The present Ph.D. dissertation is divided into two Parts: Green's function and problems of the inclusions and dislocations are addressed in the first Part, while implementation of elastoplastic constitutive laws are treated in the second. These subjects can be seen as different approaches to the investigation of the plastic behaviour of materials. In the first Part, infinite-body two-dimensional Green's functions are derived for the incremental deformation of an incompressible, anisotropic, prestressed body. These functions, given by Bigoni and Capuani, show the response of an infinite body to a concentrated force. The effect of prestress on dislocation (and inclusion) fields in non-linear elastic solids is analyzed by extending previous solutions by Eshelby and Willis. Employing a plane strain constitutive model (for incompressible incremental non-linear elasticity) to describe the behaviour a broad class of (anisotropic) materials, but with a special emphasis on ductile metals (J2-deformation theory of plasticity), it is shown that strongly localized strain patterns emerge, when a dislocation dipole is emitted by a source and the prestress level is high enough. These strain patterns may explain cascade activation of dislocation clustering along slip band directions. Several of the presented results remain valid within a three-dimensional context. Novel infinite-body three-dimensional Green's functions are derived for the incremental deformation of an incompressible, anisotropic, prestressed body. The case of a force dipole is developed within this framework. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity loss and to reveal features related to shear failure cones development in a three-dimensional solid medium. Non-standard elastoplastic constitutive laws are treated in the second Part of the present Ph.D. dissertation, based on pressure-sensitive yield functions, such that proposed by Bigoni and Piccolroaz, which describes the inelastic deformation of ceramic powders and of a broad class of rock-like and granular materials. This yield function is not defined outside the yield locus, so that 'gradient-based' integration algorithms of elastoplasticity cannot be directly employed. Therefore, two ad hoc integration algorithms are proposed: an explicit scheme based on a forward Euler technique with a 'centre-of-mass' return correction and an implicit scheme based on a 'cutoff-substepping' return algorithm.

The developments in conceptual design, material technology and efficient construction techniques enabled the creation of longer, lighter, slender and stylish Cable-Stayed Foot Bridges (CSFB). Hence, modern CSFB can be characterized by interacting phenomena like cable nonlinearities, deck dynamic instability and deck lateral oscillations due to pedestrian walking. These phenomena, if intertwined, may bring these structures out of service or to failure. In view of a better performance, additional damping can be provided by passive dampers. However, amplitude dependent behaviour of dampers and slip in connections can make them effective only above a threshold amplitude. Hence, due to high uncertainties in the complex CSFB-damper system, usually, dynamic tests are performed to investigate the performance of the overall system. In this thesis, the effectiveness of the passive vibration reduction system in a complex cablestayed footbridge characterised by two curved decks was investigated. The amplitude dependent behaviour was found both with the output-only ambient vibration and free decay tests. In order to clarify these outcomes, modal quantities were calculated instantaneously,based on time-frequency identification techniques. A thorough analysis of dynamic response signals revealed that the structure with dampers actually behaved like a threshold system: i) for low vibration levels the dampers were still, so that they performed as constraints that stiffened the structure; ii) for high vibration levels, the dampers became fully working. Moreover, a deckcable interaction between one of the longest cables and the first global mode was detected. Initially, the modal properties estimated from the dynamic tests did not match those of the numerical model. In order to have a robust FE model capable to simulate the actual behaviour of the footbridge, model updating was performed. The sensitivity-based model updating techniques and Powell's Dog-Leg method of optimisation based on the Trust-Region approach were used. The final updated model showed a considerable reduction in the percentage error of frequencies. The updated model was able to reproduce the response of the footbridge under actual wind conditions. The revealed cable-deck interaction phenomenon was a motivation to investigate in depth the dynamics of long stay cables. Therefore, efforts were made towards the identification of the nonlinear behaviour of stay cables from measured response data. In view of the fact that actual measured data contained the response of a MDoF system, the first step in this direction was to investigate the feasibility of the nonlinear identification method, i.e. a nonparametric approach applied to a SDoF cable system. The results revealed a good fitting between identified and numerical data, where only a cubic type of nonlinearity was identified. Moreover, an increase of the parameter related to damping and a decrease of the parameter relevant to linear-frequency were observed versus the loading amplitude. However, the values of the parameters stabilised at higher load amplitudes and superharmonics were present in the response. The proposed non-parametric method exhibited a good capability in the nonlinear parameter identification of cables. Approaching towards a more complete understanding of the performance of cable-stayed footbridges, it was realized that the modern footbridges are more prone to pedestrian-induced vibrations that, eventually, degrades their serviceability performance. Moreover, several researchers tried to investigate the problem of synchronous lateral excitation of footbridges, but there is no general consensus on pedestrian models. Therefore, a model of pedestrian-footbridge interaction was proposed. In detail, pedestrian was represented by a modified hybrid Van der Pol/Rayleigh (MHVR) self-sustained oscillator. Amplitude, stability and phase of the MHVR oscillator solution under a harmonic external force associated with the floor motion were analytically evaluated by the harmonic balance method and was compared with numerical results. It was shown that the phase difference tended to become constant at high excitation amplitudes. Moreover, the stability domain was found useful in predicting the percentage of pedestrians synchronized to a given oscillating floor. The numerical results of MHVR oscillator was, then, compared with the experimental result of a shake table with harmonic floor motion. A good agreement in amplitude ratio was found, however, the phase difference resulted to be underestimated by the MHVR model.

