The present thesis summarizes the research activity in the field of elastic structures subject to tangential follower forces performed in the Instability Lab of the University of Trento. Elastic structures loaded by nonconservative positional forces are interesting from different perspectives. First, they are subject to flutter instability, a dynamical instability which remains undetected using static approaches. Second, in these structures dissipation plays a fundamental and destabilizing role. Third, a critical load calculated in the limit of vanishing dissipation is found to be smaller than the critical load calculated in the same structure where the dissipation is assumed absent 'from the beginning'. This behaviour is so peculiar that is usually referred to as 'the Ziegler paradox' and was never experimentally substantiated before. Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and PflÃ1⁄4ger's columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of the rod in the latter case), have attracted, and still attract, a thorough research interest. In the present thesis, the effects of internal and external damping, crucial in the interpretation of experiments, have been investigated. Contrary to a common belief, it has been shown that the effect of external damping is qualitatively the same as the effect of internal damping, both yielding a pronounced destabilization paradox. This result corrects previous claims relative to destabilization by external damping of the Ziegler's and PflÃ1⁄4ger's elastic structures. The major challenge in the research area of follower forces is the practical realization of these forces, which was previously obtained only for the case of the Ziegler double pendulum (a two-degrees-of-freedom elastic system subject to a tangential force). Therefore, an experimental setup to introduce follower tangential forces at the end of an elastic rod was designed, realized, validated, and tested, in which the follower action is produced by exploiting Coulomb friction on an element (a freely-rotating wheel) in sliding contact against a plate (realized by a conveyor belt). It is therefore shown that follower forces can be realized in practice and the first experimental evidence is given of the flutter and divergence instability of the PflÃ1⁄4ger's column. Load thresholds for both the two instabilities are measured for the first time. Moreover, the detrimental effect of dissipation on the critical load for flutter is experimentally demonstrated. The introduced approach to follower forces discloses new horizons for testing self-oscillating structures and for exploring and documenting dynamic instabilities possible when nonconservative loads are applied.

A new trend in the mechanical design of devices for advanced technologies, such as soft robotics and micro/nano mechanics, is the exploitation of structures undergoing large deflections, in an attempt of achieving superior performances. Within this framework, non-linear modelling becomes a fundamental tool for the design of compliant structures and deformable mechanism. Two structural systems are investigated, both based on the planar elastica and subject to movable and configurational constraints. These two structures disclose unforeseen behaviours when the values of the parameters defining the models are varied. The first structural system is an elastic rod constrained by a slowly rotating clamp, while the other end is loaded with a lumped mass weight. When this weight is lower than that corresponding to buckling, the edge of the rod describes a closed curve, behaving as an elastica compass. Differently, when the load is higher than that of buckling, a release of elastic energy is observed, leading to a snapback of the structure, so that the rod realizes an elastica catapult. The clamp in the above described structure is replaced by a frictionless and fixed sliding sleeve in the second system considered in this thesis. The rod is subject to a sudden release from the underformed configuration, providing dynamic effects on the system. By means of the variational approach, the presence of a configurational force at the exit of the sliding sleeve is proven within the dynamical setting, extending previous results restricted to the quasi-static assumption. The configurational force is found to strongly affect the dynamics of the structure. In particular, two different behaviours are observed, in which the rod may either completely penetrate in ("injection") or be expelled from ("ejection") the sliding sleeve. In both the above problems, the theoretical predictions are corroborated through the experimental validation on physical models, which have been ad hoc invented and designed. A new insight is obtained in the design of flexible devices, paving the way to applications in soft robotics.

Dielectric elastomer (DE) actuators are electromechanical transducers that essentially consist of one layer of an insulating soft elastomer coated on both sides with com- pliant electrodes. When a voltage is applied between the electrodes, an electrostatic pressure deforms the elastomer triggering the motion of the actuator. In this the- sis, this principle is exploited for the development of three different actuators: an electroactive compression bandage, a hydrostatically coupled actuator for use in the field of soft manipulators and a dielectric elastomer based inchworm-like robot able to perform locomotion. By doing so, several challenges related to the design, to the modeling and to the manufacturing of this kind of devices are raised and tackled. During the development of the electroactive compression bandage, the issue of electrical insulation and prevention of electrical discharge in wearable devices was addressed by using coating layers as an interface between the DE actuator and the human body. Both experimental investigations and a finite electro-elasticity analyti- cal model showed that the passive layers play a key role for an effective transmission of the actuation from the active layers to the load. Indeed, the model showed that by increasing the number of electroactive layers, the pressure variation can be increased, although with a saturation trend, providing a useful indication for future designs of such bandages. The second piece of work here reported consists in a design upgrade of the Hy- drostatically Coupled Dielectric Elastomer Actuator (HC-DEA), already known in the literature, that enable its use in the field of soft manipulators. The new design fea- tures segmented electrodes, which stand as four independent elements on the active membrane of the actuator, enabling it for generating both out of plane and in plane motions. This novel design makes the actuator suitable for delicate transportation of a flat object. This capability was proven via an experimental investigation in which a flat Petri dish was roto-translated on a platform composed of two actuators. The electromechanical transduction performance of the actuator was characterized and its contact mechanics was modeled. Finally, a smart robot structure that exploits anisotropic friction to achieve stick- slip locomotion is presented. The robot, which is made out just of a plastic beam, a planar dielectric elastomer actuator and four bristle pads with asymmetric rigid metallic bristles, exploits the resonance condition to reach the maximum locomotion speed. The fundamental frequency of the structure, which was estimated both ana- lytically and numerically, was identified within the range of frequencies in which the top locomotion speed was observed during the experiments to be identified.

