In the last decades, powder technology has become one of the most important technological processes for the production of metallic and ceramics components; free sintering, hot isostatic pressing and hot forging are different ways to realize a key-phase in which the primary mechanical properties of the final material are obtained. A theory of sintering is necessary in order to be able to predict the final structure of a body undergoing such a kind of process. In this respect, it is crucial to be able to follow the evolution of the mechanical properties of the material (determined by this structure) during sintering and to get the final features of the compound at the end of this process. In this thesis, the influence of the pressure called “sintering stress” or “Laplace pressure” produced by the gas employed during the process and which gets trapped into the pores is analyzed. This is done for pre-compacted (micro/nano)-powdered axially-symmetric samples undergoing (i) isostatic pressing (also covering the case of free sintering), (ii) "free" forging (i.e. axial compressive load acting at the top and bottom faces of the specimens, with no lateral confinement) and (iii) constrained forging (i.e. transverse compression of the samples in a rigid die). Such cases are among the ones suggested in Olevsky, E.A., Molinari, A., “Kinetics and stability in compressive and tensile loading of porous bodies”. The role of the Laplace pressure in all of the mentioned cases is twofold. First of all, such a pressure influences the evolution of the porosity and, for instance, its residual value for a given time duration of the process. It is worth emphasizing that threshold pressures below which the sintering stress is actually not negligible are determined in this thesis; the duration of the process is indeed heavily affected by such a stress. In turn, such a duration would be underestimated otherwise. Furthermore, industrial processes often entail loading pressures lower than the thresholds mentioned above, especially of "small" grain sizes. The second aspect is based on a common feature exhibited by the two modes mentioned above: the loading parameter may be tuned in such a way that, at some stage of the sintering process, its value may equate the Laplace pressure, leading to a constant value of the porosity. Whenever this is the case, for (i) there exists a whole range of the loading parameter for which the process is actually unstable. Henceforth, in order to have stability of sintering either the loading parameter must be high enough with respect to the Laplace pressure or zero, leading to (stable) free sintering. For (ii), the stability analysis shows that the results obtained by using the different models for the shear and bulk moduli do not agree for a restricted range of external load. This is of course an intrinsic pathology of his specific loading mode. Moreover, it is worth noting that large strains occur in such a mode. Thus, both the stress and the (infinitesimal) strain employed in this analysis should be replaced by appropriate (possibly work-conjugate) choices of the stress and strain measures, although this goes beyond the aim of this work. For (iii), a stability analysis allows us to conclude that such a value represents a critical threshold, below which the sintering process cannot proceed. In the second part of the present work, the mechanical behavior of sintered specimens are investigated. Such a behavior is strongly influenced by the stress state at the end of the process, which depends on the final value of the interstitial pressure and of the loading mode used during the process. For the sake of simplicity, only the two "realistic" cases of isostatic pressing (also covering free sintering) and constrained forging are considered. For such components, isostatic pressing may induce isotropy, whereas constrained forging processes may enforce a transverse isotropic behavior in the direction of forging. Although for prestresses isotropic material the explicit constitutive law is given by Man in “Hartig's law and linear elasticity with initial stress”, the analog for the case of transversely isotropic material is deduced here, for the first time, through a method, suggested by Weiyi , “Derivation of the general form of elasticity tensor of the transverse isotropic material by tensor derivate”, based upon the partial differentiation of the strain energy with respect to both the strain tensor and the residual stress. Finally, the residual stress tensor for specimens sintered through (i) and (iii) is obtained and the correspondent stress response is deduced. Equivalent material constants (two constant in the case of isotropy, five in the case of transverse isotropy) arising in the presence of prestress may be introduced; such constants take the place of the classical material moduli characterizing the response in the absence of residual stresses. Finally, an experimental procedure to determine the values of such constants is proposed.

The asymptotic behavior of a linearly elastic composite material that contains a thin interphase is described and analyzed by means of two complementary methods: the asymptotic expansions method and the study of the weak form using variational methods on Sobolev spaces. We recover the solution of the system of linearized elasticity in the two dimensional vectorial case and we find limit transmission conditions. The same steps are followed for harmonic oscillations of the elasticity system, and different solutions are found for concentrated mass densities. The cases in which the elastic coefficients depend on the thickness of the small parameter, for soft as well as stiff materials are considered. An approximated solution is found for harmonic oscillations of the elasticity system and limit transmission conditions are derived. Considering a bounded rectangular composite domain, with a thin interphase, we describe the weak formulation of the linearized system of elasticity. In the case of constant elastic coefficients, we estimate the bounds of the strain tensor and so, the energetic functional in the rescaled domain. We perform a variational formulation of the system of linearized elasticity and find estimates for the energetic functional of the system.

