Several technologies involve the coating of a bulk material with a thin layer made up of another material, so as to achieve enhanced mechanical properties for the composite system. The use of coated solids embraces a broad field of applications, so that a strong research effort has been devoted to these systems. From a mechanical point of view, a coating layer diffuses the load on an attached solid in a non-local way, thus introducing a characteristic length, and profoundly affects the mechanical response and failure mechanisms of the coated object. Therefore, the development of mechanical models to describe the behaviour of coated materials plays an important role in engineering design. In the framework of linear elasticity, the case of an elastic thin layer, perfectly bonded to an elastic disk, is analyzed in the present thesis by providing a mathematical tool with which to determine the mechanical response of the coating/bulk complex, which may find application in micro and nano technologies, for instance in the characterization of nanowires via nanoindentation. The coating is modelled by means of an Euler-Bernoulli curved rod, assumed to be perfectly bonded on the boundary of a circular elastic disk. The elastic rod acts as a coating for the disk and its axial inextensibility imposes an isoperimetric constraint on the internal disk, which is constrained to maintain its perimeter constant during the deformation process. The mechanical model for the coating/disk system is formulated for general loading, using the complex potential formalism. The elastic rod becomes equivalent to a Benveniste-Miloh interface characterized by the bending stiffness of the rod; in this way the problem can be solved entirely on the disk through the complex potential formalism and Kolosov- Muskhelishvili potentials. The kinematics and statics of the rod, together with its axial inextensibility, lead to the formulation of a 5th-order differential equation governing the mechanical state at every point on the boundary of the disk. The solution of this equation is obtained by means of a complex Fourier series expansion for the unknown fields on the boundary of the disk, when a particular distribution of the external load is prescribed. The complex variables method shows that the unknown complex coefficients involved in the series expansion depend only on the external load. Hence, all the elastic fields become known on the coating and on the boundary and within the disk. The analytical results are complemented with experiments related to a load distribution which models two equal and opposite concentrated forces. In this regard, two coated disks were designed and then manufactured (with a CNC engraving machine) from a single block of polymethyl methacrylate so that the bonding between the coating and disk was perfect and residual stresses were absent. The samples were tested in a circular polariscope and the results strongly supported the coated disk model, so the photoelastic fringes were very well captured by the elastic solution. Different situations were investigated in order to study the non-local stress diffusion of the coating. The limit case of an isoperimetric disk was also investigated by imposing a vanishing bending stiffness for the coating. This limit situation corresponded to a disk equipped with a device able to preserve the perimeter of the disk during the deformation. Exploiting the framework developed, the bifurcation problem of the coated disk was analyzed, assuming that the coating was subject to a radial pressure of three different types. A closed-form analytical solution was obtained for the bifurcation pressure and modes, showing that the presence of the disk profoundly changed the bifurcation landscape of the coating, forming a circular elastic rod. In fact, the circular rod admits only oval modes, while the coating/disk system displays high-frequency circumferential undulations. The experimental, analytical, and numerical results presented open new possibilities for the design of coated solids of cylindrical geometry, which may find applications in micro and nano technologies, for instance in the characterization of nanowires via nanoindentation.

The main bulk of this Thesis is focused on the response of cell membranes due to chemical and mechanical stimuli. Henceforth, it is mainly devoted to deduce how the key aspect of the cell response activated by chemical signaling can be predicted by a simplified energetics, making use of both theoretical models and numerical simulations. The a ention is focused on cell membranes embedding G protein-coupled receptors (GPRCs). By analyzing the behavior of cell mem- branes, one can isolate three main contributions in order to model their respon- se: (1) diffusion of receptors and transporters embedded in the lipid membrane; (2) conformational changes of the receptors; (3) membrane elasticity. Moreover, the interplay between TM confomational changes and lateral pressure of the lipid membrane against such TMs is introduced. The chemical potential of the receptor-ligand compound, deduced as the variational derivative of such energy, is compared with the one calculated by accounting for the work done by the lateral pressure. The result yields a relationship between the conformational field, the mechanical field (interpreted as either the thickness change or the areal change) and the distribution of the compounds receptor-ligand. The analysis of such resulting constitutive equation among those three quantities shows that, essentially, the reason why ligand-GPRCs compounds prefer to live on lipid ra is a necessity involving the interplay between the work performed by the lateral pressure and the need of TMs to change their conformation during ligand binding. Henceforth, mechanobiology gives a justification to the experimental findings of Kobilka and Lei ovitz, Chemistry Nobel Prizes 2012.

