Recent experimental results have suggested important direct implications of viscoelasticity of human cells and cell cytoskeleton dynamics on some relevant collective and at single-cell behaviors such as migration, adhesion, and morphogenesis. Other experimental studies have been performed on individual cancer and healthy cells of different types, demonstrating that the former were about 70% softer than the latter. In this thesis with the aim of characterizing — and gaining insights into — the frequency response of single-cell systems to mechanical stimuli (typically LITUS), a generalized viscoelastic paradigm which combines classical and spring-pot based (fractional derivative) models is presented. Than the modelling has been enriched considering the non-linear effect of the prestress, induced in protein filaments during cell adhesion and in the cell membrane (with a simple multiscale scheme that incorporates finite elasticity and a 3-D circus tent-like model), on the overall cell stiffness and finally determining its influence on the in-frequency response of the cell. The theoretical results have shown that the differences in stiffness — at least in principle — allow us to mechanically discriminate between tumor and normal cells: the critical frequencies associated with oscillation magnitude peaks (from tens to hundreds of kilohertz) could be helpfully utilized for targeting or ad hoc altering the functions of cancer cells. An experimental validation of the theoretical results is an ongoing work and the preparation of the experimental setup is also presented. In this thesis some first models have been presented to replicate in-vivo collective behavior of cells. Coherent angular rotation of epithelial cells has been reproduced by a cell-centered based mechanical model in which units are polarized, motile, and interact with the neighboring cells via harmonic forces. Starting from this model a continuum non-linear viscoelastic model incorporating the dynamics of liquid crystals has been studied and some preliminary numerical simulations have been performed.

Several aspects of fracture nucleation and growth in brittle porous ceramics and in thin films are investigated, through analytical, numerical modelling, and experimental validation. A mechanical experimental characterization has been developed for a porous ceramic, namely, a 3D apatite, characterised by an oriented porosity and used for biomedical applications. The ceramic is produced from wood, so that the resulting porosity evidences a multi-scale nature, a feature determining peculiar failure mechanisms and an unprecedented porosity/strength ratio. In particular, the material exhibits an exfoliation-type failure, resulting in a progressive loss in mechanical properties, occurring for compression tests parallel to the grains and for highly slender specimens. Similar cohesive-brittle behaviour is also found when the compression is applied in the direction orthogonal to the porous channels, regardless of the shape ratio of the specimen. An in-depth analysis of this response is performed by means of a phase-field model. After calibrating the model, stress-strain curves and fracturing patterns are accurately reproduced. Furthermore, the effects of multi-scale porosity on mechanical behaviour are determined. Various strategies available in the literature for evaluating the properties of porous materials are compared to the proposed phase-field approach. The results open new possibilities for the prediction and characterization of complex fracturing phenomena occurring in highly porous ceramics, so to facilitate medical applications as structural bone repair. An application of the peridynamic theory of continuum mechanics is developed to obtain a dimensional reduced formulation for the characterisation of through-thickness delamination of plates. The kinematic of the plate is carefully chosen to be composed of an absolutely continuous part and a zone where jumps in the displacements are allowed; in this way, the reduced form of the elastic bond-based peridynamic energy and the reduced Lagrangian are explicitly retrieved in a closed-form. The reduction generates a hierarchy of terms, characterizing the energy stored inside the plane element. A semi-analytical solution, obtained by means of a minimization procedure, is obtained for a test case and compared with finite element simulations. Despite the fact that the numerical model is fully three-dimensional (in other words, it is not reduced), this model leads to the same moment-curvature diagrams and nucleation/growth of the delamination surface found with the reduced formulation. Finally, the convergence of the proposed reduced model to local elastic theory at vanishing internal length is determined, so that a reduced-localized cohesive model for fracture is retrieved.

