Numerical experiments reveal unusual deformation patterns in a cylindrical lattice shell, modeled as a curved two-dimensional second-gradient elastic surface.
Del VescovoDGiorgioI. Dynamic problems for metamaterials: review of existing models and ideas for further research. Int J Eng Sci2014; 80: 153–172.
2.
Dell’IsolaFSeppecherPAlibertJJ, et al. Pantographic metamaterials: an example of mathematically driven design and of its technological challenges. Contin Mech Thermodyn2019; 31(4): 851–884.
3.
Dell’IsolaFSeppecherPSpagnuoloM, et al. Advances in pantographic structures: design, manufacturing, models, experiments and image analyses. Contin Mech Thermodyn2019; 31(4): 1231–1282.
4.
GiorgioISpagnuoloMAndreausU, et al. In-depth gaze at the astonishing mechanical behavior of bone: a review for designing bio-inspired hierarchical metamaterials. Math Mech Solids2021; 26(7): 1074–1103.
5.
Dell’IsolaFAndreausUPlacidiL.At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola. Math Mech Solids2015; 20(8): 887–928.
6.
EugsterSRDell’IsolaF.Exegesis of the introduction and sect: I from “fundamentals of the mechanics of continua” by E. Hellinger. ZAMM: J Appl Math Mech/Zeitschr Angew Math Mech2017; 97(4): 477–506.
7.
EugsterSRDell’IsolaF.Exegesis of sect: II and III—a from “fundamentals of the mechanics of continua” by E. Hellinger. ZAMM: J Appl Math Mech/Zeitschr Angew Math Mech2018; 98(1): 31–68.
8.
AlibertJ-JSeppecherPDell’IsolaF.Truss modular beams with deformation energy depending on higher displacement gradients. Math Mech Solids2003; 8(1)): 51–73.
9.
SeppecherPAlibertJ-Jdell’IsolaF.Linear elastic trusses leading to continua with exotic mechanical interactions. J Phys: Conf Ser2011; 319: 012018.
10.
AndreausUDell’IsolaFGiorgioI, et al. Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity. Int J Eng Sci2016; 108: 34–50.
11.
BoutinCGiorgioIPlacidiL, et al. Linear pantographic sheets: asymptotic micro-macro models identification. Math Mech Complex Syst2017; 5(2): 127–162.
12.
EremeyevVABoutinCSteigmannD, et al. Linear pantographic sheets: existence and uniqueness of weak solutions. J Elast2018; 132(2): 175–196.
13.
EremeyevVAAlzahraniFSCazzaniA, et al. On existence and uniqueness of weak solutions for linear pantographic beam lattices models. Contin Mech Thermodyn2019; 31(6): 1843–1861.
14.
CuomoMGrecoLDell’IsolaF.Simplified analysis of a generalized bias test for fabrics with two families of inextensible fibres. Zeitschr Angew Math Phys2016; 67(3): 1–23.
15.
LekszyckiTPawlikowskiMGrygorukR, et al. Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence. Zeitschr Angew Math Phys2015; 66(6): 3473–3498.
16.
EremeyevVA.A nonlinear model of a mesh shell. Mech Solids2018; 53(4): 464–469.
17.
EremeyevVA.Two-and three-dimensional elastic networks with rigid junctions: modeling within the theory of micropolar shells and solids. Acta Mech2019; 230(11): 3875–3887.
18.
Abdoul-AnzizHSeppecherP.Strain gradient and generalized continua obtained by homogenizing frame lattices. Math Mech Comp Syst2018; 6(3): 213–250.
19.
PideriCSeppecherP.A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium. Contin Mech Thermodyn1997; 9(5): 241–257.
20.
dell’IsolaFGiorgioIPawlikowskiM, et al. Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium. Proc Royal Soc A: Math, Phys Eng Sci2016; 472(2185): 20150790.
21.
TurcoECazzaniARizziNL, et al. Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Zeitschr Angew Math Phys2016; 67(4): 1–28.
