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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.

We consider the problem of finding a net that supports prescribed point forces, yet avoids certain obstacles, with all the elements of the net being under compression (or all being under tension), and being confined within a suitable bounding box. In the case of masonry structures, when described through the simple, no-tension constitutive model, this consists, for instance, in finding a strut net that supports the forces, is contained within the physical structure, and avoids regions that may be not accessible. We solve such a problem in the two-dimensional case, where the prescribed forces are applied at the vertices of a convex polygon, and we treat the cases of both single and multiple obstacles. By approximating the obstacles by polygonal regions, the task reduces to identifying the feasible domain in a linear programming problem. For a single obstacle we show how the region Γ available to the obstacle can be enlarged as much as possible in the sense that there is no other strut net, having a region Γ ′ available to the obstacle with Γ ⊂ Γ ′ . The case where some of the forces are reactive is also treated.

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

This paper is concerned with the linear theory of elastodynamics for homogeneous, isotropic, porous elastic materials with memory effects for the intrinsic equilibrated body forces. We are able to relax the conditions on constitutive coefficients and to determine the wider class of materials for which the internal energy is positive semi-definite, when boundary conditions are homogeneous. We found the class of semi-strongly elliptic porous elastic materials. For this class of materials, the above conditions may be relaxed without loss of some well-posedness properties of the solutions. In particular, we obtain uniqueness of the solutions and we study the spatial behavior problem.

This paper deals with the design of an apparatus based on tensegrity structures for the transmission of special solitary waves with adjustable profile into a material or structure, and the detection of such waves from a material or structure. The advantages of using tensegrity building blocks in place of granular materials or different structural units for the fabrication of novel nondestructive evaluation and monitoring tools and acoustic lenses are illustrated.

The present study deals with the optimal design of a Graphene reinforced composite. The Graphene was prepared by chemical exfoliation process and was chemically blended with matrix material in acetone. Further chemically mixed solution was exposed to air for acetone vaporization. Next, this Graphene composite was extruded through twin screw extrusion (TSE) for preparation of feedstock filament with 1.75±0.05mm diameter via fused deposition modelling (FDM). The presented results suggest that statistically controlled Graphene reinforced functional prototypes can be usefully employed as sensors for bio-medical and engineering applications.

This work presents an optimized and convergent regularization procedure for the computation of the stress field exhibited by particle systems subject to self-equilibrated short-range interactions. A regularized definition of the stress field associated with arbitrary force networks is given, and its convergence behavior in the continuum limit is demonstrated analytically, for the first time in the literature. The analyzed systems of forces describe pair interactions between lumped masses in ‘atomistic’ models of 2D elastic bodies and 3D membrane shells based on non-conforming finite element methods. We derive such force networks from polyhedral stress functions defined over arbitrary triangulations of 2D domains. The stress function associated with an unstructured force network is projected onto a structured triangulation, producing a new force network with ordered structure. The latter is employed to formulate a ‘microscopic’ definition of the Cauchy stress of the system in the continuum limit. The convergence order of such a stress measure to its continuum limit is given, as the mesh size approaches zero. Benchmark examples illustrate the application of the proposed regularization procedure to the prediction of the stress field exhibited by a variety of 2D and 3D membrane networks.

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.

International audience; In this paper, we report about the effect of the application of a state of prestress on the band structure of a periodic phononic crystal characterized by an inertial amplification mechanism. Through a numerical example, we show the possibility of inducing negative group velocity in an isolated branch of the dispersion diagram. A 2-step Updated Lagrangian scheme is adopted to calculate the dispersion diagram of the structure. The proposed method include (i) the static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load and (ii) the BlochFloquet decomposition applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. The dispersion analysis is performed in terms of small amplitude motions superimposed on a deformed state, once the desired load has been applied.

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.