A Dielectric Elastomer Generator (DEG) is an electromechanical transducer, basically a highly deformable parallel-plate capacitor, made up of a soft DE membrane coated with two compliant electrodes on its opposite surfaces. This device is able to convert mechanical work, emanating from its interaction with the environment, into electrical energy. The capacitance depends on the deformation undergone by the membrane, and its variability can be exploited to extract electric energy by (i) initially stretching, (ii) then charging the capacitor, (iii) subsequently releasing the stretch and finally (iv) harvesting the charge at a higher electric potential. The optimisation procedure for a load-driven soft planar DEG is presented, assuming hyperelastic and ideal dielectric behaviour. The DEG undergoes the ideal four-stroke electromechanical cycle previously described and its performance is evaluated on the basis of the energy extracted during a cycle and of the efficiency, defined as the ratio of the harvested energy on the total invested energy. The amount of extracted energy is limited due to possible failures of the device, which are, in the most general case, electric breakdown, material rupture, buckling-like instabilities due to loss of the tensile stress state and electromechanical instability. These failure mechanisms determine the allowable state region for the generator. Hence, in order to identify the best cycle that complies with these limits, a constrained optimisation problem is formulated and the generator performance is estimated. For the different loading cases examined, namely equibiaxial stress state and plane strain, numerical results show, as expected, a critical dependence of the harvested energy on the ultimate stretch ratio and, against expectations, a universal limit on the dielectric strength of the DE membrane beyond which the optimal cycle is independent of this parameter. Thus, there is an upper bound on the harvested energy, which depends only on the ultimate stretch ratio. In addition to the simple parallel-plate configuration, an annular DEG deforming out-of-plane has been analysed. In this configuration the generator is made up of an annular membrane constrained at the boundary by a rigid ring and at the centre by a rigid plate, on which an external force is applied. Due to the loading, the membrane deforms non-homogeneously out-of-plane. In order to avoid loss of the tensile stress state, electric breakdown and electromechanical instability, the applied voltage is controlled, thereby limiting the maximum voltage and keeping the maximum stretch in an admissible range. Numerical results show that the prestretch of the membrane is crucial for an effective behaviour of the device. In fact, the unprestretched generator performs poorly with regard to both energy and efficiency. A small prestretch, of approximately 5%, ensure a sixfold improvement in the gained energy and a fivefold increment in efficiency. The performance of the generator is evaluated for different values of the applied load and of the prestretch. This analysis shows that increasing the applied force the harvested energy increases monotonically, while the efficiency increases until a peak value and then decreases. Hence, for an out-of-plane DEG, the choice of the applied force is decisive to ensure a good trade-off among energy and efficiency. Moreover, a comparison of different DEG layouts demonstrates that the annular DEG can compete with the equibiaxial planar generator, in terms not only of efficiency, but also of harvested energy. What has been so far pointed out is valid under the hypothesis of ideal, lossless material. Since polymers are affected by time-dependent effects, this hypothesis appears to be not completely realistic. Indeed, a predicting model for soft dielectric elastomer generators must include a realistic model of the electro-mechanical behaviour of the elastomer filling, the variable capacitor and of the electrical circuit connecting all the device components. To this end, the ideality assumption of the material and of the cycle has to be removed. Hence, a complete framework for a reliable simulation of soft energy harvesters is proposed for a soft viscous dielectric elastomer generator, operating in an electrical circuit for energy harvesting and subjected to a periodic mechanical stretch. The electrical model of the generator takes into account the effects of the electrodes and of the conductivity current through the dielectric material. A phenomenological electro-viscoelastic model at large strain is proposed and calibrated on the basis of experimental data available in literature for a polyacrylate elastomer (VHB-4910). The effects of viscoelasticity and of possible changes of the permittivity with strains on the generator performance are hence investigated. Numerical results underline the importance of time-dependent effects on the evaluation of the generator performance. The main outcome of this analysis is that, compared with a hyperelastic model, the efficiency is reduced by viscoelasticity for high values of the mean stretch and of the amplitude of stretch oscillation. The reduction is almost insensitive of the mechanical frequency while the efficiency is further reduced by the variation of the permittivity with strain. Moreover, viscoelastic effects modify the allowable state region of the generator. At regime condition, the failure curves relative to electromechanical instability and to loss of the tensile stress state are strongly modified by the viscous effects. This fact results in the alteration of the allowable state region of the generator. Furthermore, due to the change in shape and size of the admissible region under this condition, a more surprising result is the fact that the natural configuration is a not-allowed state. As a consequence, there is an upper bound on the maximal stretch oscillation amplitude. Focusing on the main features of the electrical circuit, an important outcome of the analysis is the identification of a value range of the external electric load for which the efficiency is maximal. Furthermore, the viscous dissipation of the material dominates the energy loss arising from the leakage current across the dielectric membrane.

