Pantographic lattices with non-orthogonal fibres: Experiments and their numerical simulations

Turco, Emilio; Gołaszewski, Maciej; Giorgio, Ivan; D’Annibale, Francesco

doi:10.1016/j.compositesb.2017.02.039

Cited by 96 publications

(57 citation statements)

References 76 publications

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“…The necessity of considering distributed loads in large deformation arises, for instance, in the field of fluid-structure interaction [19][20][21][22][23] or in the framework of microstructured continua [24,25], in particular when the microstructure can be modeled as an array of fibers that can be individually modeled as beams undergoing large deformations, while the interaction with the remaining part of the array can be modeled as a distributed load acting on the beam. Possible examples are the structures described in [18,[26][27][28][29][30][31][32][33], which contributed to motivate the present study. The importance of fibrous microstructured systems is increasing in current literature, especially since these objects can be manufactured with great precision and relatively limited costs by means of computer-aided manufacturing (see for instance [34,35] for useful reference works).…”

Section: Introductionmentioning

confidence: 82%

Large deformations of Timoshenko and Euler beams under distributed load

Corte

Battista

Dell’Isola

et al. 2019

Z. Angew. Math. Phys.

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In this paper, the general equilibrium equations for a geometrically nonlinear version of the Timoshenko beam are derived from the energy functional. The particular case in which the shear and extensional stiffnesses are infinite, which correspond to the inextensible Euler beam model, is studied under a uniformly distributed load. All the global and local minimizers of the variational problem are characterized, and the relative monotonicity and regularity properties are established. MathematicsSubject Classification. 74B20, 34B15, 49J45. Keywords. Nonlinear elasticity, Timoshenko beam, Euler beam, Stability of solutions of nonlinear ODEs.the case of concentrated load. Afterward, some numerical results for the inextensible Euler beam under distributed load were published in [37,38]. The paper is organized as follows: in Sect. 2 a nonlinear version of the extensible Timoshenko beam model is introduced and the problem of a clamped-free beam is formulated. Euler-Lagrange equations are formally derived. In Sect. 3, some numerical results concerning curled equilibrium configurations are shown. These results motivate the analytical study of the properties of the equilibrium solutions done in Sect. 4, in which the Euler-Lagrange equation is studied in the particular case of an infinite shear stiffness, which leads to the nonlinear Euler beam.

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Section: Introductionmentioning

confidence: 82%

Large deformations of Timoshenko and Euler beams under distributed load

Corte

Battista

Dell’Isola

et al. 2019

Z. Angew. Math. Phys.

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“…The experiment is studied only up to the first rupture (i.e., as long as K int > 0 ∀X ∈ B 0 ). For the discrete model [57], and in turn for the continuum homogenized model [58] (as for their respective purely elastic counterparts), it is straightforward to implement the case of non-orthogonal initially straight fibers [60].…”

Section: Damage and Failure In Pantographic Fabricsmentioning

confidence: 99%

Pantographic metamaterials: an example of mathematically driven design and of its technological challenges

Dell’Isola

Seppecher

Alibert

et al. 2018

Continuum Mech. Thermodyn.

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295

141

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Pantographic metamaterials: an example of mathematically driven design and of its technological challenges Abstract 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 investiga-tions. The problem to be solved was stated as follows: determine the material (micro)structure governed by those equations that specify a desired behavior. Addressing this problem has led to the synthesis of second gradient materials. In the second stage, it has been necessary to develop numerical integration schemes andDipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma "La Sapienza.", Via Eudossiana 18, 00184 Rome, Italy E-mail: barchiesiemilio@gmail.com the corresponding codes for solving, in physically relevant cases, the chosen equations. Finally, it has been necessary to physically construct the theoretically synthesized microstructures. This has been possible by means of the recent developments in rapid prototyping technologies, which allow for the fabrication of some complex (micro)structures considered, up to now, to be simply some mathematical dreams. We show here a panorama of the results of our efforts (1) in designing pantographic metamaterials, (2) technology of rapid prototyping, and (3) in the mechanical testing of many real prototypes. Among the key findings that have been obtained, there are the following ones: pantographic metamaterials (1) undergo very large deformations while remaining in the elastic regime, (2) are very tough in resisting to damage phenomena, (3) exhibit robust macroscopic mechanical behavior with respect to minor changes in their microstructure and micromechanical properties, (4) have superior strength to weight ratio, (5) have predictable damage behavior, and (6) possess physical properties that are critically dictated by their geometry at the microlevel.

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“…In a series of papers (see previous studies), it has been proven that, rather unexpectedly, even in presence of relatively few degrees of freedom, discrete systems show a very similar behaviour to their continuous homogenised counterparts. However, we wanted to include a rather numerous set of grains (about 900) to make the continuous identification of the whole assembly more credible.…”

Section: Numerical Simulations and Their Interpretationmentioning

confidence: 99%

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

Turco

Dell’Isola²,

Misra

2019

Num Anal Meth Geomechanics

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Summary 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 relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model.

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Pantographic lattices with non-orthogonal fibres: Experiments and their numerical simulations

Cited by 96 publications

References 76 publications

Large deformations of Timoshenko and Euler beams under distributed load

Large deformations of Timoshenko and Euler beams under distributed load

Pantographic metamaterials: an example of mathematically driven design and of its technological challenges

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

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