This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with microstructure. Two improvements are made in contrast to earlier approaches: First, the micro-rotations are parameterized with the help of an Euler–Rodrigues formula related to quaternions. Secondly, as main result, a novel two-pass preconditioning scheme for searching the energy-minimizing solutions based on the limited memory Broyden–Fletcher–Goldstein–Shanno quasi-Newton method is proposed that consists of a predictor step and a corrector-iteration. After outlining the necessary adaptations to the model, numerical simulations compare the performance and efficiency of the new and the old algorithm. The proposed numerical model can be effectively employed for studying the mechanical response of complicated materials featuring large size effects.

In this article, we derive a nonlinear strain gradient theory for porous thermoelastic diffusion materials taking into account micro-inertia effects as well. The elastic behavior is assumed to be c...

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.

A great challenge that contemporary sustainable architecture has to face is to optimize natural resources and minimize energy consumption. Such a goal calls for the design of flexible and adaptive building envelopes able to react dynamically based on the evolution of the external climatic and environmental conditions. The present work is focused on the design of active solar façade screens based on tensegrity units that are markedly lightweight and are easily integrated with solar panels and/or sound-proof panels. These units are controlled by tensioning and releasing appropriate cables of the structure and are used to direct the solar panels towards the sun. A mechanical study on the use of tensegrity systems for the design of energy efficient sunscreens inspired by the dynamic solar façades of the Al Bahar Towers in Abu Dhabi is presented. The adaptive architecture of the Al Bahar tower façade is reinterpreted through a tensegrity approach that can change its shape by reacting to the surrounding environment; it is a modern and cost-effective reinterpretation of traditional "mashrabiya" shading systems. © 2019 Taylor & Francis Group, London, UK.

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 study the highly nonlinear wave dynamics of 1d tensegrity metamaterials, with a focus on the interaction of a compression solitary pulse with an interface between elastically stiffening and softening materials. We observe an anomalous response of the examined system, which is characterized by the propagation of a train of reflected compression solitary waves in the stiffening branch, and the transmission of a solitary rarefaction wave with oscillatory tail in the softening branch.

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.

We study the mechanics of pentamode metamaterials consisting of multi-layered pentamode lattices alternated with rigid plates. The examined systems respond in the stretching-dominated regime induced by the presence of perfectly hinged connections between the rods and the stiffening plates. We anakyze the variation of the effective stiffness properties of the examined systems with the lattice constant, the solid volume fraction, the cross-section area of the rods, and the number of layers.We study the mechanics of pentamode metamaterials consisting of multi-layered pentamode lattices alternated with rigid plates. The examined systems respond in the stretching-dominated regime induced by the presence of perfectly hinged connections between the rods and the stiffening plates. We anakyze the variation of the effective stiffness properties of the examined systems with the lattice constant, the solid volume fraction, the cross-section area of the rods, and the number of layers.

This work aims to contribute to the verification of the well-posedness question, as for the uniqueness and continuous dependence issues, for a linear thermoelastic model with two main featu...

This paper experimentally and numerically investigates the lateral stability problem of metallic C-beams with uniformly varying cross-section. The results of a compression test on a physical model are compared with the numerical predictions of the lateral-torsional buckling load given by a variational approach. A good theory vs. experiment matching is observed when a correct modeling of the boundary conditions is introduced. The given numerical approach proves to be an effective tool for studying the non trivial stability problem of thin-walled beams equipped with non-uniform cross section.

Curved interfaces between material media with different characteristic speed for heat waves may be the basis for thermal lenses, concentrating the energy carried by parallel thermal rays on a focal point. This may be of practical use for the amplification of thermal signals and for the development of sensitive thermal sensors. When dissipative attenuation effects are taken into account, it turns out that these lenses could be of special interest in miniaturized probes, or in micro/nanosystems, and the optimization of the thermal lens for signal amplification may be calculated.

This work presents a study on the equilibrium problem and the infinitesimal mechanisms of class θ= 1 tensegrity prisms. Local solutions of the self-equilibrium problem are numerically obtained through Newton-Raphson iterations. The presented results suggest that the analyzed structures can be usefully employed as building blocks of novel tensegrity metamaterials, due to their rich kinematic response and the considerably large number of infinitesimal mechanisms.