The concept of "integral abutment bridge" has recently become a topic of remarka-ble interest among bridge engineers, not only for newly built bridges but also during refurbishment processes. The system constituted by the substructure and the superstructure can achieve a composite action responding as a single structural unit; the elimination of expansion joint and bearings on the abutments, greatly reduce the construction and maintenance costs. To maximize the benefits from integral abutment bridges, the direct way is to achieve the super-long integral abutment bridge. However, as the environment temperature changes, the lengths of superstructure increase and decrease, pushing the abutment against the approach fill and pulling it away. The responses of bridge superstructure, the abutment, the approach system, the foundation/piles and the foundation soil are all different. And it's important to understand their interactions effective design and satisfactory performance of integral abutment bridges. In order to build longer integral abutment bridges, therefore in this research, the lit-erature survey on the applications of integral abutment bridges in worldwide, espe-cially the current development of super-long integral abutment bridges was carried out firstly. Another literature review on soil-structure interaction was conducted to find out the most suitable methods in considering this kernel issue in design of integral abutment bridge. Through proposing finite element models for integral abutment bridges that could involve the soil-structure interaction, thermal actions, non-linearity in materials and so on, structural study was performed on an existing super-long integral abutment bridge, including parametric analysis, pushover analysis, and dynamic tests. Then, the performance of integral abutment bridge was better understood, and no critical structural problem was found for integral abutment bridge. Based on that, length limit for this kind of bridge was evaluated and investigated in an analytical way. Considering capacities of abutments and piers, and under the conditions of an existing integral abutment bridge, the length limit was found to be around 540m. With this super length, the piles need to be designed with capacity of large lateral displacement. Therefore, an effective optimization approach, associating the finite element method with global optimization algorithm was presented for pile shape design. At the end, considerations accounted in the design of super-long integral abutment bridges were discussed, making construction of super-long integral abutment bridge of great possibility.

