Emilio Turco

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• PhD
• Professor (Full) at University of Sassari

In this paper we exhibit a planar truss structure, which, once homogenised at a macro-level, will need to be modelled as a third gradient beam, i.e. as a one dimensional continuum whose deformation energy depends on the third derivative of its displacement. We call it Zigzaged Articulated Parallelograms with Articulated Braces structure (ZAPAB stru...

Multistable metamaterials have several relevant technical applications in various fields, such as soft robotics, mechanical computing, energy absorption, and wave control. These capabilities arise from the stored strain energy, characterised by a multi-well pattern. The properties determining this multistable mechanical behaviour are studied by con...

In this paper we start the analysis of the nonlinear dynamics of structural elements having an origami type micro-structure and micro-kinematics, also known as origami metamaterials. We use a finite dimensional Lagrangian system to explore, via numerical simulations, the overall behaviour of an origami beam. This provides some significant hints abo...

Is it possible to interpret the modeling decisions made by a neural network trained to simulate the constitutive behavior of simple or complex materials? The problem of the interpretability of a neural network is a crucial aspect that has been raised since the first appearance of this type of modeling tools and it is certainly not specific to appli...

The pull-out test is one of the common experiments to determine the bond strength. When the problem is modeled in the context of linear elasticity for a cylindrical reinforced concrete block, the resulting simplified 1-D model yields so-called pull-out paradox Rezaei et al. (Mech Res Commun 126:104015, 2022) due to extreme concentration of energy n...

We outline the scientific objectives, the experimental layout, and the collaborations envisaged for the GINGER (Gyroscopes in general relativity) project. The GINGER project brings together different scientific disciplines aiming at building an array of ring laser gyroscopes (RLGs), exploiting the Sagnac effect, to measure continuously, with sensit...

The present contribution proves that Kresling-patterned tubular origami metamaterials can exhibit a nonlinear buckling behavior in compression characterized by extremely significant and sudden twisting, as well as by extreme transverse dilation/contraction. It is proved that such an extreme buckling behavior can be achieved by tuning the ratio betw...

The identification of the damage in composite steel-concrete beams is addressed by implementing simple convolutional networks. By considering several damage scenarios, collections of images are generated by numerically evaluating a set of transmissibility functions relative to the generic damaged beam an by converting them into a gray level image s...

In this paper, linear wave propagation in pantographic lattices is investigated. It is assumed that the pantographic lattice is attached to a material modeled by the classical first-gradient theory with a structured interface having its own material properties. By using a variational principle, governing equations and jump conditions at the structu...

The geometrical description of the components of rubble masonries constitutes a key-point in the definition of their mechanical response. A variational autoencoder (VAE) is proposed as a tool for the automatic description and generation of rubble masonry geometries. The encoder and the decoder forming the VAE are implemented by defining two convolu...

Pantographic structures attracted the attention of scientists thanks to their interesting mechanical behaviors. Since the 3D printing technology allows to produce polyamide (PA) and metallic (ME) samples, different kinds of experiments can be carried out. In this work, a new torsional energy is proposed, which can predict the force–elongation curve...

Numerical simulations of several planar failure modes of masonry structures are presented, based on the model and solving code from a recent hemivariational block-based model inspired from granular micromechanics (Tran et al. [33]). The numerical tests include a comparison with literature results for a constant shearing load, a parametric study of...

The identification of damage in the connection of steel–concrete composite beams is pursued by means of Convolutional Neural Networks. The data used for training the networks are gray level images obtained by converting a set of transmissibility functions of the beam. It is shown how simple Convolutional Neural Networks can be trained for the ident...

Duoskelion structures have been recently introduced by Barchiesi et al. (2021) as a proof-of-concept motif for a new class of metamaterials. The properties of these periodic beam-like chiral structural elements have been investigated, up to now, by means of a discrete model formulation whose predictions are obtained by numerical methods. In this pa...

In this study, a hemivariational formulation is presented for a Hencky-type discrete model to predict damage behavior in pantographic layers. In the discrete model, elastic behavior of pantographic layers is modeled via extensional, bending and shear springs. A damage descriptor is added for each spring type. Such a damage descriptor is non-decreas...

We present and discuss the results of some numerical simulations dealing with wave motion in one-dimensional pantographic media, also known as pantographic beams. Specifically, the analysis is carried out in large displacements regime and pantographic beams are modeled by using a completely discrete approach. Nonlinear vibrations induced by a trans...

