Comptes Rendus
no. 2
Edge effects in Hypar nets
[Effets de bord dans les réseaux paraboloïdaux hyperboliques]
Ivan Giorgio1, 2  ; Francesco dell'Isola1, 2 ; David J. Steigmann3, 2
1 Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli studi di Roma La Sapienza, 00184 Roma, Italy
2 International Research Center for the Mathematics and Mechanics of Complex Systems, Università dell'Aquila, Italy
3 Department of Mechanical Engineering, University of California – Berkeley, CA 94720, USA
Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 114-123.

Les effets de bord dans les réseaux paraboloïdaux hyperboliques sont analysés à l'aide d'un modèle présentant la résistance élastique des fibres du réseau à la flexion et à la torsion en plus de l'élasticité en extension de la théorie conventionnelle des membranes pour les réseaux.

Edge effects in hyperbolic paraboloidal nets are analyzed using a model that features the elastic resistance of the fibers of the net to flexure and twist in addition to the extensional elasticity of the conventional membrane theory of networks.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2019.01.003
Keywords: Second gradient models, Geodesic bending, Shell elasticity
Mot clés : Milieux continus du second gradient, Flexion géodésique, Élasticité de la coque
Ivan Giorgio 1, 2 ; Francesco dell'Isola 1, 2 ; David J. Steigmann 3, 2

1 Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli studi di Roma La Sapienza, 00184 Roma, Italy
2 International Research Center for the Mathematics and Mechanics of Complex Systems, Università dell'Aquila, Italy
3 Department of Mechanical Engineering, University of California – Berkeley, CA 94720, USA 
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Ivan Giorgio; Francesco dell'Isola; David J. Steigmann. Edge effects in Hypar nets. Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 114-123. doi : 10.1016/j.crme.2019.01.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.01.003/

[1] W. Flügge Stresses in Shells, Springer, Berlin, 1973

[2] F. Otto Basic concepts and survey of tensile structures, Tensile Structures, vol. 2, 1966, pp. 11-96

[3] A. Viskovic Hemp cables, a sustainable alternative to harmonic steel for cable nets, Resources, Volume 7 (2018) no. 4, p. 70

[4] E.N. Kuznetsov Underconstrained Structural Systems, Springer, New York, 2012

[5] D.J. Steigmann; A.C. Pipkin Equilibrium of elastic nets, Philos. Trans. R. Soc. Lond., Ser. A, Phys. Eng. Sci. (1991), pp. 419-454

[6] P. Germain The method of virtual power in continuum mechanics, part 2: microstructure, SIAM J. Appl. Math., Volume 25 (1973) no. 3, pp. 556-575

[7] R.D. Mindlin Second gradient of strain and surface-tension in linear elasticity, Int. J. Solids Struct., Volume 1 (1965) no. 4, pp. 417-438

[8] R.A. Toupin Elastic materials with couple-stresses, Arch. Ration. Mech. Anal., Volume 11 (1962) no. 1, pp. 385-414

[9] F. dell'Isola; A. Della Corte; I. Giorgio Higher-gradient continua: the legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives, Math. Mech. Solids, Volume 22 (2017) no. 4, pp. 852-872

[10] F. dell'Isola; P. Seppecher Edge contact forces and quasi-balanced power, Meccanica, Volume 32 (1997) no. 1, pp. 33-52

[11] V.A. Eremeyev; F. dell'Isola; C. Boutin; D. Steigmann Linear pantographic sheets: existence and uniqueness of weak solutions, J. Elast., Volume 132 (2018) no. 2, pp. 175-196

[12] D.J. Steigmann; F. dell'Isola Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching, Acta Mech. Sin., Volume 31 (2015) no. 3, pp. 373-382

[13] I. Giorgio; R. Grygoruk; F. dell'Isola; D.J. Steigmann Pattern formation in the three-dimensional deformations of fibered sheets, Mech. Res. Commun., Volume 69 (2015), pp. 164-171

[14] H. Abdoul-Anziz; P. Seppecher Strain gradient and generalized continua obtained by homogenizing frame lattices, Math. Mech. Complex Syst., Volume 6 (2018) no. 3, pp. 213-250

[15] C. Pideri; P. Seppecher A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium, Contin. Mech. Thermodyn., Volume 9 (1997) no. 5, pp. 241-257

[16] H. Abdoul-Anziz; P. Seppecher Homogenization of periodic graph-based elastic structures, J. École Polytech., Math., Volume 5 (2018), pp. 259-288