This study concerns a new probabilistic framework to evaluate road/railway bridges after an earthquake by means of analytical fragility curves and inspections on the structure. In particular, the assessment is performed on existing reinforced concrete (RC) bridges with a common structural scheme in Italy (multi-span simply supported girder bridges). The framework is set up of 6 steps and each step is investigated. Steps 1 and 2 are a sort of preliminary work before the seismic event occurs: the creation of a database to collect all information about bridges in specific road/railway networks (step 1) and the generation of fragility curves for each bridge (step 2): fragility curves are instruments describing the probability of a structure being damaged beyond a specific damage state for various levels of ground shaking. Since step 2 is a crucial step for the outcomes of the framework, a wide investigation on the generation of fragility curves is presented, considering bridges located in strategic road network points in Veneto region (North-Eastern Italy) and different numerical modellings, in order to evaluate the best seismic vulnerability assessment. Moreover, particular attention is given to retrofit interventions by means of Fiber Reinforced Polymer (FRP) and their effect on bridge seismic vulnerability reduction. The other steps concern activities to carry out after a seismic event, useful for emergency and post-emergency phases. Step 3 regards a method to decide if inspections on bridge are needed in relation to the occurred earthquake seismic intensity; if the seismic intensity measure reaches a specific threshold, step 4 suggests how to perform visual inspections on bridges, under a probabilistic point of view, and to generate the damaged bridge fragility curves. After that, the last two steps try to give useful information to Institution and owners of bridges in order to reach an optimal road/railway network management in post-earthquake phases. Step 5 concerns a quick procedure to decide whether or not allowing traffic over damaged bridges, whereas step 6 gives information about economical benefits coming from a comparison between replace costs and retrofitting costs (considering FRP retrofitting interventions) of damaged bridges. In order to clarify the framework procedure, an example for each step is developed.

The Eshelbian force is the main concept of a celebrated theoretical framework associated with the motion of dislocations and, more in general, defects in solid. Similarly, it is proven that a force driving the configuration of an elastic structure is generated through the motion and release mechanism of flexural and torsional energy. This configurational force, analytically derived through different approaches and experimentally validated, provides counterintuitive but crucial effects in elasticity. In particular, it affects equilibrium paths in systems with variable length and instabilities, bifurcation and restabilization occurring in a structure penetrating in a movable constraint. Furthermore, this configurational force (called 'Eshelby-like' in analogy to continuum mechanics) opens a totally new perspective in the mechanics of deformable mechanisms, with possible broad applications in new weighing devices (the 'elastica arm scale'), torsional locomotion along perfectly smooth channel and configurational actuators, capable of transforming torque into propulsive force.

In the last decades the need for an effective seismic protection and vulnerability reduction of strategic structures and particularly the architectural heritage determined a growing interest in Structural Health Monitoring (SHM) as a measure of passive mitigation of earthquake effects. The object of monitoring is to identify, locate and classify type and severity of damages induced by external actions or degradation phenomena and to assess their effects on the structural performance. In this way it is possible to take appropriate measures to reduce the danger of collapse and, when necessary, perform strengthening interventions to improve the structural and seismic capacity. Motivated by the above reasons, this thesis aims at providing a contribution to the development of techniques and integrated methodologies, based on SHM, for the assessment and protection of Cultural Heritage (CH) buildings and monuments. Firstly, after a detailed state of the art review on specific topics related to SHM of civil engineering structures, a new methodology for the implementation of monitoring techniques on historic masonry structures is proposed. Selected case studies, equipped with distributed sensors and acquisition systems, allowed the definition and successive validation of SHM as a knowledge-based assessment tool, implemented to evaluate intervention needs, following an incremental approach during their execution, and to control the damage states of buildings in a post-seismic scenario. In order to maximize the benefits of SHM and optimize the entire process, dedicated software for static monitoring and automated algorithms for modal parameters identification have been developed, able to provide almost real time information on the health state of the monitored structure. Finally integrated procedures based on robust statistical and numerical models have been implemented to interpret and exploit SHM outputs to assess the structural conditions of the investigated CH buildings.

