Pattern formation in the three-dimensional deformations of fibered sheets

Giorgio, Ivan; Grygoruk, Roman; Dell’Isola, Francesco; Steigmann, David J.

doi:10.1016/j.mechrescom.2015.08.005

Cited by 76 publications

(57 citation statements)

References 39 publications

(24 reference statements)

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“…[10][11][12][13][14][15][16], modeled as generalized continua, we prove here that, when some specific deformation phenomena are considered, the most suitable models are not continuous. On the other hand, as seen in [1,17], when the qualitative description of their behavior is needed then second gradient continuum models may be more suitable.…”

Section: Discussionmentioning

confidence: 74%

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

Turco

Dell’Isola

Rizzi

et al. 2016

Mechanics Research Communications

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Section: Discussionmentioning

confidence: 74%

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

Turco

Dell’Isola

Rizzi

et al. 2016

Mechanics Research Communications

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“…with Furthermore, a strain energy density function, which depends on the first and second gradients of the deformation and incorporating the orthotropic symmetry conferred by the reference fiber arrangement, can be proposed [47] …”

Section: Elastic Surface Modelsmentioning

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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298

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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“…However, the same homogenization method can be extended to investigate buckling and out-plane deformation as discussed in [Giorgio et al 2015;.…”

Section: Discussionmentioning

confidence: 99%

Linear pantographic sheets: Asymptotic micro-macro models identification

Boutin

Dell’Isola

Giorgio

et al. 2017

Math. Mech. Compl. Sys.

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164

120

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In this paper we consider linear pantographic sheets, which in their natural configuration are constituted by two orthogonal arrays of straight fibers interconnected by internal pivots. We introduce a continuous model by means of a micro-macro identification procedure based on the asymptotic homogenization method of discrete media. The rescaling of the mechanical properties and of the deformation measures is calibrated in order to comply with the specific kinematics imposed by the quasi-inextensibility of the fibers together with the large pantographic deformability. The obtained high-order continuum model shows interesting and exotic features related to its extreme anisotropy and also to the subcoercivity of its deformation energy. Some initial numerical simulations are presented, showing that the model can account for experimental uncommon phenomena occurring in pantographic sheets. The paper focuses on the precise analysis and the understanding of the effective behavior based on a well-calibration of the extension and bending phenomena arising at the local scale. In an upcoming work, the analysis will be extended to oblique arrays, some analytical solutions to proposed equations and some further applications.

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Pattern formation in the three-dimensional deformations of fibered sheets

Cited by 76 publications

References 39 publications

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

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

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

Linear pantographic sheets: Asymptotic micro-macro models identification

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