In this paper, we outline the scientific objectives, the experimental layout, and the collaborations envisaged for the GINGER (Gyroscopes IN GEneral Relativity) project. The GINGER project brings together different scientific disciplines aiming at building an array of Ring Laser Gyroscopes (RLGs), exploiting the Sagnac effect, to measure continuous...

While many efforts are being currently spent to forge reliable damage laws based on the physics of the materials to be studied, damage modeling is still addressed numerically too naively in many situations. This article highlights some topical conceptual aspects that have been up to now dealt with too superficially by comparing the performances of...

A particle model devoted to the study of three-dimensional grain packages in a dynamic setting is presented and discussed. The proposed approach considers each grain as a rigid sphere immersed in an elastically deformable medium. The motion of the grains is described by using as Lagrangian parameters the grain centroid displacement and the grain ro...

Dynamic buckling of a simply-supported beam

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e. by the kinetic energy and by the potential of conservative forces. Differently from...

Pantographic metamaterials are receiving increasing attention from the scientific community working in theoretical and numerical mechanics. Nevertheless, dynamic analysis of pantographic sheets in large deformation regime is still a scarcely explored topic which deserves to be thoroughly investigated on its own. Aimed at contributing to fill this g...

In this contribution, a previously-introduced discrete model for studying the statics of duoskelion beam-like structures is extended to dynamics. The results of numerical simulations performed using such an extended model are reported to discuss the in-plane dynamic buckling of duoskelion structures under different loading and kine- matic boundary...

We present, in a nonlinear dynamic framework, a beam model suitable for metamaterials design. The beam model, formulated directly in a discrete way, is completely defined by means of the strain and the kinetic energies. Differently from Hencky's seminal work, which only considers flexibility for computing buckling loads for rectilinear Euler--Berno...

Materials and structures based on pantographic cells exhibit interesting mechanical peculiarities. They have been studied prevalently in the static case, both in linear and nonlinear regime. When the dynamical behavior is considered, available literature is scarce probably for the intrinsic difficulties in the solution of this kind of problems. The...

Although the primacy and utility of higher‐gradient theories are being increasingly accepted, values of second gradient elastic parameters are not widely available due to lack of generally applicable methodologies. In this paper, we present such values for a second‐gradient continuum. These values are obtained in the framework of finite deformation...

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was extensively test...

The problem of devising an appropriate Representative Volume Element (RVE) for the analysis of concrete-like-materials is throughly discussed in the range of the elastic behavior. To this end, assuming concrete as a two-phases material (mortar and aggregates), the geometry of the RVE is automatically generated on the basis of spherical or polyhedra...

The problem of devising an appropriate Representative Volume Element (RVE) for the analysis of concrete-like-materials is throughly discussed in the range of the elastic behavior. To this end, assuming concrete as a two-phases material (mortar and aggregates), the geometry of the RVE is automatically generated on the basis of spherical or polyhedra...

The overall behaviour of an articulated beam structure constituted by elements arranged according to a specific chirality is studied. The structure as a whole, due to its slenderness and geometry, is called duoskelion beam. The name duoskelion is a neologism which is inspired by the Greek word ‌δύοσκέλιον‌ (two-legged). A discrete model for shearab...

A possible strain energy density, incorporating Cosserat’s micro-rotations and Biot’s change in porosity conferred by the microstructure geometry, is proposed in an elastic, two-dimensional, nonlinear context. The nonlinearities are taken into account both extracting the exact macro-rotations by the polar decomposition of the standard deformation g...

Mechanical metamaterials are microstructured mechanical systems showing an overall macroscopic behaviour that depends mainly on their microgeometry and microconstitutive properties. Moreover, their exotic properties are very often extremely sensitive to small variations of mechanical and geometrical properties in their microstructure. Clearly, the...

Materials based on pantographic unit cells have very interesting mechanical peculiarities. For these reasons they are largely studied from the theoretical, experimental and numerical point of view. Numerical simulations furnish an important contribution for the the design and the optimization of such materials and, more in general, for metamaterial...

We describe a novel mechanical model of planar Timoshenko beam for large displacements analysis in elastic regime following Hencky beam model guidelines. More precisely, we model the strain energy of the beam in a discrete form by considering, besides the bending contribution, both the stretching and the sliding contributions. In this way a discret...

