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  • 1
    Electronic Resource
    Electronic Resource
    The shakedown load boundary of an elastic-perfectly plastic structure (1995)
    Springer
    Meccanica 30 (1995), S. 155-174 
    Details
    ISSN: 1572-9648
    Keywords: Shakedown theory ; Cyclic loads ; Structural plasticity ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Nell'ipotesi di piccoli spostamenti e di plasticità perfetta, si studiano le proprietà geometrico-meccaniche della frontiera del dominio dei carichi di adattamento. Si mostra come, nello spazio dei carichi, la suddetta frontiera giuoca il ruolo di superficie di plasticizzazione ed un particolare vettore di deformazione plastica accumulata—che caratterizza il meccanismo di non adattamento—segue la legge della normalità, mentre una forma specifica del teorema del massimo lavoro plastico costituisce un valido strumento per la valutazione del carico limite corrispondente ad un dato meccanismo di non adattamento. Si forniscono altresì le equazioni che governano lo stato della struttura al limite di adattamento, mostrando la capacità del relativo meccanismo di collasso a rappresentare la risposta a lungo termine della struttura a dei carichi periodici inviluppanti il dominio dei carichi con una intensità un poco al di sopra del limite di adattamento.
    Notes: Abstract In the hypothesis of small displacements and combined time-variable/steady loads, the geometrical-mechanical properties of the shakedown load boundary are investigated. It is shown that, in the load space, the shakedown load boundary plays the role of yield surface, and that a certain plastic strain accumulation vector—characterizing some impending inadaptation collapse mechanism—obeys the normality rule, whereas a specific form of the maximum plastic work theorem constitutes an effective tool for the evaluation of the shakedown limit load corresponding to a specified inadaptation collapse mode. The equations governing the state of the structure at the shakedown limit are provided and the related collapse mechanism is shown to specify the shape of the steady-state response of the structure to a periodic load enveloping the load domain with an intensity slightly above the shakedown limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00990454
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  • 2
    Electronic Resource
    Electronic Resource
    Mohr's arbelos (1995)
    Springer
    Meccanica 30 (1995), S. 417-424 
    Details
    ISSN: 1572-9648
    Keywords: Mohr's circles ; Stress representation ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si ottiene la classica rappresentazione di O. Mohr dello stato tensionale con i metodi del calcolo di estremi condizionati.
    Notes: Abstract The classical representation of the stress state due to O. Mohr is obtained by using the calculus of constrained extrema.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00993424
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  • 3
    Electronic Resource
    Electronic Resource
    Some examples of electron microscopy studies of microstructures and phase transitions in solids (1995)
    Springer
    Meccanica 30 (1995), S. 433-438 
    Details
    ISSN: 1572-9648
    Keywords: Electron microscopy ; Microstructures ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si presentano i risultati di alcuni studi fatti attraverso la microscopia elettronica sulle microstrutture relative a transizioni di fase in una varietà di materiali. I casi comprendono leghe binarie e ternarie, superconduttori TC e materiali C60 e C70; le transizioni esaminate sono diffusionali, displacive o di entrambi i tipi.
    Notes: Abstract In this contribution the results of some electron microscopy studies on microstructures related with phase transitions in a variety of materials will be presented. The materials include binary and ternary alloys, high TC superconductors as well as C60 and C70 fullerenes, while the transitions can be diffusional, displacive or both.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557075
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear dynamics and stability of microstructures in a lattice model for ferroelastic materials (1995)
    Springer
    Meccanica 30 (1995), S. 449-458 
    Details
    ISSN: 1572-9648
    Keywords: Lattice ; Nonlinear waves ; Ferroelasticity ; Phase transformations ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si propone un modello reticolare che può descrivere complessi arrangiamenti fatti di domini elastici ed interfacce. Sulla base di un modello bidimensionale in cui sono presenti interazioni contrastanti e nonlineari si esamina la dinamica della formazione di microstrutture. L'accento è posto sui meccani'smi di instabilità che determinano bande di deformazione localizzata. Si studia l'influenza delle forze applicate e degli effetti dissipativi sulla dinamica di due bande perpendicolari e si interpretano i risultati come un microtwinning in leghe cristalline. Si verificano le congetture fisiche per mezzo di simulazioni numeriche del modello microscopico.
