Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

Turco, Emilio; Dell’Isola, Francesco; Rizzi, Nicola Luigi; Grygoruk, Roman; Müller, Wolfgang; Liebold, Christian

doi:10.1016/j.mechrescom.2016.07.007

Cited by 94 publications

(68 citation statements)

References 49 publications

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“…This evidence is confirmed, through a different test [57] (see Fig. 32), since fiber elongation is the highest at the lower-left and upper-right corners.…”

Section: Damage and Failure In Pantographic Fabricssupporting

confidence: 57%

“…So far the study of damage mechanisms in pantographic fabrics has been addressed from a modeling standpoint [57,58]. Further experimental data can be found [10,59].…”

Section: Damage and Failure In Pantographic Fabricsmentioning

confidence: 99%

“…In Ref. [57], in the aforementioned discrete quasi-static Hencky spring model (Sect. 1.3) a simple irreversible rupture mechanisms is considered for the springs.…”

Section: Damage and Failure In Pantographic Fabricsmentioning

confidence: 99%

“…[57], a slow-rate (15 mm/min) of uniform horizontal displacement on the top of the specimen is prescribed. From the prescribed horizontal displacement u, a non-dimensional displacement λ can be calculated.…”

Section: Damage and Failure In Pantographic Fabricsmentioning

confidence: 99%

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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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307

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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“…This evidence is confirmed, through a different test [57] (see Fig. 32), since fiber elongation is the highest at the lower-left and upper-right corners.…”

Section: Damage and Failure In Pantographic Fabricssupporting

confidence: 57%

“…So far the study of damage mechanisms in pantographic fabrics has been addressed from a modeling standpoint [57,58]. Further experimental data can be found [10,59].…”

Section: Damage and Failure In Pantographic Fabricsmentioning

confidence: 99%

“…In Ref. [57], in the aforementioned discrete quasi-static Hencky spring model (Sect. 1.3) a simple irreversible rupture mechanisms is considered for the springs.…”

Section: Damage and Failure In Pantographic Fabricsmentioning

confidence: 99%

Section: Damage and Failure In Pantographic Fabricsmentioning

confidence: 99%

See 2 more Smart Citations

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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307

141

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“…More precisely: in order to find a class of materials whose deformation energy depends on both first and second gradient of placement field in [22] a microstructured (pantographic) fabric is introduced and its homogenized continuum model (which we call pantographic sheet) is determined. Various aspects of modelling of pantographic lattices are considered in [8,52,53,56,[62][63][64][65][66] where discrete and homogenized models are considered. Let us note that one of the sources of generalized continua and models of metamaterials is the homogenization of heterogeneous materials, see, e.g., [18,54,61] and reference therein.…”

Section: Introductionmentioning

confidence: 99%

Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

Eremeyev

Dell’Isola

Boutin

et al. 2017

J Elast

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129

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The well-posedness of the boundary value problems for second gradient elasticity has been studied under the assumption of strong ellipticity of the dependence on the second placement gradients (see, e.g., Chambon and Moullet in Comput. Methods Appl. Mech. Eng. 193:2771-2796 and Mareno and Healey in SIAM J. Math. Anal. 38:103-115, 2006.The study of the equilibrium of planar pantographic lattices has been approached in two different ways: in dell 'Isola et al. (Proc. R. Soc. Lond. Ser. A 472:20150, 2016) a discrete model was introduced involving extensional and rotational springs which is also valid in large deformations regimes while in Boutin et al. (Math. Mech. Complex Syst. 5:127-162, 2017) the lattice has been modelled as a set of beam elements interconnected by internal pivots, but the analysis was restricted to the linear case. In both papers a homogenized second gradient deformation energy, quadratic in the neighbourhood of non deformed configuration, is obtained via perturbative methods and the predictions obtained with the obtained continuum model are successfully compared with experiments. This energy is not strongly elliptic in its dependence on second gradients. We consider in this paper also the important particular case of pantographic lattices whose first gradient energy does not depend on shear deformation: this could be considered either a pathological case or an important exceptional case (see Stillwell et al. in Am. Math. Mon. 105:850-858, 1998 and Turro in Angew. Chem., Int. Ed. Engl. 39:2255Engl. 39: -2259Engl. 39: , 2000. In both cases we believe that such a particular case deserves some attention because of what we can understand by studying it (see Dyson in Science 200:677-678, 1978). This circumstance motivates the present paper, where we address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev's space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E; (iii) we prove that the set of placements for which the strain energy is vanishing (the so-called floppy modes) must strictly include rigid motions; (iv) we determine the restrictions on displacement boundary conditions which assure existence and uniqueness of linear static problems. The presented results represent one of the first mechanical applications of the concept of Anisotropic Sobolev space, initially introduced only on the basis of purely abstract mathematical considerations.

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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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Fiber rupture in sheared planar pantographic sheets: Numerical and experimental evidence

Cited by 94 publications

References 49 publications

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

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

Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

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

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