arises from assuming that the only technical limit placed on the addition of further methods to the mise en pratique is that they be compatible with one another, to avoid ambiguities in the definition of the temperature values, though without the constraint of having the same, or comparable, accuracy. As a consequence, other scales that are currently considered ‘approximations’ to the ITS-90, with no formal status other than possibly being ‘recommended’ by some official body, such as the CCT WG2, could be upgraded to implementations of the mise en pratique, though with accuracy—and precision—inferior to that of the ITS-90. This would assist the vast majority of the users of temperature scales, and could be expected to increase the support of the worldwide thermal community for the work performed by the CCT. This possibility has so far been prevented by the need to define a single written standard at only the highest state-of-the-art accuracy level, the rest being left to sparse efforts, often devoid of traceability to the written standard.