    Notes: Abstract With the view of understanding how precise macroscopic properties of a material emerge from the underlying physics of homogeneous microstructures, a lattice model which can describe complex non-linear patterns made of elastic domains and interfaces is proposed. On the basis of a two-dimensional lattice model involving non-linear and competing interactions the dynamics of microstructure formation is examined. The emphasis is placed especially on an instability mechanism of a strain band producing localized domains. The influence of applied forces and dissipative effects on the dynamics of two perpendicular strain bands is studied. The results are interpreted as a microtwinning in crystalline alloys. The physical conjectures are checked by means of numerical simulations performed directly on the microscopic system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557077
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  • 5
    Electronic Resource
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    Martensitic transformation and phonon localization in Ni-Al alloys by atomistic simulations (1995)
    Springer
    Meccanica 30 (1995), S. 439-448 
    Details
    ISSN: 1572-9648
    Keywords: Martensitic transformation ; Atomistic simulation ; Phonon localization ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario L'articolo discute un modello ‘Embedded Atom’ per l'energia potenziale di leghe Ni-Al. Il potenziale viene utilizzato in uno studio di Dinamica Molecolare e nell'approssimazione Quasi Armonica della Transformazione Martensitica (MT) che ha luogo in Ni x Al1−x per 0.61〈x〈0.64 a una temperatutaT M compresa tra ~ 0 K perx=0.61 e ~ 400 K perx=0.64. La temperature di transizione è determinata in funzione della composizione e della pressione. I risultati dimostrano la validità del potenziale nel riprodurre le proprietà note della lega. Il modello viene utilizzato per studiare la dinamica microscopica alla base della trasformazione. Lo studio mostra che nella austenite il disordine chimico legato alla non-stechiometria induce bande di fononi localizzati che si delocalizzano in modo discontinue allaMT. Viene mostrato che i modi localizzati sono associati a regioni rieche di Ni ed individuano siti di incipiente instabilità reticolare. Tali siti forniscono centri preferenziali per la nucleazione.
    Notes: Abstract We discuss an atomistic model for the potential energy of Ni-Al alloys based on the Embedded Atom Method. The potential is applied in a Molecular Dynamics and Quasi Harmonic investigation of the Martensitic Transformation (MT) that occurs in Ni x Al1− x for compositions 0.61〈x〈0.64 at a temperatureT M ranging from ~ 0 K atx=0.61 to ~ 400 K atx=0.64. We determine the transition temperature as a function of composition and pressure and we show that our potential reliably reproduces the known properties of the alloy. We exploit the model to investigate the microscopic dynamical properties underlying the transition. Our computation shows that in the austenite the compositional disorder induces several bands of localized phonons, that discontinuously de-localize at the MT. We show that specific localized modes associated with Ni-rich clusters identify regions of incipient lattice instability, and provide favourable sites for the nucleation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557076
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  • 6
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    Internal loops in pseudoelastic behaviour of Ti-Ni shape memory alloys: Experiment and modelling (1995)
    Springer
    Meccanica 30 (1995), S. 459-466 
    Details
    ISSN: 1572-9648
    Keywords: Shape memory alloys ; Titanium-nickel ; Pseudoelasticity ; Martensitic transformation ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Per leghe Ti-Ni con memoria di forma vengono analizzati i cicli di isteresi isotermici tensione-deformazione prodotti da una incompleta trasformazione martensitica. Gli esperimenti mostrano l'esistenza di due distinte linee di snervamento per la transizione di fase, una verso la trasformazione austenite→martensite (A→M), l'altra per la trasformazione inversa M→A. Il comportamento a trazione di un singolo cristallo con una sola linea di snervamento (A↔M) [1], può essere considerato un caso ideale. L'estensione ad un modello termodinamico pseudo-elastico [2] consente di analizzare queste due linee di snervamento.
    Notes: Abstract The stress-strain isothermal hysteresis loops due to the incomplete martensitic transformation are analysed for Ti-Ni shape memory alloys. Experiments show the existence of two distinct yield lines for phase transition; one for the forward transformation austenite→martensite (A→M), the other for the reverse transformation M→A. The tensile behaviour of single crystals with only one yield line (A↔M) [1] can be considered as an ‘ideal’ case. An extension of a thermodynamic model for pseudoelasticity [2] allows these two yield lines to be taken into account.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557078
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  • 7
    Electronic Resource
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    Beyond young measures (1995)
    Springer
    Meccanica 30 (1995), S. 505-526 
    Details
    ISSN: 1572-9648
    Keywords: Young measures ; H-measures ; Microstructures ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si discutono le misure di Young e le loro limitazioni. Alcune relazioni che intercorrono tra le misure di Young e le H-misure sono descritte ed utilizzate nello studio di un esempio tratto dalla meccanica di mezzi micromagnetici. Si evidenzia in particolare la necessità di migliorare la teoria delle H-misure e di altre misure semi-classiche.
