Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.

Porous Polymeric Bioresorbable Scaffolds for Tissue Engineering

Tissue engineering is a discipline that aims at regenerating damaged biological tissues by using a cell-construct engineered in vitro made of cells grown into a porous 3D scaffold. The role of the scaffold is to guide cell growth and differentiation by acting as a bioresorbable temporary substrate that will be eventually replaced by new tissue produced by cells. As a matter or fact, the obtainment of a successful engineered tissue requires a multidisciplinary approach that must integrate the basic principles of biology, engineering and material science. The present Ph.D. thesis aimed at developing and characterizing innovative polymeric bioresorbable scaffolds made of hydrolysable polyesters. The potentialities of both commercial polyesters (i.e. poly-e-caprolactone, polylactide and some lactide copolymers) and of non-commercial polyesters (i.e. poly-w-pentadecalactone and some of its copolymers) were explored and discussed. Two techniques were employed to fabricate scaffolds: supercritical carbon dioxide (scCO2) foaming and electrospinning (ES). The former is a powerful technology that enables to produce 3D microporous foams by avoiding the use of solvents that can be toxic to mammalian cells. The scCO2 process, which is commonly applied to amorphous polymers, was successfully modified to foam a highly crystalline poly(w-pentadecalactone-co-e-caprolactone) copolymer and the effect of process parameters on scaffold morphology and thermo-mechanical properties was investigated. In the course of the present research activity, sub-micrometric fibrous non-woven meshes were produced using ES technology. Electrospun materials are considered highly promising scaffolds because they resemble the 3D organization of native extra cellular matrix. A careful control of process parameters allowed to fabricate defect-free fibres with diameters ranging from hundreds of nanometers to several microns, having either smooth or porous surface. Moreover, versatility of ES technology enabled to produce electrospun scaffolds from different polyesters as well as “composite” non-woven meshes by concomitantly electrospinning different fibres in terms of both fibre morphology and polymer material. The 3D-architecture of the electrospun scaffolds fabricated in this research was controlled in terms of mutual fibre orientation by properly modifying the instrumental apparatus. This aspect is particularly interesting since the micro/nano-architecture of the scaffold is known to affect cell behaviour. Since last generation scaffolds are expected to induce specific cell response, the present research activity also explored the possibility to produce electrospun scaffolds bioactive towards cells. Bio-functionalized substrates were obtained by loading polymer fibres with growth factors (i.e. biomolecules that elicit specific cell behaviour) and it was demonstrated that, despite the high voltages applied during electrospinning, the growth factor retains its biological activity once released from the fibres upon contact with cell culture medium. A second fuctionalization approach aiming, at a final stage, at controlling cell adhesion on electrospun scaffolds, consisted in covering fibre surface with highly hydrophilic polymer brushes of glycerol monomethacrylate synthesized by Atom Transfer Radical Polymerization. Future investigations are going to exploit the hydroxyl groups of the polymer brushes for functionalizing the fibre surface with desired biomolecules. Electrospun scaffolds were employed in cell culture experiments performed in collaboration with biochemical laboratories aimed at evaluating the biocompatibility of new electrospun polymers and at investigating the effect of fibre orientation on cell behaviour. Moreover, at a preliminary stage, electrospun scaffolds were also cultured with tumour mammalian cells for developing in vitro tumour models aimed at better understanding the role of natural ECM on tumour malignity in vivo.