This work discusses some alternate models of a mixed assumed strain finite element which has been developed for laminated plates. After a brief theoretical review about this kind of plates and their possible finite element formulation, specifically devised for predicting the mechanical behavior of such structures, we discuss four possible assumptio...

We investigate the mechanical behaviour of so-called pantographic beams undergoing large deformations. To this aim, an exact-kinematics Hencky pantographic beam model has been employed in three-point bending test. Given the occurrence of local snap-through instabilities and limit points, said Hencky model has been solved by means of a step-by-step...

We discuss two examples of beam-lattice metamaterials which show attractive mechanical properties concerning their enriched buckling. The first one considers pantographic beams and the nonlinear solution is traced out numerically on the base of a Hencky’s model and an algorithm based on Riks’ arc-length scheme. The second one concerns a beam-lattic...

In this paper, we discuss well-posedness of the boundary-value problems arising in some “gradient-incomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class of metamaterials whose microstructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-in...

The nonlinear mechanical behavior of pantographic beams, mimicking the results of the Euler’s beam, is explored. In particular, using a very simple Lagrangian model already tested for pantographic lattices and an algorithm based on the Riks’ approach to reconstruct via a stepwise procedure the equilibrium path, the results of several numerical simu...

In this paper, we show that equilibrium configurations of a clamped beam under distributed load, resembling a curled pending wire—whose existence has been mathematically established—can be obtained experimentally using ‘soft’ beams, i.e. beams for which the ratio between amplitude of the load and bending stiffness is large enough. Moreover, we intr...

In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be so...

In the last decade, the exotic properties of pantographic metamaterials have been investigated and different mathematical models (both discrete or continuous) have been introduced. In a previous publication, a large part of the already existing literature about pantographic metamaterials has been presented. In this paper, we give some details about...

In this paper we reveal that the mathematical discrete model of Hencky-type, introduced in [1], is appropri- ate for describing the mechanical behavior of micro-metric pantographic elementary modules. This behavior does not differ remarkably from what has been observed for milli-metric modules, as we prove with suitably designed experiments. Theref...

It has been numerically observed and mathematically proven that for a clamped Euler’s Elastica, which is uniformly loaded, there exist, in large deformations, some ‘undocumented’ equilibrium configurations which resemble a curled pending wire. Even if Elastica is one of the most studied models in mathematical physics, we could not find in the liter...

The size estimates approach for Kirchhoff–Love elastic plates allows to determine upper and lower bounds of the area of an unknown elastic inclusion by measuring the work developed by applying a couple field on the boundary of the plate. Although the analytical process by which such bounds are determined is of constructive type, it leads to rather...

We formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to...

Synonyms Energy methods for granular materials; Varia-tional methods in granular micromechanics Definitions Granular mechanics is defined as the mechanics of materials with granular texture in which the role of grain interactions is paramount. The description of the mechanical behavior of these material systems begins from the conception of grain i...

Synonyms Energy methods for granular materials; Variational methods in granular micromechanics Definitions Continuum models of granular materials aim to describe their behavior in average sense while exploiting the paradigm of continuum mechanics. For granular materials, however, success of these continuum models is predicated upon how they treat g...

In order to get detailed information about the mechanical behavior of pantographic elementary substructure and elements, small-scale specimens were sintered using polyamide powder, constituted by three orthogonal pairs of beams interconnected through pivots forming pantographic cells. The mechanical properties of interconnecting pivots and constitu...

In this paper we describe a three-scales homogenization process which we use to determine a macroscopic model for pantographic metamaterials. The smallest scale refers to the length at which the considered deformable mechanical system can be modeled as a Cauchy’s continuum. Of course, at this scale, its geometry is rather complex. The meso-scale re...

Complex problems such as those concerning the mechanics of materials can be confronted only by considering numerical simulations. Analytical methods are useful to build guidelines or reference solutions but, for general cases of technical interest, they have to be solved numerically, especially in the case of large displacements and deformations. P...

We consider two `comprehensive' modelling approaches for engineering fabrics. We distinguish the two approaches using the terms `semi-discrete' and `continuum', reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters...

A micro-mechanical model devoted to study large deformations of cohesive granular media subjected to quasi-static external actions is presented and discussed. The model, leaving out dynamical effects, is completely described by the definition of the strain energy of the interaction between two nearby grains. The solution of the nonlinear equilibriu...