    Notes: Abstract Young measures and their limitations are discussed. Some relations between Young measures and H-measures are described and used to analyze an example from micromagnetics. The need to improve H-measures and semi-classical measures is stressed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557082
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  • 8
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    The step-wise martensite to austenite reversible transformation (1995)
    Springer
    Meccanica 30 (1995), S. 495-503 
    Details
    ISSN: 1572-9648
    Keywords: Martensitic transformation ; Shape memory alloys ; Transformation kinetics ; Phase transformations ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Con l'acronimo di SMART (step-wise martensite to austenite reversible transformation) si indica una trasformazione martensitica termoelastica in cui la cinetica di trasformazione risulta modificata dall'esecuzione di un'appropriata procedura di ciclaggio termico parziale (procedura ICH — Incomplete Cycle on Heating) nell'intervallo di temperatura in cui ha luogo la trasformazione martensitica inversa. Vengono qui presentati i risultati sperimentali relativi sia alla SMART sia agli effetti indotti dalla procedure ICH e responsabili delle modifiche della cinetica di trasformazione. Vengono inoltre discusse le ipotesi sino ad ora avanzate per spiegare i risultati sperimentali.
    Notes: Abstract The step-wise martensite to austenite reversible transformation (SMART) in shape memory alloys (SMA) is a martensitic thermoelastic transformation where a step-wise kinetics is induced by a partial cycling procedure within the hysteresis cycle (incomplete cycle on heating (ICH) procedure). The ICH procedure has been proved effective in inducing a reversible microstructural modification of the martensitic phase. Results till now obtained both on the SMART behaviour and on the effects of the ICH procedure are reviewed here: the hypotheses advanced till now are discussed to explain experimental evidences.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557081
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  • 9
    Electronic Resource
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    A Classification of thermodynamical potentials for two-variable transition systems (1995)
    Springer
    Meccanica 30 (1995), S. 475-494 
    Details
    ISSN: 1572-9648
    Keywords: Thermodynamical potential ; Nonconvex energy ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario II lavoro suggerisce una possibile classificazione dei potenziali termodinamici per sistemi con due variabili di stato soggetti a transizioni di fase e, per ogni classe individuata, mostra le caratteristiche e i diagrammi tipici dell'energia interna, l'entalpia, le energie libere di Helmholtz e Gibbs. Potenziali termodinamici a più valori appaiono essere la regola più che l'eccezione. Nell'ambito della classificazione trovata sono studiati vari esempi noti, come il gas di van der Waals e il modello di Landau-Devonshire.
    Notes: Abstract We suggest here a possible classification of the thermodynamical potentials for phase transition systems with two state variables. Within each of the single-typed classes, the characters and typical diagrams of the internal energy, enthalpy, Helmholtz and Gibbs free energy are shown. Multivalued potentials appear to be the rules rather than the exceptions. Several known examples of phase transitions, e.g. van der Waals gas, Landau-Devonshire model, are studied within the framework of the present classification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557080
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  • 10
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    The influence of surface energy on stress-free microstructures in shape memory alloys (1995)
    Springer
    Meccanica 30 (1995), S. 527-539 
    Details
    ISSN: 1572-9648
    Keywords: Microstructures ; Shape memory alloys ; Variational methods ; Surface energy ; Phase transformations ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Certe leghe come quelle di In-Tl, Ni-Ti, Ag-Cd o Cu-Al-Ni mostrano proprietà meccaniche notevoli quali la memoria di forma o la pseudoelasticità. Questo comportamento è determinato da una trasformazione di fase solido-solido che conduce a complicati arrangiamenti a livelo microscopico. In studi recenti tali microstrutture sono state analizzate attraverso la minimizzazione dell'energia elastica. Noi discutiamo l'influenza di termini addizionali di energia superficiale sull'esistenza di microstrutture in uno stato naturale sia in un contesto lineare che non lineare.
