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Madeo A.,University Claude Bernard Lyon 1 | Madeo A.,University of L'Aquila | Lekszycki T.,Polish Academy of Sciences | Lekszycki T.,University of L'Aquila | And 4 more authors.
Comptes Rendus - Mecanique | Year: 2011

We introduce a two-constituent porous continuum as a model describing the long-term growth/resorption phenomena in bone tissues grafted with bio-resorbable materials as driven by mechanical loads. The proposed model is able to account for the interplay between mechanical and biological phenomena which are known to be important for the bone tissue synthesis and the resorption of both bone tissue and bio-material. In particular, in the presented model the Lagrangian apparent mass densities of the natural bone and of the artificial material evolve in time according to precise ordinary differential equations. These latter are obtained by postulating a growth/resorption law and suitable constitutive equations conceived to account for the influence on bone resorption and synthesis of the action of different applied external loads as mediated by biological stimulus. The considered constitutive equations are chosen on the basis of the known biological phenomena occurring in bone resorption and synthesis. We present some numerical simulations for rod-bones subjected to axial external load. These numerical simulations allow for the description of the most desirable situation in which a gradual resorption of the artificial material takes place together with the contemporary formation of new bone, finally giving rise to an almost complete replacement of the artificial material with natural living tissue. © 2011 Académie des sciences.

Rosi G.,University of Rome La Sapienza | Rosi G.,University Pierre and Marie Curie | Rosi G.,Laboratorio Strutture e Materiali Intelligenti | Pouget J.,University Pierre and Marie Curie | And 2 more authors.
European Journal of Mechanics, A/Solids | Year: 2010

The aim of this work is the application of the piezoelectric effect to the reduction of the sound radiation transmitted through and radiated by an aluminium panel immersed in a light fluid. An innovative Piezoelectric Resistive Electrode (PRE) plate will be introduced here. This structure consists of an aluminium plate entirely covered by two piezoelectric layers with a controlled resistivity electrode bonded on each free piezoelectric surface. This homogeneous system is optimized for all frequencies and performs a good trade-off between good performances and easy implementation. The results will be presented by considering standard acoustic parameters, such as the Sound Reduction Index, far field sound pressure and radiated sound power at plate level. It is shown how this novel smart structure can reduce the sound transmission between two fluid media. To this end, we consider an infinite plate separating two half spaces filled with two identical light fluids, and we analyse how a sound wave is transmitted through the plate. The power of the sound and the far field pressure radiated by a finite structure due to a mechanical input, e.g. a point force, will also be considered. A detailed description of the dynamic and acoustic behaviour of the structure is presented. The performances of the PRE plate are compared with those of a standard viscoelastic damping strategy and of other passive piezoelectric smart structures. © 2010 Elsevier Masson SAS. All rights reserved.

Dell'Isola F.,University of Rome La Sapienza | Dell'Isola F.,Laboratorio Strutture e Materiali Intelligenti | Seppecher P.,University of Toulon
Continuum Mechanics and Thermodynamics | Year: 2011

In this commentary, we try to make clearer the state of the art concerning the relation between mechanical contact interactions and the different notions of stresses. We emphasize the importance of the concept of virtual displacements. Its role has been recognized in Mechanics and in Continuum Mechanics long ago (see e.g.; Vailati in Il principio dei lavori virtuali da Aristotele a Erone d'Alessandria, 113-128, 1987; Russo in The forgotten revolution, Springer, Berlin, 2003, or Cosserat and Cosserat in Sur la Théorie des Corps Déformables, Herman, Paris, 1909; Cosserat and Cosserat in Note sur la théorie de l.action euclidienne, Gauthier-Villars, Paris, 1908), and it is central as well when starting with an expression of the power expended by internal stresses and deducing the form of contact interactions as when starting with some form of the contact interactions and developing a representation theorem for these contact interactions based on the Cauchy tetrahedron construction. © 2010 Springer-Verlag.

Dell'Isola F.,University of Rome La Sapienza | Dell'Isola F.,Laboratorio Strutture e Materiali Intelligenti | Dell'Isola F.,International Center M and Mathematics | Madeo A.,INSA Lyon | And 4 more authors.
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2011

We study plane waves in second gradient solids and their reflection and transmission at plane displacement discontinuity surfaces. The needed extension of the treatment adopted to study plane wave propagation in Cauchy continua is not straightforward and is developed here. In particular, the balance of mechanical energy valid for second gradient continua is deduced. The presented results may be of interest as many boundary layer phenomena can be accounted for by second gradient models. We prove that second gradient elastic moduli may influence, in a measurable manner, how planar waves behave at discontinuity surfaces: the novel results presented here can be the basis of experimental procedures to estimate some among these moduli. We explicitly remark that reflection and transmission coefficients which we have estimated show a significant dependence on frequency, which indeed makes easier to conceive effective measurement methods. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Lekszycki T.,Polish Academy of Sciences | Lekszycki T.,Medical University of Warsaw | Lekszycki T.,International Center M and Mathematics and Mechanics of Complex Systems | Dell'Isola F.,University of Rome La Sapienza | And 2 more authors.
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2012

The multiform bio-mechanical phenomena occurring in bones grafted with the addition of artificial materials urge for the formulation of models which are sophisticated enough to describe their complexity. In the present paper we present a continuum poro-elastic mixture model in which two apparent mass densities are introduced to describe, at a macroscopic length scale, situations in which bone tissues and artificial materials coexist and interact. We focus on the final healing stage process when the bone remodelling becomes the dominant phenomenon. Artificial materials used are obviously to be bio-compatible and must resist to externally applied mechanical loads. More recently in order to favour bone tissue re-growth in grafts, which improves the long term performances of grafted bones, it has been conceived to use substitute materials which may be, similarly to bone tissue, bio-resorbed by osteoclasts and eventually replaced by newly synthesised living tissue. To account for resorption and synthesis phenomena suitable evolution equations are introduced for Lagrangian mass densities of the mixture constituents in which an integrodifferential operator defined on deformation fields appears. This operator is chosen to model some features of the coupling between mechanical compliance and biological bone tissue activity. The obtained system of integrodifferential equations is not trivial also when one considers one dimensional cases. Treating this simplified situations will allow us to individuate more easily some important remodelling scenarios. The numerical simulations which we present here show that the introduced model is promising and deserves to be developed to give previsions in more realistic applications. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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