[17] Y. Rahali; F. Dos Reis; J.-F. Ganghoffer Multiscale homogenization schemes for the construction of second-order grade anisotropic continuum media of architectured materials, Int. J. Multiscale Comput. Eng., Volume 15 (2017) no. 1

[18] Y. Rahali; J.-F. Ganghoffer; F. Chaouachi; A. Zghal Strain gradient continuum models for linear pantographic structures: a classification based on material symmetries, J. Geom. Symmetry Phys., Volume 40 (2015), pp. 35-52

[19] J.-F. Ganghoffer; G. Maurice; Y. Rahali Determination of closed form expressions of the second-gradient elastic moduli of multi-layer composites using the periodic unfolding method, Math. Mech. Solids (2018) | DOI

[20] K. ElNady; I. Goda; J.-F. Ganghoffer Computation of the effective nonlinear mechanical response of lattice materials considering geometrical nonlinearities, Comput. Mech., Volume 58 (2016) no. 6, pp. 957-979

[21] G. Rosi; L. Placidi; N. Auffray On the validity range of strain-gradient elasticity: a mixed static–dynamic identification procedure, Eur. J. Mech. A, Solids, Volume 69 (2018), pp. 179-191

[22] L. Placidi; E. Barchiesi; A. Battista An inverse method to get further analytical solutions for a class of metamaterials aimed to validate numerical integrations, Mathematical Modelling in Solid Mechanics, Springer, 2017, pp. 193-210

[23] A. Misra; P. Poorsolhjouy Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics, Math. Mech. Complex Syst., Volume 3 (2015) no. 3, pp. 285-308

[24] E. Turco; A. Misra; R. Sarikaya; T. Lekszycki Quantitative analysis of deformation mechanisms in pantographic substructures: experiments and modeling, Contin. Mech. Thermodyn. (2018), pp. 1-15 | DOI

[25] E. Turco; M. Golaszewski; A. Cazzani; N.L. Rizzi Large deformations induced in planar pantographic sheets by loads applied on fibers: experimental validation of a discrete Lagrangian model, Mech. Res. Commun., Volume 76 (2016), pp. 51-56

[26] L. Greco; M. Cuomo On the force density method for slack cable nets, Int. J. Solids Struct., Volume 49 (2012) no. 13, pp. 1526-1540

[27] L. Greco; N. Impollonia; M. Cuomo A procedure for the static analysis of cable structures following elastic catenary theory, Int. J. Solids Struct., Volume 51 (2014) no. 7–8, pp. 1521-1533

[28] J. Altenbach; H. Altenbach; V.A. Eremeyev On generalized Cosserat-type theories of plates and shells: a short review and bibliography, Arch. Appl. Mech., Volume 80 (2010) no. 1, pp. 73-92

[29] L. Placidi; E. Barchiesi; E. Turco; N.L. Rizzi A review on 2D models for the description of pantographic fabrics, Z. Angew. Math. Phys., Volume 67 (2016) no. 5, p. 121

[30] F. dell'Isola et al. Pantographic metamaterials: an example of mathematically driven design and of its technological challenges, Contin. Mech. Thermodyn. (2018) | DOI

[31] L. Placidi; L. Greco; S. Bucci; E. Turco; N.L. Rizzi A second gradient formulation for a 2D fabric sheet with inextensible fibres, Z. Angew. Math. Phys., Volume 67 (2016) no. 5, p. 114

[32] W.A. Green; J. Shi Plane deformations of membranes formed with elastic cords, Q. J. Mech. Appl. Math., Volume 43 (1990) no. 3, pp. 317-333

[33] F. dell'Isola; D. Steigmann A two-dimensional gradient-elasticity theory for woven fabrics, J. Elast., Volume 118 (2015) no. 1, pp. 113-125

[34] E.M. Haseganu; D.J. Steigmann Equilibrium analysis of finitely deformed elastic networks, Comput. Mech., Volume 17 (1996) no. 6, pp. 359-373

[35] I. Giorgio; P. Harrison; F. dell'Isola; J. Alsayednoor; E. Turco Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches, Proc. R. Soc. A, Math. Phys. Eng. Sci., Volume 474 (2018) no. 2216 (20 pages)

[36] E. Barchiesi; G. Ganzosch; C. Liebold; L. Placidi; R. Grygoruk; W.H. Müller Out-of-plane buckling of pantographic fabrics in displacement-controlled shear tests: experimental results and model validation, Contin. Mech. Thermodyn. (2018), pp. 1-13 | DOI

[37] I. Giorgio; A. Della Corte; F. dell'Isola; D.J. Steigmann Buckling modes in pantographic lattices, C. R. Mecanique, Volume 344 (2016) no. 7, pp. 487-501

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