The present doctoral thesis deals with the study and the analysis of large strain and high strain rate behavior of materials and components. Theoretical, experimental and computational aspects are taken into consideration. Particular reference is made to the modeling of metallic materials, although other kinds of materials are considered as well. The work may be divided into three main parts. The first part of the work consists in a critical review of the constitutive modeling of materials subjected to large strains and high to very high strain rates. Specific attention is paid to the opportunity of adopting so-called strength models and equations of state. Damage and failure modeling is discussed as well. In this part, specific interest is addressed to reviewing the so-called Johnson-Cook strength model, by critically highlighting its positive and negative aspects. One of the main tackled issue consists in a reasoned assessment of the various procedures adoptable in order to calibrate the parameters of the model. This phase is enriched and clarified by applying different calibration strategies to a real case, i.e. the evaluation of the model parameters for a structural steel. The consequences determined by each calibration approach are then carefully evaluated and compared. The second part of the work aims at introducing a new strength model, that consists in a generalization of the Johnson-Cook model. The motivations for the introduction of this model are first exposed and discussed. The features of the new strength model are then described. Afterwards, the various procedures adoptable for the determination of the material parameters are presented. The new strength model is then applied to a real case, i.e. a structural steel as above, and the results are compared to those obtained from the original Johnson-Cook model. Comparing to that, the obtained outcomes show that the new model displays a better capacity in reproducing experimental data. Results are discussed and commented. The third and final part of the work deals with an application of the studied topics to a real industrial case of interest. A device called perforating gun is analyzed in its structural problematics and critical aspects. This challenging application involves the modeling of several typologies of material, large strains, very high strain rate phenomena, high temperatures, explosions, hypervelocity impacts, damage, fracture and phase changes. In this regard, computational applications of the studied theories are presented and their outcomes are assessed and discussed. Several finite element techniques are considered. In particular, tridimensional Eulerian simulations are presented. The obtained results appear to be very promising in terms of the possibilities of a fruitful use in the design process of the device, in particular in order to achieve an optimization of its key features.

The mechanics of impacts is not yet well understood due to the complexity of materials behaviour under extreme stress and strain conditions and is thus of challenge for fundamental research, as well as relevant in several areas of applied sciences and engineering. The involved complex contact and strain-rate dependent phenomena include geometrical and materials non-linearities, such as wave and fracture propagation, plasticity, buckling, and friction. The theoretical description of such non-linearities has reached a level of advance maturity only singularly, but when coupled -due to the severe mathematical complexity- remains limited. Moreover, related experimental tests are difficult and expensive, and usually not able to quantify and discriminate between the phenomena involved. In this scenario, computational simulation emerges as a fundamental and complementary tool for the investigation of such otherwise intractable problems. The aim of this PhD research was the development and use of computational models to investigate the behaviour of materials and structures undergoing simultaneously extreme contact stresses and strain-rates, and at different size and time scales. We focused on basic concepts not yet understood, studying both engineering and bio-inspired solutions. In particular, the developed models were applied to the analysis and optimization of macroscopic composite and of 2D-materials-based multilayer armours, to the buckling-governed behaviour of aerographite tetrapods and of the related networks, and to the crushing behaviour under compression of modified honeycomb structures. As validation of the used approaches, numerical-experimental-analytical comparisons are also proposed for each case.