    Notes: Abstract Certain alloys such as In-Tl, Ni-Ti, Ag-Cd or Cu-Al-Ni display remarkable mechanical properties such as the shape memory effect or pseudo-elasticity. This behaviour is related to a solid-solid phase transformation which leads to a complicated microscopic arrangement of different phases. In recent studies such microstructures have been analyzed by the minimization of elastic energy. We discuss the influence of additional surface energy terms on the existence of stress-free microstructures both in the nonlinear and a geometrically linear setting.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557083
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  • 11
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    Phase transitions and hysteresis in nonlocal and order-parameter models (1995)
    Springer
    Meccanica 30 (1995), S. 541-565 
    Details
    ISSN: 1572-9648
    Keywords: Phase transitions ; Hysteresis ; Order-parameter ; Nonlocal equations ; Phase transformations ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Il lavoro descrive due tipi di regolarizzazione del problema quasistatico per un potenziale con due minimi in una dimensione. Un modello evidenzia caratteri di non località spaziale, mentre l'altro conduce ad una teoria con parametro d'ordine. Si derivano alcuni risultati di esistenza e regolarità e si presentano alcuni studi numerici che mostrano l'isteresi e il moto delle frontiere tra le fasi.
    Notes: Abstract The paper describes two types of regularization to the basic quasistatic double-well potential problem in one space dimension. One model features a spatially nonlocal term while the other incorporates the use of an order parameter. Some basic existence and regularity results for these modified models are derived and some numerical calculations that show hysteresis and motion of phase boundaries are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557084
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  • 12
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    A one-dimensional model for incoherent phase changes (1995)
    Springer
    Meccanica 30 (1995), S. 567-575 
    Details
    ISSN: 1572-9648
    Keywords: Incoherent phase transitions ; Vacancy diffusion in solids ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario In questo lavoro viene presentato un adattamento del modello di transizione di fase incoerente sviluppato da Gurtin e Cermelli in [3]. Una transizione incoerente è sempre associata alla produzione di un qualche tipo di difetto all'interfaccia: consideriamo qui un modello semplificato di continuo unidimensionale, in modo da poter studiare l'effetto dei difetti di volume (lacune) sull'evoluzione del sistema.
    Notes: Abstract We present here a simplified version of the model of incoherent solid-solid transitions with mass diffusion developed by Gurtin and Cermelli in [3]. An incoherent phase change is always associated with some kind of defect production at the interface: we consider here a one-dimensional continuum, so that the resulting equations allow study to be made of the influence of volume (vacancy) production on the evolution of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557085
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  • 13
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    Hysteresis and imperfection sensitivity in small ferromagnetic particles (1995)
    Springer
    Meccanica 30 (1995), S. 591-603 
    Details
    ISSN: 1572-9648
    Keywords: Imperfection sensitivity ; Hysteresis ; Local minimizers ; Variational methods ; Phase transformations ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si deducono i classici risultati di Stoner e Wohlfarth dalla teoria del micromagnetismo, e si dimostra la loro validità per la previsione di cicli di isteresi magnetica anche per particelle di forma non ellissoidale. Viene proposta, quale possibile spiegazione della notevole ampiezza dei cicli di isteresi caratteristici di particelle di piccole dimensioni, l'indifferenza alla presenza di rugosità superficiale.
    Notes: Abstract The classical results of Stoner and Wohlfarth for the prediction of hysteresis loops in small ferromagnetic particles are extended to specimens of non-ellipsoidal shape, and shown to be a consequence of micromagnetics. The insensitivity to surface roughness is proposed as a possible explanation of the high coercivity behavior of small particles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557087
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  • 14
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    Smectic liquid crystals as continua with latent microstructure (1995)
    Springer
    Meccanica 30 (1995), S. 621-627 
    Details
    ISSN: 1572-9648
    Keywords: Liquid crystals ; Smectics ; Nematics ; Continuum models ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario I cristalli liquidi smettici sono quasi-solidi che possiedono una microstruttura sia di tipo materiale che locale (la microstruttura nematica e le lamelle, rispettivamente). Essi esibiscono anche transizioni di fase: smettici B a smettici A, a nematici, a liquidi isotropi. Il loro studio, sebbene speciale, potrebbe evidenziare vantaggi generali e difetti di vari tipi di modelli matematici. Qui, nel provare la proprietà annunciata nel titolo, si prepara il lavoro di base per il modello continue.
    Notes: Abstract Smectic liquid crystals are quasi solids, which possess microstructure both of the material and local type (the nematic mictrostructure and the lamellae, respectively). They also exhibit phase transitions: from smectic B to smectic A, to nematic, to isotrtopic liquid (see [1], Ch. 7). Their study, though special, might show up general advantages and drawbacks of different types of mathematical models. Here, while intent on proving the property announced in the title, we set forth the groundwork for the continuum model (see, in a more specific and concrete mode [2]).
