First experimental observation of the dynamical behavior of a pantographic metamaterial

Laudato, Marco; Manzari, Luca; Barchiesi, Emilio; Cosmo, Fabio Di; Göransson, Peter

doi:10.1016/j.mechrescom.2018.11.003

Cited by 43 publications

(29 citation statements)

References 8 publications

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“…Finally, the polyamide printed pantographic structures with perfect pivots [1] have been used in dynamical studies [55][56][57] . Once the problems of precision in the printing of perfect pivots will be overcome, it may be worthwhile that similar studies are also carried out on metal specimens.…”

Section: Resultsmentioning

confidence: 99%

Phenomenological aspects of quasi-perfect pivots in metallic pantographic structures

Spagnuolo

Peyre

Dupuy

2019

Mechanics Research Communications

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This article discusses the results of the first attempts to print metal pantographic structures with perfect pivots, i.e. with rotational hinges connecting the two families of fibers composing the network without any stiffness. On the one hand, it is observed that perfect pivots do not behave as expected theoretically. On the other hand, the force measured during a bias extension test is a few orders of magnitude lower than that measured for pantographic structures with standard pivots (where a certain stiffness is associated to the interconnecting hinges). This leads to considering the pivots as quasi-perfect (non-zero stiffness, but neither the theoretical one which can be computed by means of the geometrical features of the pivot). Numerical simulations complete the analysis by showing how, by modulating the torsional stiffness of the pivots, it is possible to reproduce the force-displacement plot both in the case of standard pivots and with quasi-perfect ones.

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Section: Resultsmentioning

confidence: 99%

Phenomenological aspects of quasi-perfect pivots in metallic pantographic structures

Spagnuolo

Peyre

Dupuy

2019

Mechanics Research Communications

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“…In fact, the propagation of waves in generalized continua [64][65][66] is a non-trivial problem and can lead to unexpected results. Some preliminary results in the field of pantographic structures can be found in [67,68].…”

Section: Discussionmentioning

confidence: 99%

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

et al. 2019

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Pantographic metamaterials are known for their ability to have large deformation while remaining in the elastic regime. We have performed a set of experiments on 3D printed pantographic unit cells to parametrically investigate their response when undergoing tensile, compression, and shear loading with the aim of i) studying the role of each parameter in the resultant mechanical behavior of the sample, and ii) providing a benchmark for the mathematical models developed to describe pantographic structures. Results show the existence of local extrema in the space of the geometrical parameters, suggesting the use of optimization techniques to find optimal geometrical parameters resulting in desired functionalities. We have also performed tensile relaxation tests on the samples, with the results indicating the complexity of the dynamic behavior and the existence of multiple relaxation characteristic times. Such results can be used to for calibrating mathematical models describing pantographic structures under dynamic loadings.

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“…However, we consider the presented model as an improvement of those already considered in the literature, see [18,28,92] and the reference therein, as the process of pivot deformation or inter-fiber elastic interaction has not been taken suitably into account. Moreover, see [115], recently some attention has been paid to the vibration phenomena of pantographic specimens and the experimental evidence which has been obtained indicates that a linear elastic dynamical model can be very useful in applications. Therefore, the first development which we will address of the results presented in this paper will surely include the discussion of:…”

Section: Conclusion and Future Stepsmentioning

confidence: 99%

On existence and uniqueness of weak solutions for linear pantographic beam lattices models

Eremeyev

Alzahrani

Cazzani

et al. 2019

Continuum Mech. Thermodyn.

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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-incomplete” strain-gradient elasticity for a model in which the considered strain energy density depends on displacements and only on some specific partial derivatives among those constituting displacements first and second gradients. So, unlike to the models of strain-gradient elasticity considered up-to-now, the strain energy density which we consider here is in a sense degenerated, since it does not contain the full set of second derivatives of the displacement field. Such mathematical problem was motivated by a recently introduced new class of metamaterials (whose microstructure is constituted by the so-called pantographic beam lattices) and by woven fabrics. Indeed, as from the physical point of view such materials are strongly anisotropic, it is not surprising that the mathematical models to be introduced must reflect such property also by considering an expression for deformation energy involving only some among the higher partial derivatives of displacement fields. As a consequence, the differential operators considered here, in the framework of introduced models, are neither elliptic nor strong elliptic as, in general, they belong to the class so-called hypoelliptic operators. Following (Eremeyev et al. in J Elast 132:175–196, 2018. 10.1007/s10659-017-9660-3) we present well-posedness results in the case of the boundary-value problems for small (linearized) spatial deformations of pantographic sheets, i.e., 2D continua, when deforming in 3D space. In order to prove the existence and uniqueness of weak solutions, we introduce a class of subsets of anisotropic Sobolev’s space defined as the energy space E relative to specifically assigned boundary conditions. As introduced by Sergey M. Nikolskii, an anisotropic Sobolev space consists of functions having different differential properties in different coordinate directions.

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First experimental observation of the dynamical behavior of a pantographic metamaterial

Cited by 43 publications

References 8 publications

Phenomenological aspects of quasi-perfect pivots in metallic pantographic structures

Phenomenological aspects of quasi-perfect pivots in metallic pantographic structures

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

On existence and uniqueness of weak solutions for linear pantographic beam lattices models

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