The problem of the synthesis of second gradient (meta)materials, via architectured microstructures made of micro-lattices, has been solved (Alibert et al., 2003; Seppecher et al., 2011) by choosing ideal pivots as preferred constraints. The obtained homogenized macro-equations (Boutin et al., 2017; Eremeyev et al., 2017) show some pathologies that...

The standard finite elements approach for the dynamics of curved beam is usually based on the same energy functional used for straight beam, in other words an energy form that is essentially derived from de Saint–Venant’s theory. In case of strongly curved elements this approximation yields to not negligible errors, in particular for stress assessm...

On the wake of the results obtained so far at the SPARC\_LAB test-facility at the Laboratori Nazionali di Frascati (Italy), we are currently investigating the possibility to design and build a new multi-disciplinary user-facility, equipped with a soft X-ray Free Electron Laser (FEL) driven by a $\sim$1 GeV high brightness linac based on plasma acce...

On the wake of the results obtained so far at the SPARC\_LAB test-facility at the Laboratori Nazionali di Frascati (Italy), we are currently investigating the possibility to design and build a new multi-disciplinary user-facility, equipped with a soft X-ray Free Electron Laser (FEL) driven by a $\sim$1 GeV high brightness linac based on plasma acce...

Samples of differently sized so-called pantographic structures are subjected to large deformation loading tests up to rupture, while their response to the deformation is recorded by an optical 3D-measurement system. Digital image correlation is used to calculate the deformation that took place perpendicular to the reference plane by the help of a f...

Quasi-isospectral Sturm-Liouville operators play an important role in inverse spectral theory and are typically used for determining exact solutions to suitable classes of eigenvalue problems with variable coefficients. In this work we investigate on alternative applications of quasi-isospectral operators as key tool for structural identification p...

A nonlinear two-dimensional (2D) continuum with a latent internal structure is introduced as a coarse model of a plane network of beams which, in turn, is assumed as a model of a pantographic structure made up by two families of equispaced beams, superimposed and connected by pivots. The deformation measures of the beams of the network and that of...

One of the most interesting challenges in the modern theory of materials consists in the determination of those microstructures which produce, at the macro-level, a class of metamaterials whose elastic range is many orders of magnitude wider than the one exhibited by ‘standard’ materials. In Dell’Isola et al. (2015 Zeitschrift für angewandte Mathem...

We consider the inverse problem of reconstructing the axial stiffness of a damaged rod from the knowledge of a finite number of resonant frequencies of the free axial vibration under supported end conditions. The damage is described as a reduction of the axial stiffness, and the undamaged and damaged configurations of the rod are assumed to be symm...

3D printing puts theoretical mathematics into practice to produce hyperelastic metamaterials Researchers in Italy and Poland demonstrate a mathematical approach to predicting the structure of 3D printed elastic structures. By practically realizing elastic theory, the study opens up the potential of 3D printed metamaterials that act " against their...

Current research in metamaterials design is pushing to fill the gap between mathematical modeling and technological applications. To meet these requirements, predictive and computationally effective numerical tools need to be conceived and applied. In this paper we compare the performances of a discrete model already presented in [1], strongly infl...

Current research in metamaterials design is pushing to fill the gap between mathematical modelling and technological applications. To meet these requirements predictive and computationally effective, numerical tools need to be conceived and applied. In this paper, we describe the performances of a discrete model based on the microstructure architec...

With the advancements in 3D printing technology, rapid manufacturing of fabric materials with complex geometries became possible. By exploiting this technique, different materials with different structures have been developed in the recent past with the objective of making generalized continuum theories useful for technological applications. So-cal...

This work is focused on the analysis of three-dimensional bodies whose mechanical behavior can be modeled by an elastoplastic pressure-sensitive material description. To this end the yield condition is assessed with respect to a general quadratic function capable to represent both standard surfaces, such as Drucker–Prager surface, or more generic s...

In this paper we deal with the problem of choosing the best linear model capable to describe the mechanical characteristics and the behavior of media with viscoelastic properties. Two different cases are studied: asphalt concrete subject to forced vibrations and PVC cantilever beam subject to free vibrations. In both cases, experimental results are...

Fibre-reinforced plates and shells are finding an increasing interest in engineering applications; in most cases dynamic phenomena need to be taken into account. Consequently, effective and robust computational tools are sought in order to provide reliable results for the analysis of such structural models. In this paper the mixed assumed-strain la...