Finite plane strain bending is solved for a multilayered elastic–incompressible thick plate. This multilayered solution, previously considered only in the case of homogeneity, is in itself interesting and reveals complex stress states such as the existence of more than one neutral axis for certain geometries. The bending solution is employed to investigate possible in-plane and out-of-plane incremental bifurcations. The analysis reveals that a multilayered structure can behave in a completely different way from the corresponding homogeneous plate. For a thick plate of neo-Hookean material for instance, the presence of a stiff coating strongly affects the bifurcation critical angle. Experiments designed and performed to substantiate our theoretical findings demonstrate that the theory can be effectively used as a design tool for predicting the capability of an elastic multilayered structure.

The research presented in this thesis was focused on timber floor diaphragms in unreinforced masonry (URM) buildings. The work was divided into two phases. The first phase was aimed at the investigation of the effects of the in-plane behavior of timber diaphragms on the global seismic response of URM buildings. The second phase was dedicated to the assessment and retrofit of timber floors, with particular attention to the out-of-plane behavior. A study on the equivalent frame method, which is a more and more appreciated masonry modeling technique, is presented. Both as-built and strengthened timber floors were addressed. In order to understand the influence of the masonry modeling method on the seismic response of URM structures when flexible diaphragms are concerned, a simplified elastic no tension method was proposed. Such method is able to describe the characteristic nonlinear behavior of masonry (due to extremely low tensile strength) by means of a series of linear analyses based on a Rankine failure criterion. An in-situ testing campaign on full-scale 100 year old timber diaphragms is presented. Both mechanical and dynamic in-plane properties of wood diaphragms were investigated. Cyclic and snap back tests were carried out thanks to an innovative ad hoc loading system, developed by means of wire ropes and steel pulleys. The loading system was designed to reproduce a realistic inertial load distribution and to be lightweight, versatile and easily relocatable from one diaphragm section to the next. The effect of different refurbishment techniques was also probed during the experimental campaign. The outcomes of a testing campaign regarding out-of-plane refurbishment techniques of existing timber floors by means of timber to timber composite structures are described. A numerical model based on the theory of composite beams with incomplete interaction, was calibrated to take into account the real load distribution and connector spacing. An original procedure to camber timber beams by employing the compression pressure generated by screw fasteners is presented. The camber deflection is attained by superposing a timber reinforcement element on top of a beam and then connecting the two elements by means of screws inserted at 45° to the beam axis. Such method which is currently patent pending, was validated using data obtained from experimental testing. A mathematical formulation was also developed to describe the cambering procedure. A specific experimental campaign was therefore performed to precisely evaluate the amount of pressure that each screw is capable of yielding. Many parameters supposed to affect the compression force, were explored through 170 tests.

The thesis aims to investigate the dynamical criticality of a pedestrian footbridge and the use of a semi-active tuned mass damper. In this respect, the work appears threefold since the first and third part regard identification of a realistic model for the damping device and semi-active control of the magneto-rheological damper. In this respect, input identification techniques are a useful tool and an aid for the control law design. As a consequence, the second part involves both input identification strategies for a dynamic system and analysis of issues related to the inherent delay. In this respect, the so called “collocation” of measurement devices with respect to the application points of the input is critical, together with the concept of kernel.