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    URL: http://dx.doi.org/10.1007/BF01557089
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  • 15
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    Inertial and self interactions in structured continua: Liquid crystals and magnetostrictive solids (1995)
    Springer
    Meccanica 30 (1995), S. 629-640 
    Details
    ISSN: 1572-9648
    Keywords: Liquid crystals ; Magnetostrictive solids ; Continua with microstructure ; Phase transformations ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si discutono equazioni di evoluzione per cristalli liquidi e per solidi magnetostrittivi nell'ambito di una teoria dei continui con microstruttura che contempla la possibilità sia di autointerazioni meccaniche che di termini inerziali non standard.
    Notes: Abstract Evolution equations for liquid crystals and for magnetostrictive solids are discussed within the framework of a theory of continua with microstructure that allows for mechanical self-interactions and non-standard inertial terms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557090
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  • 16
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    The dynamics of configurational forces at phase-transition fronts (1995)
    Springer
    Meccanica 30 (1995), S. 605-619 
    Details
    ISSN: 1572-9648
    Keywords: Thermoelasticity ; Dynamics ; Configurational forces ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si osserva preliminarmente che, per alcune trasformazioni di fase nei solidi, la più naturale descrizione del fenomeno nell'ambito del continuo sembra essere quella basata sul moto inverse in dinamica, o sulla deformazione inversa in statica. In tale quadro, la nozione di ‘coerenza di fase’, suggerita dalla congruenza geometricocinematica tra due distinti reticoli cristallini a contatto, trova la sua espressione più significativa nella condizione di continuità degli ‘spostamenti di siti’ nel riferimento cristalline. Sulla base di argomentazioni svolte in precedenti lavori dagli autori per il caso dinamico e da M. Epstein per il caso statico e termostatico, si presuppone valida un'equazione di bilancio ‘materiale’: quella dellapseudo-quantità di moto. Si richiede che tale bilancio sia soddisfatto attraverso una superficie di contatto tra le due fasi. Tale superficie o fronte, avanzando, determina la trasformazione del materiale da una fase nell'altra. Il fronte è suppostoomotermo ed il materiale termoelastico in ciascuna delle due fasi. Un ruolo chiave è svolto dal tensore degli sforzi materiali di Eshelby. Infatti, la potenza sviluppata dalle forze di disomogeneità attraverso il fronte che avanza è unicamente determinata dalla discontinuità del tensore di Eshelby lungo la normale al fronte. Inoltre, l'espressione che detta potenza assume permette di evidenziare una quantità scalare che proponiamo di denominareforza configurazionale di Hugoniot-Gibbs per le analogie che essa suggerisce. Si sviluppa infine una trattazione parallela sulla base di una formulazione termodinamica classica del continuo. Un confronto dei risultati permette di Stabilire che la potenza sviluppata dalla forza configurazionale viene dissipata mentre il fronte avanza.
    Notes: Abstract First we recognize that the coherence of certain phase transformations in solids is most vividly expressed using the material manifold and within the kinematic continuum description based on the so-calledinverse motion. In this fully dynamical framework the equation of interest is theun-balance of pseudomomentum for thermoelastic conductors. On computing the power developed by the accompanying surface source of quasi-inhomogeneities at the phase-transition front, we show that this relates directly to the normal jump of the Eshelby stress — devoid of any kinetic energy, but computed from the free energy — a scalar quantity which may be referred to as theHugoniot-Gibbs configurational force at the front. The thermodynamic analysis also establishes that this power is dissipated as the material progresses at the front that ishomothermal. The jump relation including this dissipation is that associated with the heat propagation equation valid at regular points. In all, this approach is based on the theory of material uniformity and inhomogeneities as developed in recent years by M. Epstein and the authors. All reasonings are made in full dynamics, for finite strains, and any anisotropy in three dimensions.
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    Finite-scale microstructures and metastability in one-dimensional elasticity (1995)
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    Meccanica 30 (1995), S. 577-589 
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    ISSN: 1572-9648
    Keywords: Microstructures ; Interface energy ; Non convex variational problems ; Phase transitions ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Il lavoro riguarda la non unicità messa in luce da J.L. Ericksen nella sua analisi dell'equilibrio di barre elastiche con energia non convessa. Seguendo le linee di precedenti lavori, per investigare questa degenerazione si ricorre ad una regolarizzazione del problema e si dà un esplicito quadro di riferimento per lo studio della ricca varietà delle microstrutture di scala finita e della loro stabilità. Si chiarisce in particolare il ruolo dell'energia di interfaccia nella creazione di microstrutture di scala finita considerando l'effetto combinato di termini inibitori e favorevoli all'insorgere di oscillazioni nel funzionale energia.
