P. Harrison, Modelling the forming mechanics of engineering fabrics using a mutually constrained pantographic beam and membrane mesh, Compos. Part A Appl. Sci. Manuf, vol.81, pp.145-157, 2016.

U. Andreaus, F. Dell'isola, I. Giorgio, L. Placidi, T. Lekszycki et al., Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity, Int. J. Eng. Sci, vol.108, pp.34-50, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01378498

N. Auffray, J. Dirrenberger, and G. Rosi, A complete description of bi-dimensional anisotropic strain-gradient elasticity, Int. J. Solids Struct, vol.69, pp.195-206, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01145736

A. Battista, L. Rosa, R. Dell'erba, and L. Greco, Numerical investigation of a particle system compared with first and second gradient continua: deformation and fracture phenomena, Math. Mech. Solids, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01998612

D. J. Steigmann, The variational structure of a nonlinear theory for spatial lattices, Meccanica, vol.31, pp.441-455, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00782160

F. Dell'isola, T. Lekszycki, M. Pawlikowski, R. Grygoruk, and L. Greco, Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence, Z. für Angew. Math. Phys, vol.66, pp.3473-3498, 2015.

I. Giorgio, A. Della-corte, F. Dell'isola, and D. J. Steigmann, Buckling modes in pantographic lattices, C. R. Mec, vol.344, pp.487-501, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01294032

I. Giorgio, A. Della-corte, and F. Dell'isola, Dynamics of 1D nonlinear pantographic continua, Nonlinear Dyn, vol.88, pp.21-31, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01400478

E. Turco, A. Misra, M. Pawlikowski, F. Dell'isola, and F. Hild, Enhanced Piola-Hencky discrete models for pantographic sheets with pivots without deformation energy: numerics and experiments, Int. J. Solids Struct, vol.147, pp.94-109, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01791894

E. Turco, M. Golaszewski, A. Cazzani, and N. Rizzi, Large deformations induced in planar pantographic sheets by loads applied on fibers: experimental validation of a discrete Lagrangian model, Mech. Res. Commun, vol.76, pp.51-56, 2016.

E. Turco, K. Barcz, M. Pawlikowski, and N. Rizzi, Non-standard coupled extensional and bending bias tests for planar pantographic lattices. Part I: numerical simulations, Z. für Angew. Math. Phys, vol.67, p.122, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01456148

J. J. Alibert, P. Seppecher, and F. Dell'isola, Truss modular beams with deformation energy depending on higher displacement gradients, Math. Mech. Solids, vol.8, pp.51-73, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00497327

U. Andreaus, M. Spagnuolo, T. Lekszycki, and S. R. Eugster, A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams, Contin. Mech. Thermodyn, vol.30, pp.1103-1123, 2018.

M. Spagnuolo, K. Barcz, A. Pfaff, F. Dell'isola, and P. Franciosi, Qualitative pivot damage analysis in aluminum printed pantographic sheets: numerics and experiments, Mech. Res. Commun, vol.83, pp.47-52, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01529257

D. Scerrato, I. A. Zhurba-eremeeva, T. Lekszycki, and N. L. Rizzi, On the effect of shear stiffness on the plane deformation of linear second gradient pantographic sheets, ZAMM J. Appl. Math. Mech. Z. für Angew. Math. Mech, vol.96, pp.1268-1279, 2016.

M. Cuomo, F. Dell'isola, and L. Greco, Simplified analysis of a generalized bias test for fabrics with two families of inextensible fibres, Z. für Angew. Math. Phys, vol.67, p.61, 2016.

F. Dell'isola, I. Giorgio, M. Pawlikowski, and N. L. Rizzi, Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium, Proc. R. Soc. A, vol.472, p.20150790, 2016.

A. Misra, T. Lekszycki, I. Giorgio, G. Ganzosch, W. H. Müller et al., Pantographic metamaterials show a typical Poynting effect reversal, Mech. Res. Commun, vol.89, pp.6-10, 2018.

V. A. Eremeyev, F. Isola, C. Boutin, and D. Steigmann, Linear pantographic sheets: Existence and uniqueness of weak solutions, J. Elast, vol.132, pp.1-22, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01630819

L. Placidi, E. Barchiesi, E. Turco, and N. Rizzi, A review on 2D models for the description of pantographic fabrics, Z. für Angew. Math. Phys, vol.67, issue.5, p.121, 2016.

L. Placidi, U. Andreaus, and I. Giorgio, Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model, J. Eng. Math, vol.103, pp.1-21, 2016.

I. Giorgio, Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures, Z. für Angew. Math. Phys, vol.67, issue.4, p.95, 2016.

I. Babu?ka, Homogenization approach in engineering, Computing Methods in Applied Sciences and Engineering, pp.137-153, 1976.