Through the last decades several nonlocal models of linear elasticity have been introduced as enhancements of the Cauchy-elastic model, often with the purpose of providing an improved mechanical description of solids at the microscale level. Although many efforts have been devoted to the analytical formulation of these advanced constitutive models, a definitive interpretation of the relevant static quantities is still incomplete and Finite Element (FE) solvers are practically unavailable. In this thesis, after providing a mechanical interpretation to the static quantities involved in strain gradient (of Mindlin type) elastic materials, an overview on the possible quadrilateral Hermitian finite elements is given to treat quasi-static plane problems. Beside the classical finite elements inspired by those adopted for modeling Kirchhoff plates, an alternative quadrilateral self-constrained finite element formulated through Lagrange multipliers is also proposed. With reference to a hexagonal lattice structure, for which the equivalent constitutive tensors have been recently derived as closed-form expressions, the developed FE codes are exploited to assess the reliability of modelling lattices through higher-order constitutive equations. These analyses are developed for one-dimensional and two dimensional problems, where the former are considered for both homogeneous layers (with a finite size in one direction) and rod-type structures (with a finite uniform cross section along one direction). It is confirmed that higher-order modelling improves the mechanical description. In particular, the macroscale response is shown to be strongly affected by higher-order contributions in the presence of extreme elastic contrast between microstructural elements. Indeed, in this last case, only higher-order modeling captures a non-null residual stiffness, which vanishes in the framework of classical models. Therefore, higher-order modeling becomes important not only to describe the mechanical response at a microlevel, but also for macrolevel modelling, when extreme mechanical properties are addressed. The presented results pave the way to a refined modelling of architected materials leading to improved design of microstructures displaying innovative mechanical features.

Theoretical modelling of challenging multiscale problems arising in complex (and sometimes bioinspired) solids are presented. Such activities are supported by analytical, numerical and experimental studies. For instance, this is the case for studying the response of hierarchical and nano-composites, nanostructured solid/semi-fluid membranes, polymeric nanocomposites, to electromagnetic, mechanical, thermal, and sometimes biological, electrical, and chemical agents. Such actions are notoriously important for sensors, polymeric films, artificial muscles, cell membranes, metamaterials, hierarchical composite interfaces and other novel class of materials. The main purpose of this project is to make significant advancements in the study of such composites, with a focus on the electromagnetic and mechanical performances of the mentioned structures, with particular regards to novel concept devices for sensing. These latter ones have been studied with different configuration, from 3D colloidal to 2D quasi-hemispherical micro voids elastomeric grating as strain sensors. Exhibited time-rate dependent behavior and structural phenomena induced by the nano/micro-structure and their adaptation to the applied actions, have been explored. Such, and similar, ordered submicroscopic systems undergoing thermal and mechanical stimuli often exhibit an anomalous response. Indeed, they neither follow Fourier’s law for heat transport nor their mechanical time-dependent behavior exhibiting classical hereditariness. Such features are known both for natural and artificial materials, such as bone, lipid membranes, metallic and polymeric “spongy” composites (like foams) and many others. Strong efforts have been made in the last years to scale-up the thermal, mechanical and micro-fluidic properties of such solids, to the extent of understanding their effective bulk and interface features. The analysis of the physical grounds highlighted above has led to findings that allow the describing of those materials’ effective characteristics through their fractional-order response. Fractional-order frameworks have also been employed in analyzing heat transfer to the extent of generalizing the classical Fourier and Cattaneo transport equations and also for studying consolidation phenomenon. Overall, the research outcomes have fulfilled all the research objectives of this thesis thanks to the strong interconnection between several disciplines, ranging from mechanics to physics, from structural health monitoring to chemistry, both from an analytical and numerical point of view to the experimental one.

This thesis focuses on the study of the creep deformations exhibited by concrete structures, with a particular attention to long-span prestressed box girders. During their service life, such structures can experience excessive multidecade deflections mainly due to the creep phenomenon and the large difference in shrinkage between the top and bottom slabs, sometimes causing damages of structural elements and huge economic losses. In order to prevent such consequences, the multidecade deflections of this class of structures need to be carefully predicted; therefore, very refined creep constitutive laws are required for relevant creep analyses. The most widely used creep model for the prediction of the time-dependent behavior of highly creep-sensitive structures is Model B3, which was calibrated through a data bank comprising results coming from different laboratories spread throughout the world. In this thesis, an already existing viscoelastic formulation, conceived for any viscous kernel, is integrated with Model B3 and the resulting finite element scheme is successfully applied to study the long-term behavior of a realistic structure, the Colle Isarco viaduct in Italy. Another contribution to this research work concerns the prediction of multidecade deflections exhibited by concrete structures through a novel creep constitutive law based on variable-order fractional calculus, resulting in an excellent feature with respect to classical creep models. Indeed, the creep deformations obtained through the proposed model are very close to the deformations evaluated by means of Model B3. Moreover, the suggested creep law is characterized by less aging terms than Model B3, with the consequent advantage to exactly derive the relevant relaxation function from the fundamental relationship of linear viscoelasticity. In order to perform creep analyses with the suggested fractional-order law, a numerical integration scheme characterized by a fractional-order viscous kernel is also developed and verified on realistic concrete structures subjected to multiple load histories. To the best of the author's knowledge, this research work presents the first creep constitutive lawavailable in literature that, through fractional operators, explores the time-dependent behavior of aging materials. Furthermore, a suitable numerical integration scheme is introduced and successfully applied to representative concrete structures.