    Notes: Abstract This paper addresses the non-uniqueness pointed out by Ericksen in his classical analysis of the equilibrium of a one-dimensional elastic bar with non-convex energy [1]. Following some previous work in this area, we suitably regularize the problem in order to investigate this degenerancy. Our approach gives an explicit framework for the the study of the rich variety offinite-scale equilibrium microstructures for the bar in a hard loading device, and their stability properties. In this way we clarify the role of interfacial energy in creating finitescale microstructures, by considering the combined effect of the oscillation-inducing and oscillation-inhibiting terms in the energy functional.
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    A two-dimensional polycrystal model in a ‘deep’ space representation (1995)
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    Meccanica 30 (1995), S. 641-663 
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    ISSN: 1572-9648
    Keywords: Polycrystal ; Rate-independent plasticity ; Texture ; Phase transformations ; Solid mechanics
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Proponiamo un modello che collega la deformazione macroscopica all'evoluzione della tessitura cristallina. Questo modello si rifà a variabili microstrutturali per descriverelo stato ‘profondo’ del policristallo; le velocità di tali variabili entrano nell'espressione della potenza virtuale in uno con le microtensioni ad esse associate. Termini supplementari appropriati appaiono inoltre nelle equazioni di bilancio dell'energia e dell'entropia. Viene utilizzato il criterio di Schmid per i singoli sistemi di scivolamento per scrivere una delle equazioni costitutive necessarie. Viene quindi introdotto un assunto simile al criterio di Taylor-Bishop-Hill per i policristalli per mettere in relazione il gradiente di velocità e la velocità di rotazione del reticolo cristallino via la combinazione di scivolamenti attiva. Il modello viene applicato ad un esempio mostrando buon accordo con un policristallo piano alla Taylor per una scelta particolare dei legami costitutivi delle microtensioni.
    Notes: Abstract We propose a model which links macroscopic deformations with changes in crystalline texture. The model calls upon microstructural variables to describe the state of the polycrystal; their time-rates, together with the corresponding microstresses, enter the expression of virtual power. Appropriate supplementary terms also appear in the equations of balance of energy and entropy. Schmid's law for single slip systems is invoked to provide one of the additional constitutive equations. A constitutive statement similar to the Taylor-Bishop-Hill criterion for polycrystals is introduced to relate the velocity gradient and the lattice spin via the active spin combination. The model is applied to an example agreeing with a Taylor planar polycrystal for a particular choice of constitutive laws for the microstresses.
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    A new form of the coherency energy in pseudoelasticity (1995)
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    Meccanica 30 (1995), S. 467-474 
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    ISSN: 1572-9648
    Keywords: Pseudoelasticity ; Coherency ; Hysteresis ; Phase transitions ; Solid mechanics
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Nella modellazione delle trasformazioni martensitiche gioca un ruolo essenziale la rappresentazione dell'energia di coerenza tra le fasi. Seguendo una recente proposta di Rogers, in questo lavoro si investiga una forma di tale energia che dipende dalla deformazione di trasformazione.
    Notes: Abstract In some previous papers [1], [2] pseudoelasticity in tensile experiments has been treated thermodynamically under the assumption that the relevant constitutive ingredients are (i) a non-convex free energy; (ii) coherency between the austenitic and martensitic phase. The form of the coherency energy was assumed to be proportional to the product of phase fractions of the two phases. Recently Rogers [3] has proposed a slight variation of this ansatz: The factor of proportionality should depend on the transformation strain. This new form of coherence energy is investigated in this paper. An attractive feature of this new assumption is that the strains of the coexisting phases in equilibrium remain unchanged as the transformation proceeds. The entropy production inside the pseudoelastic hysteresis is explored for various straight (P, d)-curves.
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    Braided Hopf algebras and differential calculus (1995)
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    Letters in mathematical physics 33 (1995), S. 33-38 
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    Keywords: 17B37 ; 81R50
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    Notes: Abstract We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross-product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf algebra can be reproduced by extending the exterior derivative to tensor products.
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    Lie groups whose coadjoint orbits are of dimension smaller or equal to two (1995)
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    Letters in mathematical physics 33 (1995), S. 183-186 
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    Keywords: 16W30 ; 17Bxx ; 17B05 ; 81R50
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    Notes: Abstract We give a complete classification of the class of connected, simply connected Lie groups whose coadjoint orbits are of dimension smaller or equal to two.
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    Integration over the group space of SUq(2), Clebsch-Gordan coefficients, and related identities (1995)
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    Letters in mathematical physics 33 (1995), S. 221-229 
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    Keywords: 81R50 ; 17B37
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    Notes: Abstract We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.
