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We study the propagation of shear waves in an anisotropic incompressible medium composed of an elastic fiber-reinforced material. We first derive the general determining equations of such motions when the fibers are arbitrarily arranged with respect to the direction of propagation of the waves. Then, we examine the “standard reinforced model” so as to root the nonlinearity of the dynamic problem directly to the presence of the reinforcing fibers, and finally, we consider an asymptotic model in terms of the limit of finite but small amplitude of the waves. Clearly, if the fibers are arranged along the direction of propagation of the waves, the mechanical behavior of the material will be isotropic. When the fibers are tilted an amount of the same order of the amplitude of the wave with respect to this direction, the asymptotic first-order reduced system is characterized by a peculiar mixed second-/third-order nonlinearity. This contrasts to what occurs for larger tilting angles where only quadratic nonlinearities must be considered. In the latter case, as we may expect, in the asymptotic limit, we reduce the system to an inviscid classical Burger’s equation. Our results are fundamental to the study of the dynamics of fiber-reinforced materials and equally when we consider dissipative and/or dispersive effects.

We consider the problem of modelling nanobeams that dissipate thermal energy by radiation. We approach such a problem in a one-dimensional case by discussing the behavior of nonlocal nanobeams based on the Euler–Bernoulli assumptions. With these premises, we propose a thermoelastic model that takes into account the effects of thermal energy radiation to the external environment, employing an extension of the type II Green–Naghdi (GN-II) theory. We also deepen the formulated theoretical model making use of wave-form solutions, to highlight the presence of dissipative effects.

Truss structures composed of members that work exclusively in tension or in compression appear in several problems of science and engineering, e.g., in the study of the resisting mechanisms of masonry structures, as well as in the design of spider web-inspired web structures. This work generalizes previous results on the existence of cable webs that are able to support assigned sets of nodal forces under tension. We extend such a problem to the limit analysis of compression-only 'strut nets' subjected to fixed and variable nodal loads. These systems provide discrete element models of masonry bodies, which lie inside the polygon/polyhedron with vertices at the points of application of the given forces ('underlying masonry structures'). It is assumed that fixed nodal forces are combined with variable forces growing proportionally to a scalar multiplier (load multiplier), and that the supporting strut net is subjected to kinematic constraints at given nodal positions., Comment: 20 pages, 10 figures

In the framework of weakly nonlocal thermodynamic theory, in this paper we derive a nonlocal and nonlinear heat-transport equation beyond the Fourier law by means of thermodynamic considerations in agreement with the second law. The obtained equation describes the transitions among different heat-transport regimes. The stability of the solution of that equation is also analyzed in a special case.

Infrastructures and buildings must have sufficient protection for design level earthquake excitations while minimizing major damage to comply with existing seismic design criteria. This paper explores the computational modeling of a tensegrity based brace, which helps dissipate energy while preventing inter-story drifts. The proposed brace integrates a D-bar tensegrity structure, shaped like a rhombus, with Shape-Memory Alloy (SMA) cables or tendons. These tendons grow austenitic-martensiticaustenetic (solid to solid) transformations, which make them more susceptible to mechanical stress when taking strain, and amplifying the stress into broad superelastic hysteresis, even after repeated mechanical cycles that require strains of up to 6% 8%. In addition in this article two special classes of the tensegrities are discussed namely 2D and 3D braces. 3D braces have been proven more efficient because of an enhaced capacity of energy dissipation, and also due to their improved safety against buckling. The effectiveness of the planned bracing paves the way to the development of innovative systems of seismic energy dissipation that combine tensegrity concepts with superelasticity.

There is growing demand in industrialized and developing countries to provide people and structures with effective earthquake protection. Here, we employ architectured material concepts and a bio-inspired approach to trail-blaze a new path to seismic isolation. We develop a novel seismic isolator whose unit cell is formed by linkages that replicate the bones of human limbs. Deformable tendons connect the limb members to a central post carrying the vertical load, which can slide against the bottom plate of the system. While the displacement capacity of the device depends only on the geometry of the limbs, its vibration period is tuned by dynamically stretching the tendons in the nonlinear stress–strain regime, so as to avoid resonance with seismic excitations. This biomimetic, sliding–stretching isolator can be scaled to seismically protect infrastructure, buildings, artworks and equipment with customized properties and sustainable materials. It does not require heavy industry or expensive materials and is easily assembled from metallic parts and 3D-printed components.