G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal, vol.23, pp.1482-1518, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01111805

L. Tartar, The general theory of homogenization: A personalized introduction, 2009.

W. Yu and T. Tang, Variational asymptotic method for unit cell homogenization, Advances in Mathematical Modeling and Experimental Methods for Materials and Structures, pp.117-130, 2009.

M. Golaszewski, R. Grygoruk, I. Giorgio, M. Laudato, and F. Di-cosmo, Metamaterials with relative displacements in their microstructure: technological challenges in 3D printing, experiments and numerical predictions, Continuum Mech Thermodyn, vol.31, issue.4, pp.1015-1034, 2019.

T. Yang and Y. Bellouard, 3D electrostatic actuator fabricated by non-ablative femtosecond laser exposure and chemical etching, MATEC Web of Conferences, vol.32, 2015.

F. Koch, D. Lehr, O. Schönbrodt, T. Glaser, R. Fechner et al., Manufacturing of highly-dispersive, high-efficiency transmission gratings by laser interference lithography and dry etching, Microelectron. Eng, vol.191, pp.60-65, 2018.

K. Yamada, M. Yamada, H. Maki, and K. Itoh, Fabrication of arrays of tapered silicon micro-/nano-pillars by metalassisted chemical etching and anisotropic wet etching, Nanotechnology, vol.29, pp.28-29, 2018.

M. P. Larsson, Arbitrarily profiled 3D polymer MEMS through Si micro-moulding and bulk micromachining. Microelectron, Eng, vol.83, pp.1257-1260, 2006.

G. Milton, M. Briane, and D. Harutyunyan, On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials, Math. Mech. Complex Syst, vol.5, pp.41-94, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01341865

G. Milton, D. Harutyunyan, and M. Briane, Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase, Math. Mech. Complex Syst, vol.5, pp.95-113, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01355783

H. Abdoul-anziz and P. Seppecher, Strain gradient and generalized continua obtained by homogenizing frame lattices, Math. Mech. Complex Syst, vol.6, pp.213-250, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01672898

E. Barchiesi, M. Spagnuolo, and L. Placidi, Mechanical metamaterials: a state of the art, Math. Mech. Solids, vol.24, pp.212-234, 2018.

D. Cosmo, F. Laudato, M. Spagnuolo, M. Altenbach, H. Pouget et al., Acoustic metamaterials based on local resonances: homogenization, optimization and applications, Generalized Models and Non-classical Approaches in Complex Materials, vol.1, pp.247-274, 2018.

E. Barchiesi, F. Dell'isola, M. Laudato, L. Placidi, and P. Seppecher, A 1D continuum model for beams with pantographic microstructure: asymptotic micro-macro identification and numerical results, Advances in Mechanics of Microstructured Media and Structures, pp.43-74, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01817742

P. Seppecher, J. J. Alibert, and F. Isola, Linear elastic trusses leading to continua with exotic mechanical interactions, J. Phys. Conf. Ser, vol.319, pp.12-18, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00630098

J. J. Alibert, A. Della-corte, I. Giorgio, and A. Battista, Extensional Elastica in large deformation as ?-limit of a discrete 1D mechanical system, Z. Angew. Math. Phys, vol.68, p.42, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02185404

V. A. Eremeyev and W. Pietraszkiewicz, The nonlinear theory of elastic shells with phase transitions, J. Elast, vol.74, pp.67-86, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00831721

S. R. Eugster and C. Glocker, On the notion of stress in classical continuum mechanics, Math. Mech. Complex Syst, vol.5, pp.299-338, 2017.

D. Steigmann and M. Faulkner, Variational theory for spatial rods, J. Elast, vol.33, pp.1-26, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00782186

P. Germain, The method of virtual power in continuum mechanics. Part 2: microstructure, SIAM J. Appl. Math, vol.25, pp.556-575, 1973.

S. Forest and R. Sievert, Size-dependent Mechanics of Materials, Int. J. Solids Struct, vol.43, pp.7224-7245, 2006.

V. A. Eremeyev, L. P. Lebedev, and H. Altenbach, Foundations of Micropolar Mechanics, 2012.

H. Altenbach, M. Bîrsan, and V. A. Eremeyev, Cosserat-type rods, Generalized Continua from the Theory to Engineering Applications, pp.179-248, 2013.

M. Spagnuolo and U. Andreaus, A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling, Math. Mech. Solids, vol.24, pp.258-280, 2018.

B. Abali, W. Müller, and V. Eremeyev, Strain gradient elasticity with geometric nonlinearities and its computational evaluation. Mech, Adv. Mater. Mod. Process, vol.1, p.4, 2015.

B. E. Abali, W. H. Müller, and F. Isola, Theory and computation of higher gradient elasticity theories based on action principles, Arch. Appl. Mech, vol.87, pp.1495-1510, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01579839

E. Riks, An incremental approach to the solution of snapping and buckling problems, Int. J. Solids Struct, vol.15, pp.529-551, 1979.

, La Sapienza

E. Barchiesi, L. Placidi, and F. Dell,