Whenever two bodies are in contact due to a normal load and one is sliding against the other, a tangential force arises, as opposed to the motion. This force is called friction force and involves different mechanisms, such as asperity interactions, energy dissipation, chemical and physical alterations of the surface topography and wear. The friction coefficient is defined as the ratio between the friction force and the applied normal load. Despite this apparently simple definition, friction appears to be a very complex phenomenon, which also involves several aspects at both the micro- and nano-scale, including adhesion and phase transformation. Moreover, it plays a key role in a variety of systems, and must be either enhanced (e.g. for locomotion) or minimized (e.g. in bearings), depending on the application. Considering friction as a multiscale problem, an analytical model has been proposed, starting from the literature, to describe friction in the presence of anisotropy, adhesion and wear between surfaces with hierarchical structures, e.g. self-similar. This model has been implemented in a MATLAB code for the design of the tribological properties of hierarchical surfaces and has been applied to study the ice friction, comparing analytical predictions with experimental tests. Furthermore, particular isotropic or anisotropic surface morphologies (e.g., microholes of different shapes and sizes) has been investigated for their influence to the static and dynamic friction coefficients with respect to a flat counterpart. In particular, it has been proved that the presence of grooves on surfaces could decrease the friction coefficients and thus reduce wear and energy dissipation. Experimental tests were performed with a setup realized ad hoc and the results were compared with full numerical simulations. If patterned surfaces showed that they can reduce sliding friction, other applications could require an increase in energy dissipation, e.g. to enhance the toughness of microfibers. Specifically, the applied method consists of introducing sliding frictional elements (sliding knots) in biological (silkworm silk, natural or degummed) and synthetic fibres, reproducing the concept of molecules, where the sacrificial bonds provide higher toughness to the molecular backbone, with a hidden length, which occurs after their breakage. A variety of slip knot topologies with different unfastening mechanisms have been investigated, including even complex knots usually adopted in the textile industry. The knots were made by manipulation of fibres with tweezers and the resulting knotted fibres were characterized through nanotensile tests to obtain their stress-strain curve until failure. The presence of sliding knots strongly increases the dissipated energy per unit mass, without compromising the structural integrity of the fibre itself.

An elastic-visco-plastic thermomechanical model for cold forming of ceramic powders and subsequent sintering is introduced and based on micromechanical modelling of the compaction process of granulates. Micromechanics is shown to yield an upper-bound estimate to the compaction curve of a granular material, which compares well with other models and finite element simulations. The parameters of the thermomechanical model are determined on the basis of available data and dilatometer experiments. Finally, after computer implementation, validation of the model is performed with a specially designed ceramic piece showing zones of different density. The mechanical model is found to accurately describe forming and sintering of stoneware ceramics and can therefore be used to analyze and optimize industrial processes involving compaction of powders and subsequent firing of the greens.

A second-gradient elastic material has been identified as the equivalent homogeneous material of an hexagonal lattice made up of three different orders of linear elastic bars (hinged at each junction). In particular, the material equivalent to the lattice exhibits: (i.) non-locality, (ii.) non-centrosymmetry, and (iii.) anisotropy (even if the hexagonal geometry leads to isotropy at first-order). A Cauchy elastic equivalent solid is only recovered in the limit of vanishing length of the lattice’s bars. The identification of the second-gradient elastic material is complemented by analyses of positive definiteness and symmetry of the constitutive operators. Solutions of specific mechanical problems in which the lattice response is compared to the corresponding response of an equivalent boundary value problem for the homogeneous second-gradient elastic material are presented. These comparisons show the efficacy of the proposed identification procedure.