This work establishes a tensegrity model of spider dragline silk. Tensegrity systems are ubiquitous in nature, being able to capture the mechanics of biological shapes through simple and effective modes of deformation via extension and contraction. Guided by quantitative microstructural characterization via air plasma etching and low voltage scanning electron microscopy, we report that this model is able to capture experimentally observed phenomena such as the Poisson effect, tensile stress-strain response, and fibre toughness. This is achieved by accounting for spider silks&rsquo, hierarchical organization into microfibrils with radially variable properties. Each fibril is described as a chain of polypeptide tensegrity units formed by crystalline granules operating under compression, which are connected to each other by amorphous links acting under tension. Our results demonstrate, for the first time, that a radial variability in the ductility of tensegrity chains is responsible for high fibre toughness, a defining and desirable feature of spider silk. Based on this model, a discussion about the use of graded tensegrity structures for the optimal design of next-generation biomimetic fibres is presented.

Purpose This study aims to focus on a short review on recent results dealing with the mechanical modelling and experimental characterization of a novel class of tensegrity structures, named class θ = 1 tensegrity prisms. The examined structures exhibit six bars connected by two disjoint sets of strings. Design/methodology/approach First, the self-equilibrium problem of tensegrity θ = 1 prisms is numerically investigated for varying values of two aspect parameters and, next, their prestress stability is studied. The mechanical behavior of the examined structures in the large displacements regime under uniform compression loading is also numerically computed through a path-following procedure. Finally, the predicted constitutive response is validated through experimental tests. Findings The presented results highlight that the examined structures exhibit a large number of infinitesimal mechanisms from the freestanding configuration, and reveal that they exhibit tunable elastic response switching from stiffening to softening. Originality/value This multi-faceted elastic response is in agreement with previous literature results on the elastic response of minimal tensegrity prism, and suggests that such units can be usefully used as non-linear springs in next-generation tensegrity metamaterials.

Purpose This paper aims to review recent literature results on the mechanical response of confined pentamode structures behaving either in the stretching-dominated or the bending-dominated regimes. Design/methodology/approach The analyzed structures consist of multilayer systems formed by pentamode lattices alternated with stiffening plates and are equipped with rigid or hinged connections. Findings It is shown that such structures are able to carry unidirectional compressive loads with sufficiently high stiffness, while showing markedly low stiffness against shear loads. In particular, their shear stiffness may approach zero in the stretching-dominated regime. Originality/value The presented results highlight the high engineering potential of laminated pentamode metamaterials as novel isolation devices to be used for the protection of buildings against shear waves.

This work studies the constitutive response of two- and three-dimensional lattice materials subject to isotropic prestress. The unit cell of the examined lattices is formed by an arbitrary number of junctions attached to a junction. Analytic formulae for second-order elastic constants and elastic stiffness coefficients of stretching-dominated lattices are provided. In addition, numerical results for the incremental elastic moduli of composite lattices equipped with hard and soft rods are presented. The given results highlight that isotropically pre-tensioned lattices may exhibit marked variations of the elastic stiffness moduli in the prestressed state, over the values competing to the stress-free configuration. This study also discloses that prestressed lattices may feature incremental auxetic response, when composite architectures suitably combining hard and soft materials are employed for their fabrication., Comment: 20 pages, 3 figures, 6 tables

Fused deposition modelling (FDM) is one of the commonly used additive manufacturing (AM) technologies. In commercial FDM setup a plastic material based filament (usually of ABS) is unwound from a coil to produce functional/non-functional prototypes. The application domain of FDM is limited presently, because of selective material availability in commercial market as regards to the wear of functional prototypes is concerned. In order to enhance the application domain of commercial FDM setup, an effort has been made to develop new polymer composite (with hybrid reinforcement) wire of Nylon6-SiC-Al 2 O 3 with enhanced wear resistant properties. In this research work experimental investigations has been carried out for optimizing wear properties of Nylon6-SiC-Al 2 O 3 based feed stock filament of FDM. Further mathematical model for above mentioned property has been developed and counter verified as a case study.

This work deals with the multiscale modeling of the mechanical response of pentamode lattices, and a preliminary study on engineering applications of structural bearings formed by pentamode lattices confined between stiffening plates. Numerical and experimental results show that the confinement effect played by the stiffening plates, the geometry and mechanical properties of the junctions strongly influence the overall stiffness properties of such structures. As a result, the mechanics of confined pentamode lattices significantly differs from that of unconfined lattices, being able to accommodate compression and tension vertical loads, and featuring performance-based response under shear loading. Their application for use in anti-seismic system development and/or as shear-wave band gap systems awaits attention.