Nature develops several materials with remarkable functional properties composed of comparatively simple base substances. Biological materials are often composites, which optime the conformation to their function. On the other hand, synthetic materials are designed a priori, structuring them according to the performance to be achieved. 3D printing manufacturing is the most direct method for specific component production and earmarks the sample with material and geometry designed ad-hoc for a defined purpose, starting from a biomimetic approach to functional structures. The technique has the advantage of being quick, accurate, and with a limited waste of materials. The sample printing occurs through the deposition of material layer by layer. Furthermore, the material is often a composite, which matches the characteristics of components with different geometry and properties, achieving better mechanical and physical performances. This thesis analyses the mechanics of natural and custom-made composites: the spider body and the manufacturing of metallic and non-metallic graphene composites. The spider body is investigated in different sections of the exoskeleton and specifically the fangs. The study involves the mechanical characterization of the single components by the nanoindentation technique, with a special focus on the hardness and Young's modulus. The experimental results were mapped, purposing to present an accurate comparison of the mechanical properties of the spider body. The different stiffness of components is due to the tuning of the same basic material (the cuticle, i.e. mainly composed of chitin) for achieving different mechanical functions, which have improved the animal adaptation to specific evolutive requirements. The synthetic composites, suitable for 3D printing fabrication, are metallic and non-metallic matrices combined with carbon-based fillers. Non-metallic graphene composites are multiscale compounds. Specifically, the material is a blend of acrylonitrile-butadiene-styrene (ABS) matrix and different percentages of micro-carbon fibers (MCF). In the second step, nanoscale filler of carbon nanotubes (CNT) or graphene nanoplatelets (GNP) are added to the base mixture. The production process of composite materials followed a specific protocol for the optimal procedure and the machine parameters, as also foreseen in the literature. This method allowed the control over the percentages of the different materials to be adopted and ensured a homogeneous distribution of fillers in the plastic matrix. Multiscale compounds provide the basic materials for the extrusion of fused filaments, suitable for 3D printing of the samples. The composites were tested in the configuration of compression moulded sheets, as reference tests, and also in the corresponding 3D printed specimens. The addition of the micro-filler inside the ABS matrix caused a notable increment in stiffness and a slight increase in strength, with a significant reduction in deformation at the break. Concurrently, the addition of nanofillers was very effective in improving electrical conductivity compared to pure ABS and micro-composites, even at the lowest filler content. Composites with GNP as a nano-filler had a good impact on the stiffness of the materials, while the electrical conductivity of the composites is favoured by the presence of CNTs. Moreover, the extrusion of the filament and the print of fused filament fabrication led to the creation of voids within the structure, causing a significant loss of mechanical properties and a slight improvement in the electrical conductivity of the multiscale moulded composites. The final aim of this work is the identification of 3D-printed multiscale composites capable of the best matching of mechanical and electrical properties among the different compounds proposed. Since structures with metallic matrix and high mechanical performances are suitable for aerospace and automotive industry applications, metallic graphene composites are studied in the additive manufacturing sector. A comprehensive study of the mechanical and electrical properties of an innovative copper-graphene oxide composite (Cu-GO) was developed in collaboration with Fondazione E. Amaldi, in Rome. An extensive survey campaign on the working conditions was developed, leading to the definition of an optimal protocol of printing parameters for obtaining the samples with the highest density. The composite powders were prepared following two different routes to disperse the nanofiller into Cu matrix and, afterward, were processed by selective laser melting (SLM) technique. Analyses of the morphology, macroscopic and microscopic structure, and degree of oxidation of the printed samples were performed. Samples prepared followed the mechanical mixing procedure showed a better response to the 3D printing process in all tests. The mechanical characterization has instead provided a clear increase in the resistance of the material prepared with the ultrasonicated bath method, despite the greater porosity of specimens. The interesting comparison obtained between samples from different routes highlights the influence of powder preparation and working conditions on the printing results. We hope that the research could be useful to investigate in detail the potential applications suitable for composites in different technological fields and stimulate further comparative analysis.

The first part of this Thesis deals with the analysis of piecewise-smooth mechanical systems and the definition of special stability criteria in presence of non-conservative follower forces. To illustrate the peculiar stability properties of this kind of dynamical system, a reference 2 d.o.f. structure has been considered, composed of a rigid bar, with one and constrained to slide, without friction, along a curved profile, whereas the other and is subject to a follower force. In particular, the curved constraint is assumed to be composed of two circular profiles, with different and opposite curvatures, defining two separated subsystems. Due to this jump in the curvature, located at the junction point between the curved profiles, the entire mechanical structure can be modelled by discontinuous equations of motion, the differential equations valid in each subsystem can be combined, leading to the definition of a piecewise-smooth dynamical system. When a follower force acts on the structure, an unexpected and counterintuitive behaviour may occur: although the two subsystems are stable when analysed separately, the composed structure is unstable