In dell’Isola et al. (Zeitschrift für Angewandte Math und Physik 66(6):3473–3498, 2015, Proc R Soc Lond A Math Phys Eng Sci 472(2185):1–23, 2016) pantographic sheets are proposed as a basic constituent for a novel metamaterial. In Part I, see Turco et al. (Zeitschrift für Angewandte Math und Physik, doi:10.1007/s00033-016-0713-4, 2016), two differe...

In dell’Isola et al. (Zeitschrift für Angewandte Math und Physik 66(6):3473–3498, 2015, Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016), the concept of pantographic sheet is proposed. The aim is to design a metamaterial showing: (i) a large range of elastic response; (ii) an extreme toughness in extensional deformation; (iii) a convenient rati...

A review on models for pantographic fabrics, a new promising kind of metamaterials, is presented. We treat those models that are able to capture the peculiar effects conferred by their specific microstructure and that can be generalized for the description of more complex metamaterials. For each approach, model formulation and modeling assumptions...

In 3D printing process, when small length scales are attained, it is more frequent the onset of imperfections. In the present paper it is studied how the performances of pantographic structures (as defined and introduced in dell'Isola et al. (2005) [1]) are affected by statistically distributed defects. The relevance of the treated problem is more...

We present numerical simulations of rectangular woven fabrics made of two, initially orthogonal, families of inextensible fibres. We consider an energy functional which includes both first and second gradients of the displacement. The energy density is expressed in terms of the angles between the fibres directions, using trigonometric functions and...

In [1] a novel metamaterial has been designed and studied, whose performances include an enhanced toughness in extension: one of the problems to be solved in the further development of the concept involves the study of its deformation induced by loads concentrated on fibers (fiber pull-out test). A continuum model seems particularly unfit for the d...

Hencky (Über die angenäherte Lösung von Stabilitätsproblemen im Raum mittels der elastischen Gelenkkette. Ph.D. thesis, Engelmann, 1921) proposed a discrete model for elasticae by introducing rigid bars and rotational springs. Hencky (Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016) approach has been introduced to heuristically motivate the nee...

The problem of free vibrations of the Timoshenko beam model has been addressed in the first part of this paper. A careful analysis of the governing equations has shown that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. Her...

The problem of free vibrations of the Timoshenko beam model is here addressed. A careful analysis of the governing equations allows identifying that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. For both parts of the spect...

The theoretical results relevant to the vibration modes of Timoshenko beams are here used as benchmarks for assessing the correctness of the numerical values provided by several finite element models, based on either the traditional Lagrangian interpolation or on the recently developed isogeometric approach. Comparison of results is performed on bo...

A multiscale approach to analyse historical masonry buildings is presented and the numerical results deriving from its implementation are discussed. The modelling of this kind of heterogeneous material composed by irregular, stones and mortar joints is performed at the level of the microstructure by also describing the nonlinear behaviour of stones...

The current development of the isogeometric approach in various fields of mechanics is explained by the high-accuracy results which can be achieved at a reduced computational cost by codes based on non-uniform rational B-splines (NURBS). In the case of strongly curved beams the simple diagonal de Saint-Venant’s constitutive model can lead to signif...

In this work, the author gives a review of the state of the art on the computational strategies developed for the analysis of inverse problems. Starting from the definition of the inverse problem, and focusing the intrinsic difficulties in their solution, various computational tools developed for their solution are presented and discussed. This all...

This paper proposes a new method for the reconstruction of the blockage area function in a symmetric duct by resonant frequencies under a given set of end conditions, i.e., open-open or closed-closed ends. The analysis is based on the explicit determination of quasi-isospectral ducts, that is duct profiles which have the same spectrum as a given du...

The 64 m diameter Sardinia Radio Telescope (SRT), located near Cagliari (Italy), is the world’s second largest fully steerable radio telescope with an active surface. Among its peculiarities is the capability of modifying the configuration of the primary mirror surface by means of electromechanical actuators. This capability enables, within a fixed...

The Sardinia Radio Telescope (SRT), located near Cagliari (Italy), is the world’s second largest fully steerable radio telescope endowed with an active-surface system. Its primary mirror has a quasi-parabolic shape with a diameter of 64 m. The configuration of the primary mirror surface can be modified by means of electro-mechanical actuators. This...

The present article deals with the dynamic behavior of 2D continua representing the homogenized limit of microstructured pantographic systems, i.e., the structures in which two orders of fibers are interconnected by means of pivots. The strain energy density of the continuum model depends on the first and second gradient of the displacement. Numeri...