This work reconsiders the Becker-Doering model for nucleation under isothermal conditions in the presence of phase transitions. Based on thermodynamic principles a modified model is derived where the condensation and evaporation rates may depend on the phase parameter. The existence and uniqueness of weak solutions to the proposed model are shown and the corresponding equilibrium states are characterized in terms of response functions and constitutive variables., 16 pages, 1 figure

We investigate the acoustic band structure of tensegrity mass-spring chains as a function of the applied, local and global states of prestress. We first study the bandgap response of linear monoatomic chains, which show lumped masses connected to tensegrity prisms acting as mechanical springs. Next, we present a numerical study on the nonlinear wave dynamics of the examined systems in the geometrically nonlinear regime that is induced by the presence of moderately large relative displacements between the lumped masses. Such a study confirms the results of the linear analysis in the case of an elastically hardening system.

We present some peculiar results about the solitary-wave dynamics of novel tensegrity-based metamaterials. It has been previously shown that one-dimensional chains of triangu-lar tensegrity prisms with stiffening behavior support the propagation of compressive solitarywaves. We show that such result can be generalized to two-dimensional and three-dimensionalmodular tensegrity lattices composed of polygonal and polyhedral units. Differently from theone-dimensional case, the stiffening response of these lattices originates at the interface be-tween adjacent units, not from the unit themselves. We present numerical results on the responseto impulsive loads of slender assemblies composed by square units in two-dimensions, and cu-bic units in three-dimensions. We observed compact compressive waves forming at impactlocations, together with localized thermalization effects. Such compact waves propagate withnearly constant speed and energy, while maintaining their shape, and emerge from collisionwith other compact waves almost unaltered, losing a small fraction of their energy. These re-sults suggest the investigation of the dynamics of regular and quasi-regular tessellations formedby other types of polygonal and polyhedral units.

In the present research work investigations have been made for surface hardness of Al-SiC metal matrix composite (MMC) prepared by combining fused deposition modelling (FDM), vacuum moulding(VM) and stir casting process. This combination resulted into novel method for preparation of MMC as green process in single step with significant reduction in time. The input process parameters (namely:SiC particle size, proportion of SiC, vacuum pressure and VM sand grin size) were studied at three levels using Taguchi L9 orthogonal array to find out there effect on surface hardness of casted specimens. Microstructure analysis was conducted to support hardness data.

A numerical study on the elastic response of single- and multi-layer systems formed by alternating pentamode lattices and stiffening plates is presented. Finite element simulations are conducted to analyze the dependence of the effective elastic moduli of such structures upon suitable aspect ratios, which characterize the geometry of the generic pentamode layer at the micro- and macro-scale, and the lamination scheme of the layered structure. The given numerical results highlight that the examined structures exhibit bending-dominated response, and are able to achieve low values of the effective shear modulus and, contemporarily, high values of the effective compression modulus. We are lead to conclude that confined pentamode lattices can be regarded as novel metamaterials that are well suited for seismic isolation and impact protection purposes. Their elastic response can be finely tuned by playing with several geometrical and mechanical design variables.

An experimental investigation on the mechanical response of confined pentamode lattices in the elastic and post-yield regimes is presented. An Electron Beam Melting facility is employed to additively manufacture pentamode lattices confined by terminal plates in a titanium alloy. The given experimental results show that the geometry of the microstructure, and the macroscopic aspect ratio of the confined lattices strongly influence the lateral and vertical stiffness properties of the structure. The post-elastic response of the analyzed materials features acceptable energy dissipation capacity. The presented results highlight several analogies between the mechanical response of confined pentamode lattices and that of elastomeric bearings formed by soft rubber pads and stiffening steel or fiber-reinforced composite layers. They pave the way to future studies on the use of pentamode materials for the fabrication of innovative seismic isolation devices and/or shear-wave band gap systems.

To optimize the seismic performance prescribed by modern structural codes, buildings and infrastructures must provide adequate safety for design level earthquake excitations, with limited levels of damage. This paper deals with the computational modelling of a bracing system with tensegrity architecture, which operates as a lightweight mechanical amplifier of longitudinal displacements in the transverse direction, efficiently limiting the interstory drifts while dissipating energy. The proposed brace is based on a D-bar tensegrity structure with a rhomboidal shape comprising Shape-Memory Alloy (SMA) tendons. The SMA tendons can develop austenitic-martensitic (solid to solid) transformations, which enable them to amplify the signals into wide super elastic hysteresis, while subjected to mechanical cycles, comprising strains up to 6÷8%, with no residual deformations. The enhanced energy dissipation of the proposed SMA-D-bar (SMAD) braces are demonstrated through computational simulations of the response of braced frame to real earthquake events. The efficiency of the intended bracing to minimize the seismic impact of the served structure lays the foundation for the development of novel seismic energy dissipation systems integrating principles of tensegrity with superelasticity.