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    Fock spaces with generalized statistics (1995)
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    Letters in mathematical physics 33 (1995), S. 283-295 
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    Keywords: 81T05 ; 81R50 ; 81S05
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    Notes: Abstract Fock representations for quantum fields which obey generalized statistics are explicitly constructed. The main features of these representations are investigated.
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    Cohomology and deformation of Leibniz pairs (1995)
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    Letters in mathematical physics 34 (1995), S. 77-90 
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    Keywords: 16E40 ; 16W30 ; 17B37 ; 81R50
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    Notes: Abstract Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebraA together with a Lie algebraL mapped into the derivations ofA. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential.
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    BRST structures and symplectic geometry on a class of supermanifolds (1995)
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    Letters in mathematical physics 33 (1995), S. 207-219 
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    Keywords: 81R50 ; 17B37 ; 58A50 ; 81Q60
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    Notes: Abstract By investigating the symplectic geometry and geometric quantization of a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed andq-deformed cases in the classical as well as in the quantum cases.
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    A star-product approach to noncompact quantum groups (1995)
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    Letters in mathematical physics 33 (1995), S. 231-240 
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    Keywords: AMS classification 17B37 ; 16W30 ; 22D05 ; 46H99 ; 81R50
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    Notes: Abstract Using the duality and the topological theory of well-behaved Hopf algebras, we construct star-product models of noncompact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple Lie algebras. Our star-products act not only on coefficient functions of finite-dimensional representations, but actually on allC ∞ functions, and they even exist for nonlinear (semi-simple) Lie groups.
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    Projective quantum spaces (1995)
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    Letters in mathematical physics 35 (1995), S. 91-97 
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    Keywords: 81R50 ; 14M15 ; 14M17
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    Notes: Abstract Associated to the standard SU q (n) R-matrices, we introduce quantum spheresS q 2n-1 , projective quantum spaces ℂℙ q n-1 , and quantum Grassmann manifoldsG k(ℂ q n ). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzeziński and S. Majid.
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    Noncommutative symmetric functions and laplace operators for classical Lie algebras (1995)
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    Letters in mathematical physics 35 (1995), S. 135-143 
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    Keywords: 17B35 ; 17B37 ; 81R50
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    Notes: Abstract New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).
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    Bicovariant differential geometry of the quantum group SL h (2) (1995)
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    Letters in mathematical physics 35 (1995), S. 303-311 
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    Notes: Abstract There are only two quantum group structures on the space of two by two unimodular matrices, these are the SL q (2) and the SL h (2) quantum groups. The differential geometry of SL q (2) is well known. In this Letter, we develop the differential geometry of SL h (2), and show that the space of left invariant vector fields is three-dimensional.
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    Quantum algebras for maximal motion groups ofN-dimensional flat spaces (1995)
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    Letters in mathematical physics 33 (1995), S. 273-281 
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    Notes: Abstract An embedding method to getq-deformations for the nonsemisimple algebras generating the motion groups ofN-dimensional flat spaces is presented. This method gives a global and simultaneous scheme ofq-deformation for all iso(p, q) algebras and for those obtained from them by some Inönü-Wigner contractions, such as theN-dimensional Euclidean, Poincaré, and Galilei algebras.
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    GL q (N)-covariant braided differential bialgebras (1995)
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    Letters in mathematical physics 33 (1995), S. 297-302 
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    Keywords: 81R50
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    Notes: Abstract We study the possibility of defining the (braided) comultiplication for the GL q (N)-covariant differential complexes on some quantum spaces. We discover suchdifferential bialgebras (and Hopf algebras) on the bosonic and fermionic quantum hyperplanes (with additive coproduct) and on the braided matrix algebra BM q (N) with both multiplicative and additive coproducts. The latter case is related (forN = 2) to theq-Minkowski space andq-Poincaré algebra.
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    A quantum dual pair $$\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n $$ and the associated Capelli identity (1995)
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    Letters in mathematical physics 34 (1995), S. 1-8 
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    Notes: Abstract A quantum analogue of the dual pair $$\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n $$ is introduced in terms of the oscillator representation of U q $$(\mathfrak{s}\mathfrak{l}_2 )$$ . Its commutant and the associated identity of Capelli type are discussed.
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    Deformations of multiparameter quantum gl(N) (1995)
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    Letters in mathematical physics 34 (1995), S. 25-36 
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    Keywords: 81R50 ; 70G50
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    Notes: Abstract Multiparameter quantum gl(N) is not a rigid structure. This Letter defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of the parameters. All the equivalence classes of first-order essential deformations are found, as well as a class of exact deformations. This work provides quantization of all the classical Lie bialgebra structures (constantr-matrices) found by Belavin and Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a cubic root of unity, stands out.