22.
TurcoEGolaszewskiMGiorgioI, et al. Pantographic lattices with non-orthogonal fibres: experiments and their numerical simulations. Comp Part B: Eng2017; 118: 1–14.
23.
GiorgioIGrygorukRdell’IsolaF, et al. Pattern formation in the three-dimensional deformations of fibered sheets. Mech Res Commun2015; 69: 164–171.
24.
GiorgioI.Lattice shells composed of two families of curved Kirchhoff rods: an archetypal example, topology optimization of a cycloidal metamaterial. Contin Mech Thermodyn2021; 33(4): 1063–1082.
25.
ScerratoDGiorgioI.Equilibrium of two-dimensional cycloidal pantographic metamaterials in three-dimensional deformations. Symmetry2019; 11(12): 1523.
26.
GiorgioIDell’IsolaFSteigmannDJ.Axisymmetric deformations of a 2nd grade elastic cylinder. Mech Res Commun2018; 94: 45–48.
27.
GiorgioICiallellaAScerratoD.A study about the impact of the topological arrangement of fibers on fiber-reinforced composites: some guidelines aiming at the development of new ultra-stiff and ultra-soft metamaterials. Int J Solids Struct2020; 203: 73–83.
28.
SteigmannDJ.Equilibrium of elastic lattice shells. J Eng Math2018; 109(1): 47–61.
29.
SpencerAJMSoldatosKP.Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness. Int J Nonl Mech2007; 42(2): 355–368.
30.
De AngeloMBarchiesiEGiorgioI, et al. Numerical identification of constitutive parameters in reduced-order bi-dimensional models for pantographic structures: application to out-of-plane buckling. Arch Appl Mech2019; 89(7): 1333–1358.
31.
GiorgioIHarrisonPDell’IsolaF, et al. Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches. Proc Royal Soc A: Math, Phys Eng Sci2018; 474(2216): 20180063.
32.
AbaliBEKlunkerABarchiesiE, et al. A novel phase-field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable. ZAMM: Zeitschr Angew Math Mech2021; 101: e202000289.
33.
ForestS.Micromorphic approach for gradient elasticity, viscoplasticity, and damage. J Eng Mech2009; 135(3): 117–131.
34.
ScerratoDZhurba, EremeevaIALekszyckiT, et al. On the effect of shear stiffness on the plane deformation of linear second gradient pantographic sheets. ZAMM: Zeitschr Angew Math Mech2016; 96(11): 1268–1279.
35.
ReiherJCGiorgioIBertramA.Finite-element analysis of polyhedra under point and line forces in second-strain gradient elasticity. J Eng Mech2017; 143(2): 04016112.
36.
BedoyaJMeyerCATimminsLH, et al. Effects of stent design parameters on normal artery wall mechanics. J Biomech Eng2006; 128: 757–765.
37.
LewisG.Materials, fluid dynamics, and solid mechanics aspects of coronary artery stents: a state-of-the-art review. J Biomed Mater Res Part B: Appl Biomater2008; 86(2): 569–590.
38.
ZhaoSGuLFroemmingSR.On the importance of modeling stent procedure for predicting arterial mechanics. J Biomech Eng2012; 134(12): 121005.
39.
CianchettiMRanzaniTGerboniG, et al. Soft robotics technologies to address shortcomings in today’s minimally invasive surgery: the stiff-flop approach. Soft Robot2014; 1(2)): 122–131.
40.
MajidiC.Soft robotics: a perspective—current trends and prospects for the future. Soft Robot2014; 1(1)): 5–11.
41.
GiorgioIVaranoVDell’IsolaF, et al. Two layers pantographs: a 2D continuum model accounting for the beams’ offset and relative rotations as averages in so (3) lie groups. Int J Solids Struct2021; 216: 43–58.
42.
SpagnuoloMBarczKPfaffA, et al. Qualitative pivot damage analysis in aluminum printed pantographic sheets: numerics and experiments. Mech Res Commun2017; 83: 47–52.