and exhibits flutter-like exponentially-growing oscillations. This special form of instability, previously known only from a mathematical point of view, has been analysed in depth from an engineering perspective, thus finding a mechanical interpretation based on the concept of non-conservative follower load. Moreover, the goal of this work is also the definition of some stability criteria that may help the design of these mechanical piecewise-smooth systems, since classical theorems cannot be used for the investigation of equilibrium configurations located at the discontinuity. In the literature, this unusual behaviour has been explained, from a mathematical perspective, through the existence of a discontinuous invariant cone in the phase space. For this reason, starting from the mechanical system described above, the existence of invariant cones in 2 d.o.f. mechanical systems is investigated through Poincaré maps. A complete theoretical analysis on piecewise-smooth dynamical systems is presented and special mathematical properties have been discovered, valid for generic 2~d.o.f. piecewise-smooth mechanical systems, which are useful for the characterisation of the stability of the equilibrium configurations. Numerical tools are implemented for the analysis of a 2~d.o.f. piecewise-smooth mechanical system, valid for piecewise-linear cases and extendible to the nonlinear ones. A numerical code has been developed, with the aim of predicting the stability of a piecewise-linear dynamical system a priori, varying the mechanical parameters. Moreover, “design maps” are produced for a given subset of the parameters space, so that a system with a desired stable or unstable behaviour can easily be designed. The aforementioned results can find applications in soft actuation or energy harvesting. In particular, in systems devoted to exploiting the flutter-like instability, the range of design parameters can be extended by using piecewise-smooth instead of smooth structures, since unstable flutter-like behaviour is possible also when each subsystem is actually stable. The second part of this Thesis deals with the numerical analysis of an elastic cloak for transient flexural waves in Kirchhoff-Love plates and the design of special metamaterials for this goal. In the literature, relevant applications of transformation elastodynamics have revealed that flexural waves in thin elastic plates can be diverted and channelled, with the aim of shielding a given region of the ambient space. However, the theoretical transformations which define the elastic properties of this “invisibility cloak” lead to the presence of a strong compressive prestress, which may be unfeasible for real applications. Moreover, this theoretical cloak must present, at the same time, high bending stiffness and a null twisting rigidity. In this Thesis, an orthotropic meta-structural plate is proposed as an approximated elastic cloak and the presence of the prestress has been neglected in order to be closer to a realistic design. With the aim of estimating the performance of this approximated cloak, a Finite Element code is implemented, based on a sub-parametric technique. The tool allows the investigation of the sensitivity of specific stiffness parameters that may be difficult to match in a real cloak design. Moreover, the Finite Element code is extended to investigate a meta-plate interacting with a Winkler foundation, to analyse how the substrate modulus transforms in the cloak region. This second topic of the Thesis may find applications in the realization of approximated invisibility cloaks, which can be employed to reduce the destructive effects of earthquakes on civil structures or to shield mechanical components from unwanted vibrations.

The static and dynamic response of lattice materials is investigated to disclose and control the connection between microstructure and effective behavior. The analytical methods developed in the thesis aim at providing a new understanding of material instabilities and strain localizations as well as effective tools for controlling wave propagation in lattice structures. The time-harmonic dynamics of arbitrary beam lattices, deforming flexurally and axially in a plane, is formulated analytically to analyze the influence of the mechanical parameters on the dispersion properties of the spectrum of Floquet-Bloch waves. Several forms of dynamic localizations are shown to occur for in-plane wave propagation of grid-like elastic lattices. It is demonstrated that lattices of rods, despite being `simple' structures, can exhibit a completely different channeled response depending on the characteristics of the forcing source (i.e. frequency and direction) as well as on the slenderness of the elastic links. It is also shown how the lattice parameters can be tuned to attain specific dispersion properties, such as flat bands and sharp Dirac cones. In the research field of material instabilities, a key result proposed in this thesis is the development of both static and dynamic homogenization methods capable of accounting for second-order effects in the macroscopic response of prestressed lattices. These methods, the former based on an incremental strain-energy equivalence and the latter based on the asymptotic analysis of lattice waves, allow the identification of the incremental constitutive operator capturing the macroscopic incremental response of arbitrary lattice configurations. The homogenization framework has allowed the systematic analysis of prestress-induced phenomena on the incremental response of both the lattice structure and its `effective' elastic solid, which in turn has enabled the identification of the complex interplay between microstructure, prestress, loss of ellipticity (shear band formation) and short-wavelength bifurcations. Potential new applications for the control of wave propagation are also shown to be possible by leveraging the inclusion of second-order terms in the incremental dynamics. In particular, the tunability of the prestress state in a square lattice structure has been exploited to obtain dynamic interfaces with designable transmission properties. The interface can be introduced in a material domain by selectively prestressing the desired set of ligaments and the prestress level can be tuned to achieve total reflection, negative refraction, and wave channeling. The obtained results open new possibilities for the realization of engineered materials endowed with a desired constitutive response, as well as to enable the identification of novel dynamic material instabilities.