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    On the schwarz problem for the $$\widehat{{\text{su}}}_{\text{2}} $$ Knizhnik-Zamolodchikov equation (1995)
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    Letters in mathematical physics 35 (1995), S. 123-134 
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    Keywords: 81T40 ; 81R10 ; 81R50
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    Notes: Abstract We study the monodromy representationsℬ k,Iof the mapping class groupℬ 4 acting on 4-point blocks satisfying the Knizhnik-Zamolodchikov equation for the levelk su2 current algebra. We classify all irreducibleℬ k,Iwhich are realized by finite groups; we also display finite irreducible components for the reducible representations corresponding tok = 10.
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    Coherent states of theq-Weyl algebra (1995)
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    Letters in mathematical physics 35 (1995), S. 179-185 
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    Keywords: 17B37 ; 33D80 ; 81R50
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    Notes: Abstract New coherent states of theq-Weyl algebraAA † −qA † A = 1,0 〈q 〈 1, are constructed. They are defined as eigenstates of the operatorA † which is the lowering operator for nonhighest weight representations describing positive energy states. Depending on whether the positive spectrum is discrete or continuous, these coherent states are related either to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of theq-Weyl algebra whenA † A ∞ d2/dx2 is used for illustrations.
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    q-transformation theory (1995)
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    Letters in mathematical physics 35 (1995), S. 221-227 
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    Keywords: 81R50 ; 81S05 ; 81P99
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    Notes: Abstract We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU q (2) algebra. To obtain transition probabilities, one must take the ‘Woronowicz square.’
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    The quantum super-Yangian and Casimir operators of Uq(gl(M |N)) (1995)
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    Letters in mathematical physics 33 (1995), S. 263-272 
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    Keywords: 17B37 ; 81R50 ; 17A70
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    Notes: Abstract TheZ 2 graded Yangian Yq(gl(M |N)) associated with the Perk-SchultzR matrix is introduced. Its structural properties, the central algebra in particular, are studied. AZ 2-graded associative algebra epimorphism Yq(gl(M |N)) → Uq (gl(M |N)) is obtained in explicit form. Images of central elements of the quantum super-Yangian under this epimorphism yield the Casimir operators of the quantum supergroup Uq(gl(M |N)) constructed in an earlier publication.
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    The two-dimensional Euclidean quantum algebra at roots of unity (1995)
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    Letters in mathematical physics 34 (1995), S. 37-48 
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    Keywords: 16S32 ; 81R50
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    Notes: Abstract The two-dimensional Euclidean quantum algebra is considered at roots of unity. The algebraic properties and the Poisson-Hopf structure are first investigated. We then determine the irreducible representations and study the reduction of the tensor product of two of them.
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    Transformation theory ofq-quantum mechanics (1995)
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    Letters in mathematical physics 34 (1995), S. 275-283 
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    Keywords: 81P99 ; 81R50 ; 81S05
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    Notes: Abstract Although there is no empirical motivation for replacing the commutators of dynamically conjugate operators in quantum mechanics byq-commutators, it appears possible to construct a consistent mathematical formulism based on this idea. To examine such a possibility further, we have studied the relation of this proposal to the Schwinger action principle, since the entire quantum mechanical formulism may be inferred from this principle. In particular, we have discussed the quantum transformation theory within this framework.
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    Interrelations between quantum groups and reflection equation (braided) algebras (1995)
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    Letters in mathematical physics 34 (1995), S. 333-341 
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    Notes: Abstract We show that the differential complex Ω B over the braided matrix algebra BM q (N) represents a covariant comodule with respect to the coaction of the Hopf algebra Ω A which is a differential extension of GL q (N). On the other hand, the algebra Ω A is a covariant braided comodule with respect to the coaction of the braided Hopf algebra Ω B . Geometrical aspects of these results are discussed.
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    Unitary group representations in fock spaces with generalized exchange properties (1995)
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    Letters in mathematical physics 35 (1995), S. 163-177 
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    Keywords: 81T05 ; 81R05 ; 81R50
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    Notes: Abstract We investigate the notion of secondR-quantization - a suitable deformation of the standard second quantization which properly takes into account the nontrivial exchange properties characterizing generalized statistics. We also perform theR-quantization of a class of unitary one-particle representations relevant for the description of symmetries. The Euclidean covariance of anyons is analyzed within this context.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750766
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