Tribology is known as the science of surfaces in relative motion and involves complex interactions over multiple length and time scales. Therefore, friction, lubrication and wear of materials are intrinsically highly multiphysics and multiscale phenomena. Several modelling and simulation tools have been developed in the last decades, always requiring a trade-off between the available computational power and the accurate replication of the experimental results. Despite nowadays it is possible to model with extreme precision elastic problems at various scales, further eorts are needed for taking into account phenomena like plasticity, adhesion, wear, third-body friction and boundary and solid lubrication. The situation becomes even more challenging if considering non-conventional nano-, as in the case of polymer surfaces and interfaces, or microstructures, as for the hierarchical organisations observed in biological systems. Specically, biological surface structures have been demonstrated to present exceptional tribological properties, for instance in terms of adhesion (e.g., the gecko pad), superhydrophobicity (e.g., the lotus leaf) or fluid-dynamic drag reduction (e.g., the shark skin). This has suggested the study and development of hierarchical and/or bio-inspired structures for applications in tribology. Therefore, by taking inspiration from Nature, we investigate the effect of property gradients on the frictional behaviour of sliding interfaces, considering lateral variations in surface and bulk properties. 3D finite-element simulations are compared with a 2D spring-block model to show how lateral gradients can be used to tune the macroscopic coefficients of friction and control the propagation of detachment fronts. Complex microscale phenomena govern the macroscopic behaviour also of lubricated contacts. An example is represented by solid lubrication or third-body friction, which we study with 3D discreteelement simulations. We show the effects of surface waviness and of the modelling parameters on the macroscopic coefficient of friction. Many other natural systems present complex interfacial interactions and tribological behaviour. Plant roots, for instance, display optimised performance during the frictional penetration of soil, especially thanks to a particular apex morphology. Starting from experimental investigations of different probe geometries, we employ the discrete-element method to compute the expended work during the penetration of a granular packing, conrming the optimal bio-inspired shape. This has allowed to follow also an integrated approach including image acquisition and processing of the actual geometries, 3D printing, experiments and numerical simulations. Finally, another interesting example of advanced biological interface with optimised behaviour is represented by biosensing strucviii tures. We employ fluid-structure interaction numerical simulations for studying the response of spiders' trichobothria, which are among the most sensitive biosensors in Nature. Our results highlight the role of the fluid-dynamic drag on the system performance and allow to determine the optimal hair density observed experimentally. Both the third-body problem and the possibility to tune the frictional properties can be considered as the next grand challenges in tribology, which is going to live a "golden age" in the coming years. We believe the results discussed in this Doctoral Thesis could pave the way towards the design of novel bio-inspired structures with optimal tribological properties, for the future development of smart materials and innovative solutions for sliding interfaces.