We study the evolutionary development of an acceleration wave propagating in a saturated porous material according to a Biot theory proposed by Donskoy, Khashanah and McKee. The theory is fully nonlinear, includes dissipation, and the analysis presented is exact. We derive sufficient conditions to show that two distinct waves propagate, a fast wave and a slower wave. A solution for the wave amplitude is presented for a wave moving into an equilibrium region.

A physical model of a tensegrity columns is additively manufactured in a titanium alloy. After removing sacrificial supports, such a model is post-tensioned through suitable insertion of Spectra® cables. The wave dynamics of the examined system is first experimentally investigated by recording the motion through high-speed cameras assisted by a digital image correlation algorithm, which returns time-histories of the axial displacements of the bases of each prism of the column. Next, the experimental response is mechanically simulated by means of two different models: a stick-and-spring model accounting for the presence of bending-stiff connections between the 3D-printed elements (mixed bending-stretching response), and a tensegrity model accounting for a purely stretching response. The comparison of theory and experiment reveals that the presence of bending-stiff connections weakens the nonlinearity of the wave dynamics of the system. A stretching-dominated response instead supports highly compact solitary waves in the presence of small prestress and negligible bending stiffness of connections.

We study lightweight, elastic metamaterials consisting of tensegrity-inspired prisms, which present wide, low-frequency band gaps. For their realization, we alternate tensegrity elements with solid discs in periodic arrangements that we call "accordion-like" meta-structures. We show through analytical calculations and numerical simulations that these structures are characterized by low-frequency band gaps with strong uniform wave attenuation due to the coupling of Bragg scattering and local resonance mechanisms. This coupling helps to overcome the inherent limit of a narrow band-gap width for conventional locally-resonant metamaterials and to extend the wave attenuation to wider frequency ranges. Moreover, the band gaps can be further increased, provided a minimum structural damping is present, and tuned to desired frequencies by changing the applied prestress levels in the tensegrity structure. Results are corroborated by parametric studies showing that the band-gap frequencies are preserved for wide variations of geometric and material structural properties., 31 pages, 11 figures

This work studies the acoustic band structure of tensegrity mass-spring chains, and the possibility to tune the dispersion relation of such systems by suitably varying local and global prestress variables. Building on established results of the Bloch–Floquet theory, the paper first investigates the linearized response of chains composed of tensegrity units and lumped masses, which undergo small oscillations around an initial equilibrium state. The stiffness of the units in such a state varies with an internal self-stress induced by prestretching the cables forming the tensegrity units, and the global prestress induced by the application of compression forces to the terminal bases. The given results show that frequency band gaps of monoatomic and biatomic chains can be effectively altered by the fine tuning of local and global prestress parameters, while keeping material properties unchanged. Numerical results on the wave dynamics of chains under moderately large displacements confirm the presence of frequency band gaps of the examined systems in the elastically hardening regime. Novel engineering uses of the examined systems are discussed.

This study examines the mechanical behavior of a novel class of mechanical metamaterials alternating pentamode lattices and stiffening plates. The unit cell of such lattices consists of a sub-lattice of the face cubic-centered unit cell typically analyzed in the current literature on pentamode materials. The studied systems exhibit only three soft deformation modes in the infinitesimal stretch-dominated regime, as opposed to the five zero-energy modes of unconfined pentamode lattices. We develop analytical formulae for the vertical and bending stiffness properties and study the dependence of such quantities on the main design parameters: the lattice constant, the solid volume fraction, the cross-section area of the rods, and the layer thickness. A noteworthy result is that the effective compression modulus of the analyzed structures is equal to two thirds of the Young modulus of the stiffest isotropic elastic networks currently available in the literature, being accompanied by zero-rigidity against infinitesimal shear and twisting mechanisms. The use of the proposed metamaterials as novel seismic-isolation devices and impact-protection equipment is discussed by drawing comparisons with the response of alternative devices already available or under development.

An investigation on the additive manufacturing and the experimental testing of 3D models of tensegrity prisms and columns is presented. An electron beam melting facility (Arcam EBM S12) is employed to 3D print structures composed of tensegrity prisms endowed with rigid bases and temporary supports, which are made out of the titanium alloy Ti6Al4V. The temporary supports are removed after the additive manufacturing phase, when Spectra cross-strings are added to the 3D printed models, and a suitable state of internal prestress is applied to the structure. The experimental part of the study shows that the examined structures feature sitffening-type elastic response under large or moderately large axial strains induced by compressive loading. Such a geometrically nonlinear behavior confirms previous theoretical results available in the literature, and paves the way to the use of tensegrity prisms and columns as innovative mechanical metamaterials and smart devices.

