My activity deals with three complementary and concurrent lines of research summed up as follows: 1) classical micromechanics: generalizations and applications of the Eshelby theory, homogenization techniques, 2) multiphysics micromechanics: magnetoelectric multiferroic devices (combination of magnetoelastic and piezoelectric materials), 3) statistical mechanics of heterogeneous systems: theoretical and numerical study of thermo-elastic behavior of polymer chains and fiber bundles of biological interest.
The first line of research concerns the classical micromechanics, that is the analysis of the effective properties of heterogeneous materials (linear or non-linear, isotropic or anisotropic). Manufactured materials used both in industry and in our daily lives are very seldom homogeneous, and have complicated internal structures. The combination of two or more constituents to produce materials with desired properties has been exploited since ancient civilization and composite materials have found intensive application in contemporary technology. A way to obtain macroscopically desired responses is to enhance a material property by the addition of microscopic matter, i.e. to manipulate the microstructure. The link between the structures and the properties, therefore, plays a central role in the development of new materials and devices. This is the objective of micromechanics, which studies the interplay between micromorphology and properties of constituents for the development of mathematical models predicting the macro-properties. The classical Eshelby theory allows to calculate the elastic fields inside and outside an elastic inhomogeneity inserted into a homogeneous matrix. Indeed, when the inclusion and the matrix have a linear elastic behavior, and the medium is subjected to a uniform mechanical load, the stress and strain fields inside the inclusion are uniform. This result is the basis of most effective medium approximations that determine the behavior of a heterogeneous environment in terms of the nature of the heterogeneities and their interactions.
The second line deals with the multiphysics micromechanics, i.e. the analysis of heterogeneous systems which exhibit the coupling among different physical properties (thermo-magneto-electro-elastic coupling). In this context, I am not only interested in the determination of the effective properties but also in studying the dynamic and thermal behavior. In fact, there is an increasing need for a multidisciplinary, system-oriented approach to manufacturing nano-devices that exhibit specific functions and physical responses. Indeed, devices are rarely constructed of a single material, but rather a collection of materials, each providing a critical function and often working in conjunction with each other. To approach the problem, I introduced the combination of the Eshelby theory with the Landau-Lifchitz-Gilbert formalism and the Langevin/Fokker-Planck methodology. Only the combination of these methods allows the analysis of the behaviour of magnetoelastic (ferromagnetic) particles embedded in different matrices (e.g. piezoelectric). The Eshelby theory allows for the determination of all coupled fields within the particle, the Landau-Lifchitz-Gilbert equation describes the dynamics of the magnetization in single-domain ferromagnetic particles and, finally, the Langevin/Fokker-Planck methodology is able to take into account the thermal bath where the system is embedded and, therefore, to introduce the temperature in these systems. This research finds direct applications to the analysis of the stress-mediated magnetization switching in particles and the design of magnetoelectric memories. Moreover, the introduction of the statistical mechanics in these systems permits to analyze the thermal effects on the stress-mediated switching and on the memory stability (i.e. the determination of the probability error). Another application concerns the motion of domain wall in magnetoelastic materials driven by elastic fields.
The third line of research is devoted to the statistical mechanics of heterogeneous molecular systems. When the structure of the heterogeneous systems is displayed at the nanoscopic scale, the homogenization schemes used in the previous two activities cannot be applied directly and we are forced to use the statistical mechanics to describe the underlying physics. As an example of this approach, I performed the theoretical and numerical study of the thermo-elastic behavior of polymers of biological interest. The thermoelasticity of a polymeric chain is studied with a uniform tension (generated by an applied force) or a non-uniform tension (generated by an external field). Analytical solutions, as well as molecular dynamics Monte Carlo simulations, are developed starting from two different classical models: the freely-jointed chain (FJC), and the worm-like chain (WLC). It is found that when the thermodynamic limit is not satisfied (limited number of monomers), different elastic behaviors can be observed by changing the boundary conditions (Helmholtz isometric ensemble or Gibbs isotensional one), showing the fascinating complexity of the small systems thermodynamics. I also studied the equivalence of the two ensembles when the number of monomers approaches infinity. The observed complexity is even more suggestive when we look at the behavior of bistable molecules whose domains have transitions between two stable states. This system can show cooperative or non-cooperative responses, according to the statistical ensemble considered. These theories have been generalized to study the response of bundles of fibers and applied for studying the degradation of fiber bundles subjected to the action of external fields (for example the degradation of DNA bundles is useful to better understand the effect of ionizing radiations used for cancer therapy).
Meccanica dei solidi continui in regime lineare elastico
Colombo Luciano, Giordano Stefano.
2007, ISBN: 978-88-470-0697-3
La meccanica dei solidi rappresenta un corpus di conoscenze di formidabile robustezza concettuale, di raffinata eleganza matematico-formale e di grandissima utilità applicativa. Come tale ha una valenza formativa molto forte in diversi campi delle scienze naturali (fisica della materia, scienza dei materiali), ingegneristiche (scienza delle costruzioni, ingegneria strutturale e meccanica) e matematiche (matematica applicata).
La teoria della elasticità costituisce inoltre uno dei punti-cardine su cui si articola il moderno paradigma di ricerca detto "modellazione multi-scala dei materiali", secondo il quale le proprietà di un materiale sono descritte tramite la concorrenza di metodi teorici affatto diversi: mentre alla nanoscala opera la meccanica quantistica, alla micro- e meso-scala opera il continuo. La conoscenza del continuo elastico abilita lo Studente di Fisica, di Scienza dei Materiali, di Matematica o l'Allievo Ingegnere a confrontarsi con questo moderno e affascinate strumento di ricerca sui materiali.
Questa opera introduce lo Studente alla teoria della elasticità attraverso la scelta di un numero selezionato di argomenti di paradigmatica importanza concettuale e tramite lo svolgimento di numerosi esercizi e problemi di approfondimento. Gli argomenti spaziano dalle proprietà formali dei tensori di sforzo e deformazione, alla teoria del continuo elastico lineare, alla termodinamica delle deformazioni, alla propagazione di onde elastiche, alla teoria della frattura fragile in regime lineare elastico.
Gli ultimi due capitoli del libro presentano in modo didatticamente accessibile la sofisticata teoria di Eshelby, la cui conoscenza è molto importante sotto il profilo formativo. Tale teoria, infatti, ha un numero strabiliante di applicazioni pratiche e consente di unificare molti risultati del continuo elastico in un'unica struttura formale di validità generale.
Electronic version @ www.springerlink.com
Electronic version @ www.springerlink.com
Prof. Luciano Colombo, University of Cagliari, Italy.
Dr. Michele Brun, University of Cagliari, Italy.
Dr. Walter Rocchia, Istituto Italiano di Tecnologia (IIT), Genova, Italy.
Dr. Pierre-Michel Déjardin, LAMPS, Université de Perpignan Via Domitia.
Stefano Giordano
Chargè de Recherche (CRCN) CNRS
Fax :(+33) 03 20 19 79 84
Adresse email: Stefano.Giordano@univ-lille.fr
WEB: www.giordanostefano.it
IEMN UMR 8520 IEMN
Equipe: AIMAN - FILM (LEMAC-LICS)
Adresse postale
Laboratoire Central de l'IEMN-UMR 8520 CNRS
Avenue Poincarè - BP 69
59652 Villeneuve d'Ascq Cedex
France
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