Scientists are continuously fascinated by the high degree of sophistication found in natural materials, arising from evolutionary optimisation. In living organisms, nature provides a wide variety of materials, architectures, systems and functions, often based on weak constituents at the lower scales. One of the most extensively studied natural materials is spider silk, renowned for its outstanding mechanical properties, which include exceptional strength and toughness. Owing to its wide range of properties, which vary depending on factors such as the type of silk (up to seven) that each spider can produce, and the species of spider, it can be considered a class of semi-crystalline polymeric material. Indeed, spider silk cleverly combines, depending on the application required, the great deformability of an amorphous phase with the stiffness and strength conferred by pseudo-crystals consisting of specific secondary structures of some of the proteins constituting the material. Based on the countless studies conducted on spider silk, it is now also clear that its remarkable performance are the result of a sophisticated optimisation of the material's hierarchical structure. Nevertheless, many of the multiscale mechanisms that give rise to the striking macroscopic properties are still unclear. Many open problems are also related to the relevant effects of environmental conditions and in particular on temperature and humidity, strongly conditioning the mechanical performances. In this thesis, aimed at unveiling some of these open problems, we introduce a multiscale model for the thermo-hygro-mechanical response, starting with the influence of water molecules modifying the microstructure, up to the effects at the macroscopic scale, including softening, increase in elongation at break and supercontraction, i.e. the shortening (up to half the initial length) of the spider threads in wet environments. Thereafter, we describe how the supercontraction effect can be adopted to obtain humidity-driven actuators, and in particular, we determine the maximum actuation force depending on the silk properties at the molecular scale and on the constraining system representing other silk threads or the actuated device. The spider silk actuation properties turned out to be extraordinary, making spider silk potentially the best performing humidity-driven actuator known to date in terms of work density. As observed in many natural materials, spider silks are characterized by a strong variability in both chemical and structural organization, as for example described in the recently published experimental database of properties at different scales of about a thousand different spider silks, where evident correlations among quantities are scarce. This large variability makes the theoretical understanding of the observed material behavior, in relation of the complex hierarchical structure, particularly intriguing. To address this novel amount of experimental data without losing sight of theoretical analytical modelling, we propose a new data modelling methodology to obtain simple and interpretable relationships linking quantities at different scales. In particular, we employ a symbolic regression technique, known as 'Evolutionary Polynomial Regression', which integrates regression capabilities with the Genetic Programming paradigm, enabling the derivation of explicit analytical formulas, finally delivering a deeper comprehension of the analysed physical phenomenon. Eventually, we provide insights to improve our multiscale theoretical model accounting for the humidity effects on spider silks. This approach may represent a proof of concept for modelling in fields governed by multiscale, hierarchical differential equations. We believe that the analytical description of the macroscopic behaviour from microscale properties is of great value both for the full understanding of biological materials, as well as in the perspective of bioinspired materials and structures.

Real-time structural health monitoring is a well established tool for post-earthquake damage estimation. A key component in the monitoring campaign is the approach used for processing the data from the structural health monitoring system. There is a large body of literature on signal processing approaches aimed at identifying ground-motion induced damage in civil engineering structures. This dissertation expands on a specific subgroup of processing approaches dealing with the identification of damage induced high-frequency transients in the monitoring data. The underlying intuition guiding the current research can be formulated in the following hypothesis - the time difference between the occurrence of a high-frequency transient and the closest deformation extremum forward in time is proportional to the degree of damage. A mathematical deduction is provided in support of the above hypothesis followed by a set of shaking table tests. For the purposes of this research two shaking table tests of reinforced concrete bridge piers were performed. Data from a shaking table test performed by another research group was also analyzed. The cases in which the proposed procedure could find a practical application are examined along with the present limitations.