Cells physical properties and functions like adhesion, migration and division are all regulated by an interplay between mechanical and biochemical processes occurring within and across the cell membrane. It is however known that mechanical forces spread through the cytoskeletal elements and reach equilibrium with characteristic times at least one order of magnitude smaller than the ones typically governing propagation of biochemical signals and biological phenomena like polymerization/depolymerization of protein microfilaments or even cell duplication and differentiation. This somehow allows to study as uncoupled many biochemo- mechanical events although they appear simultaneously and as concatenated. In this work, the complex machinery of the cell is hence deprived of its biochemical processes with the aim to bring out the crucial role that mechanics plays in regulating the cell as a whole as well as in terms of some interactions occurring at the interface with the extra-cellular matrix. In this sense, the single-cell is here described as a mechanical unit, endowed with an internal micro-architecture –the cytoskeleton– able to sense extra-cellular physical stimuli and to react to them through coordinated structural remodelling and stress redistribution that obey specific equilibrium principles. By coupling discrete and continuum theoretical models, cell mechanics is investigated from different perspectives, thus deriving the cell overall elastic response as the macroscopic projection of micro-structural kinematics involving subcellular constituents. Finally, some optimal arrangements of adherent cells in response to substrate-mediated elastic interactions with external loads are explored and compared with experimental evidences from the literature.

During my PhD activities, I studied the introduction of carbon-based nanofillers in materials at different scales, while focusing primarily on fibres and fibrillar materials. Several production techniques were exploited. Little is known about the interaction of graphene with electrospun polymeric fibres. Manufacturing composite fibres is complex since fillers have lateral sizes nearing that of the embedding fibre. Indeed, graphene has a direct effect in both the assembly of the electrospun composite fibres and their mechanical performance. Moreover, the tensile behaviour of hollow micrometric electrospun fibres was compared with macroscopic hollow structures such as drinking straws. The acquired insights helped to explain the toughening mechanisms at the micro-scale and develop a model capable of predicting the stress-strain response of such structures. Among natural materials, wood has the most relevant structural applications even at large scales. Its main structural component is cellulose that has a high resistance and a low light absorption. Several structural modifications of wood derived materials were recently investigated in order to enhance the mechanical and optical properties of cellulose. These enhancements can take place after the internal structure is chemically modified with the removal of lignin and after a structural densification. Potentially, any type of wood-like materials, such as giant reed (that is a fast-growing and invasive species), can be turned into a strong structural composite. Such modifications lead to an open and interconnected internal structure that is the ideal scaffold for nanoparticle intercalation. Graphene oxide and silicon carbide nanoparticles were intercalated into densified reed. They produced an even stiffer, stronger and tougher composite compared to the best up-to-date process available. Moreover, its capabilities to resist fire and water-absorption were tested. Finally, the previous process was further developed on wood to achieve a combination of improved transparency and electrical conductivity. Graphene and carbon nanotubes were introduced into the structure of wood to foster conductivity and explore the viability of its application as a self-strain sensor.

No description available.

Dielectric elastomers (DEs) are an important class of materials, currently employed in the design and realization of electrically-driven, highly deformable actuators and devices, which find application in several fields of technology and engineering, including aerospace, biomedical and mechanical engineering. Subject to a voltage, a membrane of a soft dielectric elastomer coated by compliant electrodes reduces its thickness and expands its area, possibly deforming in-plane well beyond 100%: this principle is exploited to conceive transducers for a broad range of applications, including soft robots, adaptive optics, Braille displays and energy harvesters. Soft dielectrics undergo finite strains, and their modelling requires a formulation based on the Mechanics of Solids at large deformations. A major problem that limits the widespread diffusion of such devices in everyday technology is the high voltage required to activate large strains, because of the low dielectric permittivity of typical materials (acrylic elastomers or silicones), in the order of few unities, which governs the electromechanical coupling. Composite materials (reinforcing a soft matrix with stiff and high-permittivity particles) provide a way to overcome these limitations, as suggested by some experiments. In addition, composites can display failure modes and instabilities not displayed by homogeneous specimens that must be thoroughly investigated. Commonly, instability phenomena are seen as a serious drawback, that should be predicted and avoided. However, in some cases they can be used to activate snap-through actuation, as in the case of buckling-like or highly-deformable balloon-like actuators. Soft dielectric elastomers display electrostrictive properties (permittivity depending on the deformation) and we show how to take into account such a phenomenon within the theory of electroelasticity. Original results regard the investigation of diffuse modes (buckling like instabilities etc.), surface mode instabilities and localized modes. New (analytical) solutions for band-localization instability are provided and then it has been investigated how such instabilities are related to electrostriction. Regarding DE composites, the goal is to evaluate in detail the behaviour of two-phase rank-1 laminates in terms of different types of actuation, geometric and mechanical properties of phases, applied boundary conditions, and instabilities phenomena, in order to establish precise ranges in which the performance enhancement is effective with respect to the homogeneous counterpart.