Daria Scerrato

A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials

In this paper, the phenomena of resorption and growth of bone tissue and resorption of the biomaterial inside a bicomponent system are studied by means of a numerical method based on finite elements. The material behavior is described by a poro-viscoelastic model with infiltrated voids. The mechanical stimulus that drives these processes is a linear combination of density of strain energy and viscous dissipation. The external excitation is represented by a bending load slowly variable with sinusoidal law characterized by different frequencies. Investigated aspects are the influence of the load frequency, of type of the stimulus and of the effective porosity on the time evolution of the mass densities of considered system.

Euromech 563 Cisterna di Latina 17–21 March 2014 Generalized continua and their applications to the design of composites and metamaterials: A review of presentations and discussions

In the present paper, a rational report on Euromech 563, Generalized continua and their applications to the design of composites and metamaterials (Cisterna di Latina 17–21 March 2014), is provided. The frank and constructive spirit which animated the workshop by Dell’Isola et al. (ZAMM 2014; 94(5): 367–372) also characterized Euromech Colloquium 563. All presentations were video-recorded and are freely available online at the address http://www.memocsevents.eu/euromech563/?page_id=1013. The topics treated were selected by the organizers in order to allow a comparison of the available experimental evidence with the predictive capability of current theoretical models. The numerical investigations selected and presented aimed to make more effective the aforementioned comparison. The interested reader will find more details about the colloquium at the dedicated webpage http://www.memocsevents.eu/euromech563. The design and use of advanced materials and structural elements requires an extensive and rigorous process of mathematical modeling. The organizers of Euromech 563, being aware of this need, have chosen as participants renowned and reputed scientists (and some promising young researchers) who all agree on recognizing to mathematical sciences their role of unifying and coordinating tool in the effort for the advance of technology. The Colloquium has indeed surely contributed to the development of more advanced technological possibilities and to the theoretical conception of completely new ones.

Multi-scale concrete model with rate-dependent internal friction

In this paper, a micromorphic, non-linear 3D model aiming to describe internal friction phenomena in concrete is considered. A reduced two-degrees-of-freedom model is employed for the sake of easy handling to explain dissipative loops which have been observed in some concrete specimens tested under cyclic uniaxial compression loading with different frequencies and having various amplitudes but never inducing large strains. As (linear or non-linear) viscoelastic models do not seem suitable to describe neither qualitatively nor quantitatively the measured dissipation loops, we propose to introduce a multi-scale micromechanism of Coulomb-type internal dissipation associated to the relative motion of the faces of the microcracks present in the material and to the asperities inside the microcracks. We finally present numerical simulations showing that the proposed model is suitable to describe some of the available experimental evidence.

Intorno alle equazioni fondamentali del movimento di corpi qualsivogliono, considerati secondo la naturale loro forma e costituzione

Avviene non di rado che i nuovi ritrovamenti mediante i quali fu accresciuto qualche ramo delle Matematiche applicate, non appajano subito nel concetto e nella esposizione sgombri da superfluita o lungaggini. La complicazione de’ procedimenti analitici puo giungere anche a tale da non parer piu possibile l’andare innanzi: ed e invece allora che talvolta si scopre un punto di vista piu generale, si concentrano molte particolarita e si forma una teorica compendiosa e cosi bene assicurata da infondere lena per ulteriori progressi. Sarebbe desiderabile che questo avvenisse anche per le ultime aggiunte fatte da moderni Geometri alla Meccanica razionale: e quanto a me direi che il modo di riuscirvi l’abbiamo nelle nostre mani: resta da vedere se altri vorranno essere del mio avviso.

Modeling of a non-local stimulus for bone remodeling process under cyclic load: Application to a dental implant using a bioresorbable porous material

In this paper, a numerical method based on finite elements is used to study the phenomena of resorption and growth of bone tissue and resorption of the biomaterial in the neighborhood of a dental implant fixture of the type IntraMobil Zylinder. The mechanical stimulus that drives these processes is a linear combination of strain energy and viscous dissipation. To simulate the implant, an axisymmetric model has been used from the point of view of the geometry; the material behavior is described in the poro-visco-elastic frame. The external action is represented by a load variable with sinusoidal law characterized by different frequencies. Investigated aspects are the influence of the load frequency and of the lazy zone on the remodeling process.

Modeling and designing micro- and nano-structured metamaterials: Towards the application of exotic behaviors

The lack of suitable computational methods has significantly restricted the creativity of engineers in designing the materials to be used in technological applications. When one wants exact analytical solutions for a given physical system, then usually drastic and restrictive simplifying assumptions are needed. In particular, homogeneity of physical and geometrical properties at lower length-scale is the standard assumption in continuum mechanics. On the other hand, it is well-known since the pioneering work of Gabrio Piola, and then re-established in the works by Mindlin, Toupin, Green, Adkins and Germain, that it is possible to synthetically describe microscopic inhomogeneity by means of field theories incorporating additional kinematical fields. The characteristic length-scale affecting macro-behavior can even be of the order of nanometers, in which case the intuition due to Richard Feynman about the importance of quantum effects at macro-scale could open the path to technological advancements. In the present paper we review some of the literature in the field and try to indicate some research perspectives that seem to us potentially ground-breaking. In particular, following the suggestion of Professor dell’Isola, we briefly describe his concept of pantographic lattices and sheets whose importance in nano-technology could be relevant.

Di un principio controverso della meccanica analitica di lagrange e delle molteplici sue applicazioni

I principj ed i metodi generali esposti dal sommo Lagrange nella Meccanica Analitica vennero in molta parte abbandonati dai geometri che dopo di lui trattarono questioni di Matematica applicata. L’essere alcuni di quei principj, o non dimostrati, o dimostrati incompletamente, pare sia la cagione principale di quell’abbandono, e ne abbiamo quasi una prova nel vedere adoperate tuttora le formole date da Lagrange nella Sezione IV della seconda parte, le quali, appunto perche rigorosamente dimostrate, non vennero lasciate in disparte anche dopo i lavori di Hamilton e di Jacobi sullo stesso argomento. Fra questi principj il piu importante per le applicazioni e certamente quello indicato dall’autore nella Sezione II, ed esposto con maggior chiarezza nella Sezione IV della prima parte della M. A., intorno al modo di introdurre l’effetto delle forze interne nella equazione generale per l’equilibrio e pel moto, e che il difetto di dimostrazione rese quasi sterile pei successori di Lagrange.

On the Applications of Principles of Analytical Mechanics by Lagrange to the Principal Problems

In this chapter it is presented the translation of the opera “Sull’applicazione de’ principj della Meccanica Analitica del Lagrange ai principali problemi” by Gabrio Piola. It was presented for the contest for the prize and crowned by the I.R. Istituto di Scienze the 4th of October 1824.