We study the geometrically nonlinear behavior of uniformly compressed tensegrity prisms through fully elastic and rigid-elastic models. The given models predict a variety of mechanical behaviors in the regime of large displacements, including an extreme stiffening-type response, already known in the literature, and a newly discovered, extreme softening behavior. The latter may lead to a snap buckling event producing an axial collapse of the structure. The switching from one mechanical regime to another depends on the aspect ratio of the structure, the magnitude of the applied prestress, and the material properties of the constituent elements. We discuss potential mechanical and acoustic applications of such behaviors, which are related to the design and manufacture of tensegrity lattices and innovative metamaterials.

The present paper is concerned with the formulation of new assembly methods of bi-material tensegrity prisms, and the experimental characterization of the compressive response of such structures. The presented assembly techniques are easy to implement, including a string-first approach in the case of ordinary tensegrity prisms, and a base-first approach in the case of systems equipped with rigid bases. The experimental section shows that the compressive response of tensegrity prisms switches from stiffening to softening under large displacements, in dependence on the current values of suitable geometric and prestress variables. Future research lines regarding the mechanical modeling of tensegrity prisms and their use as building blocks of nonlinear periodic lattices and acoustic metamaterials are discussed.

Using chains of bistable springs, a model is derived to investigate the plastic behavior of carbon nanotube arrays with damage. We study the preconditioning effect due to the loading history by computing analytically the stress-strain pattern corresponding to a fatigue-type damage of the structure. We identify the convergence of the discrete response to the limiting case of infinitely many springs, both analytically in the framework of Gamma-convergence, as well as numerically., Comment: 11 pages, 1 figure

This article is concerned with the mechanical properties of dense, vertically aligned CNT foams subject to one-dimensional compressive loading. We develop a discrete model directly inspired by the micromechanical response reported experimentally for CNT foams, where infinitesimal portions of the tubes are represented by collections of uniform bi-stable springs. Under cyclic loading, the given model predicts an initial elastic deformation, a non-homogeneous buckling regime, and a densification response, accompanied by a hysteretic unloading path. We compute the dynamic dissipation of such a model through an analytic approach. The continuum limit of the microscopic spring chain defines a mesoscopic dissipative element (micro-meso transition) which represents a finite portion of the foam thickness. An upper-scale model formed by a chain of non-uniform mesoscopic springs is employed to describe the entire CNT foam. A numerical approximation illustrates the main features of the proposed multiscale approach. Available experimental results on the compressive response of CNT foams are fitted with excellent agreement.

International audience; Tensegrity structures have recently shown great potential as bracing devices for seismic control due to their unique ability to passively dissipate energy in structures subjected to severe deformations. Indeed, behaving as nonlinear springs, they are able to dissipate a great amount of energy energy during mechanical loading-unloading cycles. Planar tensegrity D-bar systems composed of four bars forming a rhombus, internally stabilized through a set of two perpendicular Shape Memory Alloy (SMA) cables, represent excellent candidates to act as braces for seismically resistant structures. However, although their tapered configuration maximizes in-plane buckling resistance with minimal mass, the out-of-plane buckling of such systems can compromise their overall structural efficiency, potentially engendering damage into adjacent non structural elements. In this paper, the efficiency of three-dimensional D-bar tensegrity structures under compressive loads is examined with the aim of proposing an advantageous design of D-bar-based bracing systems with optimized masses. We show that, by introducing a pre-strain in the superelastic cables, it is possible to achieve a wide shaped hysteresis, which yields to a significant amount of equivalent viscous damping (up to 30$\%$). The presented numerical results on the energy dissipation properties of the examined structures, corroborated by experimental measurements of the buckling response, shed light on the research field of three-dimensional tensegrity structures, as efficient and lightweight bracing devices for seismic control.

This paper reviews recent literature results on the mechanics of structures formed by layers of pentamode lattices alternating with stiffening plates, which can be effectively employed for the development of seismic isolation devices and vibration attenuation tools, with nearly complete band gaps for shear waves. It is shown that such structures, named pentamode bearings, can respond either in the stretching-dominated regime, or in the bending-dominated regime, depending on the nature of the joints connecting the different members. Their response is characterized by high vertical stiffness and theoretically zero shear stiffness in the stretching dominated regime, or considerably low values of such a quantity in the bending dominated regime. Available results on the experimental response of 3d printed models to combined compression and shear loading highlight that the examined structures are able to exhibit energy dissipation capacity and effective damping that are suitable for seismic isolation devices. Their fabrication does not necessarily require heavy industry, and expensive materials, being possible with ordinary 3-D printers.