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Review Article

Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response

[+] Author and Article Information
Francesco dell'Isola

DISG,
University of Rome La Sapienza,
Rome 00184, Italy
e-mail: francesco.dellisola@uniroma1.it

David Steigmann

Faculty of Mechanical Engineering,
University of California,
Berkeley, CA 94720-1740
e-mail: dsteigmann@berkeley.edu

Alessandro Della Corte

DIMA,
University of Rome La Sapienza,
Rome 00185, Italy
e-mail: alessandro.dellacorte@uniroma1.it

1Corresponding author.

Manuscript received July 24, 2015; final manuscript received December 7, 2015; published online January 6, 2016. Assoc. Editor: Rui Huang.

Appl. Mech. Rev 67(6), 060804 (Jan 06, 2016) (21 pages) Paper No: AMR-15-1085; doi: 10.1115/1.4032206 History: Received July 24, 2015; Revised December 07, 2015

In Mechanics, material properties are most often regarded as being given, and based on this, many technical solutions are usually conceived and constructed. However, nowadays manufacturing processes have advanced to the point that metamaterials having selected properties can be designed and fabricated. Three-dimensional printing, electrospinning, self-assembly, and many other advanced manufacturing techniques are raising a number of scientific questions which must be addressed if the potential of these new technologies is to be fully realized. In this work, we report on the status of modeling and analysis of metamaterials exhibiting a rich and varied macroscopic response conferred by complex microstructures and particularly focus on strongly interacting inextensible or nearly inextensible fibers. The principal aim is to furnish a framework in which the mechanics of 3D rapid prototyping of microstructured lattices and fabrics can be clearly understood and exploited. Moreover, several-related open questions will be identified and discussed, and some methodological considerations of general interest are provided.

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Giorgio, I. , Grygoruk, R. , dell'Isola, F. , and Steigmann, D. J. , 2015, “ Pattern Formation in the Three-Dimensional Deformations of Fibered Sheets,” Mech. Res. Commun., 69, pp. 164–171. [CrossRef]
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Figures

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Fig. 1

Bias test on a 3D-printed pantographic sheet (top) and simulation, as studied in Ref. [358] (original picture by the authors); we remark that the picture is relative to a continuum simulation, and that the curves represent sets of material points which are straight lines in the reference configuration

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Fig. 2

Three-dimensional simulation for a pantographic structure as studied in Ref. [359]. Top: the deformation energy isstored in the pivots; bottom: the employed mesh is visible (original picture by the authors).

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Fig. 3

A prestretched electrospun polyurethane metamaterial used as a scaffold for tissue growth; left: single tissue spheroid attached to the electrospun scaffold; right: seven fused tissue spheroids attached to the scaffold. Arrows indicate the areas of attachment-dependent cell and tissue spreading; scale-bar 300 μm (from Ref. [274]; free licence from SAGE webpage2).

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Fig. 4

Left: tissue spheroids adherent to the electrospun scaffold; right: SEM image of the adhesion of tissue spheroids to the electrospun matrix (from Ref. [274]; free licence from SAGE webpage3)

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Fig. 5

Handicraft metamaterial exhibiting interesting mechanical properties (high damping, negative stiffness, snap-through, etc.): Tachi-Miura polyhedron realized by means of origami structures made of paper as studied in Ref. [275]. Left: digital image of the prototypes; right: photo of the top of the prototype (original pictures by the authors).

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Fig. 6

Left: three different configurations of the papermade Tachi-Miura polyhedron (studied in Ref. [275]) under the same normalized force; right: force-folding ratio relationship and snap-through response (original rendering of pictures provided by the authors)

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Fig. 7

Another example of handicraft metamaterial: hollow plastic spheres (138 mm high) with a central impervious cylinder studied in Ref. [276]. Spheres might be impervious hollow spheres, or resonators, or both (see Table 1 in the reference paper for details). The interspheres space might be occupied either by air or filled by a granular medium. Left: geometry of the prototype; middle: a prototype; right: cut of the two types of Helmholtz resonators (original pictures by Professor Claude Boutin).

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Fig. 8

Sound absorption coefficient at ambient condition of temperature and pressure for the system studied in Ref. [276] and represented in Fig. 7. Measurement is represented by the thick line and simulation by the dashed one (original picture by Professor Claude Boutin).

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Fig. 9

Left: shaking table (Bristol Laboratory for Advanced Dynamics Engineering) equipped with aluminum sheets acting as resonators as studied in Ref. [277]; right: zoom on the sheets (original pictures by Professor Claude Boutin)

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Fig. 10

Changes in spectrum surface/table for the system studied in Ref. [277] and shown in Fig. 9. The curve for one resonator is very close to usual layer's resonance; the curve corresponding to 37 resonators shows drastic changes in layer's resonance in x resonant direction and usual resonance peak in y inert direction; in black: standard impedance analysis is also shown; UΓ and Ub are, respectively, the displacements of the material points belonging to the upper surface and to the base of the sample (original picture by Prof. Claude Boutin).

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Fig. 11

ZnO crystal and ZnO nanotubes (Reproduced with permission from Özgür et al. [294]. Copyright 2005 by AIP.)

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Fig. 12

ZnO nanoarray (respectively, 300×, 1200×, 5000×, and 10,000× from top left to bottom right) (Reproduced with permission from Ma et al. [298]. Copyright 2008 by Elsevier.)

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Fig. 13

“Black silicon” for solar cells (Reproduced with permission from Spinelli et al. [301]. Copyright 2012 by Nature Publishing Group.)

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Fig. 14

Deformation energy for a second gradient lattice mesomodel of a sheet with inextensible fibers, with an imposed elongation of 60%, as studied in Ref. [359] (original picture by the authors)

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Fig. 15

Deformation energy for a mixed first and second gradient lattice mesomodel of a sheet with inextensible fibers, with an imposed elongation of 80%, as studied in Ref. [359] (original picture by the authors)

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Fig. 16

Three-dimensional simulation for a pantographic structure in traction as studied in Ref. [359] (original picture by the authors)

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Fig. 17

Waves traveling in opposite directions in a pantographic structure (Reproduced with permission from Madeo et al. [240]. Copyright 2014 by Proceedings of the Estonian Academy of Sciences.)

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Fig. 18

Damping of a wave by means of an array of vertical springs in a pantographic structure (Reproduced with permission from Madeo et al. [240]. Copyright 2014 by Proceedings of the Estonian Academy of Sciences.)

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Fig. 19

Out-of-plane twisting of a squared pantographic sheet as studied in Ref. [358]. The picture is relative to a continuum simulation, and that the curves represent sets of material points which are straight lines in the reference configuration (original picture by the authors).

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Fig. 20

Epidermal flexible plate (Reproduced with permission from Kim et al. [361]. Copyright 2011 by AAAS.)

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Fig. 21

An architectured material employed for a vascular implant made of NiTi knitted fabric and inserted in a silicone elastomer (original rendering of a photo from Ref. [369])

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Fig. 22

A pantographic sheet under extensional bias test as studied in Ref. [358]: a concept for a new lightweight, extremely resistant and safe in failure architectured material (original picture by the authors)

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Fig. 23

Three-dimensional simulation for a pantographic structure in traction and torsion as studied in Ref. [359] (original picture by the authors)

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Fig. 24

Out-of-plane twisting of a pantographic sheet with combined traction and torsion as studied in Ref. [358]. The picture is relative to a continuum simulation, and thatthe curves represent sets of material points which are straight lines in the reference configuration (original picture by the authors).

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