The ability of plant roots to penetrate soils is affected by several stimuli from the surrounding medium such as mechanical stresses and chemical changes. Therefore, roots have developed multiple responses to the several outer stimuli. Since plant roots have to face very complex problems to grow deeply into the ground, they are remarkable examples of problem-solving behaviour and adaptation to the outer constraints. The adaptation strategies of a natural root are not yet completely known and understood with exhaustive explanations. For this reason, mathematical models and experimental techniques applied to biological phenomena can perform a key role in translating the Nature adaptive solutions into engineering applications. The aim of this thesis is to provide further insights in understanding biological phenomena for the development of new technologies inspired by the adaptive ability of plant roots. Accordingly, both theoretical and experimental explanations to the adaptive behaviour of plant roots are proposed. The mathematical modelling is based on a modified version of the extended West, Brown and Enquist universal law, considering the root growth as an inclusion problem. The proposed equation has as a particular case a growth equation exploiting an approach similar to Lockhart taking into account the soil impedance. The influence of mechanical stresses and nutrient availability on the root growth are studied. The solutions of the analytical models are compared with experimental data collected in real and artificial soils. In addition, the theories and hypotheses of the root ability to grow in the apical region through nanoindentation, wettability, and photoelasticity are investigated. The first technique provided insights for the possible role and function at both different tissues levels and distances from the tip in the root movement and penetration during the growth. The investigation of root tissue properties revealed that the penetration and adaptation strategies adopted by plant roots could be enhanced by a combination of soft and stiff tissues. The second technique aimed to highlight the wettability of the apical zone and root hairs for the acquisition of water and nutrients. Finally, photoelastic experiments provided a non-invasive and in situ observation of plant roots growth and, by exploiting the fringe multiplication, a set up for the study of plant roots growing in edible gelatine is proposed.

The study of local and global instability and bifurcation phenomena is crucial for many engineering applications in the field of solid mechanics. In particular, interfaces within solid bodies are of great importance in the bifurcation analysis, as they constitute localized zones in which discontinuities or jumps in displacement, strain or stress may occur. Different instability phenomena, heavily conditioned by the presence of interfaces, were analyzed in the present thesis. The first phenomenon that has been considered is the propagation of a shear band, which is a localized shear deformation developing in a ductile material. This shear band, assumed to be already present inside of a ductile matrix material (obeying von Mises plasticity with linear hardening), is modelled as a discontinuity interface following two different approaches. In the first approach, the conditions describing the behavior of a layer of material in which localized strain develop are introduced and implemented in a finite element computer code. A shear deformation is simulated by imposing appropriate displacement conditions on the boundaries of the matrix material, in which the shear band is present and modelled through an imperfect interface, having null thickness. The second approach is based on a perturbative technique, developed for a J2-deformation theory material, in which the shear band is modeled as the emergence of a discontinuity surface for displacements at a certain stage of a uniform deformation process, restricted to plane strain conditions. Both the approaches concur in showing that shear bands (differently from cracks) propagate rectilinearly under shear loading and that a strong stress concentration is expected to be present at the tip of the shear band, two key features in the understanding of failure mechanisms of ductile materials [results of this study have been reported in (Bordignon et al. 2015)]. The second type of interface analyzed in the present thesis is a perfectly frictionless sliding interface, subject to large deformations and assumed to be present within a uniformly strained nonlinear elastic solid. This type of interface may model lubricated sliding contact between soft solids, a topic of interest in biomechanics and for the design of small-scale engineering devices. The analyzed problem is posed as follows. Two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so that this formulation has been developed in the thesis. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or ‘spring-type’ interfacial conditions are not able to predict bifurcations in tension, while experiments (one of which, ad hoc designed, is reported) show that these bifurcations are a reality and can be predicted when the correct sliding interface model is used. Therefore, the presented approach introduces a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact [results of this study have been reported in (Bigoni et al. 2018)].

A shear band of finite length, formed inside a ductile material at a certain stage of a continued homogeneous strain, provides a dynamic perturbation to an incident wave field, which strongly influences the dynamics of the material and affects its path to failure. The investigation of this perturbation is presented for a ductile metal, with reference to the incremental mechanics of a material obeying the J_2-deformation theory of plasticity (a special form of prestressed, elastic, anisotropic, and incompressible solid). The treatment originates from the derivation of integral representations relating the incremental mechanical fields at every point of the medium to the incremental displacement jump across the shear band faces, generated by an impinging wave. The boundary integral equations (under the plane strain assumption) are numerically approached through a collocation technique, which takes account of the singularity at the shear band tips and permits the analysis of an incident wave impinging on a shear band. It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, parallel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band. Moreover, the approach is generalised to study the interaction of multiple shear bands showing that it may lead to resonance and corresponding growth of shear bands, but also to their annihilation. At the same time, multiple scattering may bring about focusing or, conversely, shielding from waves. Due to the difficulties inherent to the experimental analysis of time-harmonic dynamics of shear bands, the proposed mechanical model represents the only practical possibility of analyzing the fine micromechanisms governing material collapse and discloses the complex interplay between dynamics and shear band growth or arrest.

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.

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.