The mechanical and structural engineering community are increasingly resorting to the use of periodic metamaterials and metastructures to mitigate high amplitude vibrations; and nonlinearities are also an active area of research because they potentially provide different methods for controlling elastic waves. While the theory of propagation of linear elastic waves seems to be fairly complete and has led to remarkable discoveries in a variety of disciplines, there is still much to investigate about nonlinear waves, both in terms of their dispersion analytical description and their numerical characterization. This thesis mainly relies on the latter aspect and focuses on the analysis of nonlinear metamaterials and metastructures for both the mitigation and control of elastic waves. In particular, the thesis covers four main topics, each associated with a different nonlinearity: i) dispersion curves and mechanical parameters identification of a weakly nonlinear cubic 1D locally resonant metamaterial; ii) manipulation of surface acoustic waves (SAWs) through a postbuckling-based switching mechanism; iii) seismic vibration mitigation of a multiple-degrees-of-freedom (MDoF) system, the so-called metafoundation, by means of hysteretic nonlinear lattices; iv) seismic vibration mitigation of a periodic coupled system pipeline-pipe rack (PPR), by means of a vibro-impact system (VIS). To identify the dispersion curves of a cubic nonlinear 1D locally resonant metamaterial, a simple experimentally-informed reference subsystem (RS) which embodies the unit cell is employed. The system identification relies on the Floquet--Bloch (FB) periodic conditions applied to the RS. Instead, the parametric identification is carried out with a revised application of the subspace identification (SSI) method involving harmonic, non-persistent excitation. It is remarkable that the proposed methodology, despite the linearization caused by the FB boundary conditions, is responsive to the amplitude of the excitation that affects the dispersion curves. The FB theorem, in fact, is often adopted to reduce the computational burden in calculating the dispersion curves of metamaterials. In contrast, the experimental dispersion reconstruction requires multiple velocity measurements by means of laser Doppler vibrometers (LDVs), as for the case of SAWs. To manipulate SAWs, a proof-of-concept experiment was performed for a postbuckling-based mechanical switching mechanism. Precompressed beams are periodically arranged on one face of an elastic plate to manipulate the dispersion of the SAWs propagating as edge waves. By compressing the columns over their Euler critical load, in fact, it is possible to manipulate the surface wave dispersion: the dispersion curve’s dispersive branches, originally caused by the beams in the undeformed configuration, are cleared, and the original path of the group velocity is restored. This concept is introduced analytically and numerically in this thesis, and a novel device is proposed for controlling the SAWs. With regard to the mitigation of seismic waves, this thesis presents the application of two nonlinear dissipative devices to periodic components and structures of industrial facilities. Firstly, a finite locally resonant metafoundation of an MDoF fuel storage tank is equipped with fully nonlinear hysteretic devices to mitigate absolute accelerations and displacements in the low-frequency regime. Secondly, for mitigating the vibrations in PPRs, spatial periodicity and internal damping are combined to obtain an enhancement in the attenuation rate of the system. At the same time, the seismic performance of the PPR is improved by means of an external nonlinear VIS. These investigations show the characterization of the structures’ responses due to the stochastic nature of the input; and for the case of the VIS, a chaotic behavior is sometimes observed and demonstrated. In conclusion, this thesis investigates the nonlinear response of different periodic structures and their potential for wave control and mitigation in various applications. The results of this research contribute to the understanding of the nonlinear behavior of these periodic structures and provide insights into the design, the optimization, and the identification of metamaterials and metastructures performance.

Undulatory locomotion is a common and powerful strategy used in nature at different biological scales by a broad range of living organisms, from flagellated bacteria to prehistoric snakes, which have overcome the complexity of living in ”flowable” media. By taking inspiration from this evolution-induced strategy, we aim at modelling the locomotion in a granular and viscous environment with the objective to provide more insights for designing robots for soil-like media exploration. Moreover, in contrast to common types of movement, the granular locomotion is still not well understood and is an open and challenging field. We approached this phenomenon with several tools: (i.) numerically, via coupling the Finite Element Method (FEM) with the Discrete Element Method (DEM) using ABAQUS; (ii.) analytically, by employing the Lagrangian formalism to derive the equations of motion of a discrete and continuous system subject to non-conservative forces, and (iii.) experimentally, by creating an ad-hoc set up in order to observe the migration of microfibres used for the treatment of spinal cord injuries. The computational attempts to model the motion in a granular medium involved the simulation of the dynamics of an elastic beam (FEM) surrounded by rigid spherical particles (DEM). A propulsion mechanism was introduced by sinusoidally forcing the beam’s tip normally to the longitudinal axis, while the performance of the locomotion was evaluated by means of a parametric study. Depending on the parameters of the external excitation, after a transient phase, the slender body reached a steady-state with a constant translational velocity. In order to gain physical insights, we studied a simplified version of the previous continuous beam by introducing a discrete multi-bar system. The dynamics of the latter was analytically derived, by taking into account the forces exchanged between the locomotor and the environment, according to the Resistive Force Theory. By numerically solving the equations of motion and evaluating the input energy and dissipations, we were able to define the efficiency and thus provide an effective tool to optimise the locomotion. It is worth mentioning that the two approaches, despite the different physical hypothesis, show a qualitatively and quantitatively good accordance. The numerical and analytical models previously analysed have shown promising results for the interpretation of "ad-hoc" experiments that demonstrate the migration of a microfibre embedded in a spinal cord-like matrix. This migration needs to be avoided, once the regenerative microfibre is implanted in the lesioned spinal cord, for the sake of the patients health.