R. A. Toupin, Theories of elasticity with couple-stress, Archive for Rational Mechanics, Mechanics Research Communications, vol.17, issue.2, p.90, 1964.

E. Turco, M. Golaszewski, A. Cazzani, and N. Rizzi, Large deformations induced in planar pantographic sheets by loads applied on bers: 510 experimental validation of a discrete lagrangian model, Mechanics Research Communications, vol.76, p.5156, 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, Zeitschrift für angewandte Mathematik und Physik, vol.515, issue.5, p.122, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01456148

E. Turco and N. Rizzi, Pantographic structures presenting statistically distributed defects: numerical investigations of the eects on deformation elds, vol.77, p.6569, 2016.

E. Turco, I. Giorgio, A. Misra, and F. , King post truss as a motif 520 for internal structure of (meta) material with controlled elastic properties, Royal Society Open Science, vol.4, issue.10, 2017.

E. Turco, A. Misra, M. Pawlikowski, F. Isola, and F. Hild, Enhanced piolahencky discrete models for pantographic sheets with pivots without deformation energy: Numerics and experiments, International Journal of 525 Solids and Structures, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01791894

U. Andreaus, M. Spagnuolo, T. Lekszycki, and S. R. Eugster, A ritz approach for the static analysis of planar pantographic structures modeled with nonlinear eulerbernoulli beams, Continuum Mechanics and Thermodynamics, p.121, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02453436

D. Steigmann and M. Faulkner, Variational theory for spatial rods, Journal of Elasticity, vol.33, issue.1, p.126, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00782186

A. Cazzani, M. Malagù, E. Turco, and F. Stochino, Constitutive models for strongly curved beams in the frame of isogeometric analysis, vol.21, p.182209, 2016.

A. Cazzani, M. Malagù, and E. Turco, Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches, Continuum Mechanics and Thermodynamics, vol.28, issue.1-2, p.139156, 2016.

M. Spagnuolo and U. Andreaus, A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-540 buckling, 2018.

H. Altenbach and V. Eremeyev, On the linear theory of micropolar plates, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für
URL : https://hal.archives-ouvertes.fr/hal-00824928

, Angewandte Mathematik und Mechanik, vol.89, issue.4, p.242256, 2009.

V. A. Eremeyev, L. P. Lebedev, and H. Altenbach, Foundations of micropolar mechanics, 2012.

H. Altenbach, M. Bîrsan, and V. A. Eremeyev, Generalized Continua from the Theory to Engineering Applications, p.179248, 2013.

V. A. Eremeyev, F. Isola, C. Boutin, and D. Steigmann, Linear pantographic sheets: existence and uniqueness of weak solutions, Journal of Elasticity, p.122, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01466979

L. Placidi and A. E. Dhaba, Semi-inverse method à la saint-venant for two-dimensional linear isotropic homogeneous second-gradient elasticity, p.555

, Mathematics and Mechanics of Solids, vol.22, issue.5, p.919937, 2017.

L. Placidi, U. Andreaus, A. Della-corte, and T. Lekszycki, Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coecients, Zeitschrift für angewandte Mathematik und Physik, vol.66, issue.6, p.36993725, 2015.

L. Placidi, U. Andreaus, and I. Giorgio, Identication of two-dimensional pantographic structure via a linear d4 orthotropic second gradient elastic model, Journal of Engineering Mathematics, p.121, 2016.

B. E. Abali, W. H. Müller, and V. A. Eremeyev, Strain gradient elasticity with geometric nonlinearities and its computational evaluation, p.565

, Advanced Materials and Modern Processes, vol.1, issue.1, p.4, 2015.

J. Niiranen, S. Khakalo, V. Balobanov, and A. H. Niemi, Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems, Computer Methods in Applied Mechanics and Engineering, vol.308, p.182, 2016.

S. Khakalo and J. Niiranen, Isogeometric analysis of higher-order gradient elasticity by user elements of a commercial nite element software, Computer-Aided Design, vol.82, p.154169, 2017.

V. Balobanov, J. Kiendl, S. Khakalo, and J. Niiranen, Kirchholove shells 575 within strain gradient elasticity: Weak and strong formulations and an h3-conforming isogeometric implementation, Computer Methods in Applied Mechanics and Engineering, vol.344, p.837857, 2019.

L. Placidi, L. Greco, S. Bucci, E. Turco, and N. Rizzi, A second gradient formulation for a 2d fabric sheet with inextensible bres, Zeitschrift für, p.580

, angewandte Mathematik und Physik, vol.67, issue.5, 2016.

E. Barchiesi, M. Spagnuolo, and L. Placidi, Mechanical metamaterials: a state of the art, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02453434

F. Isola, P. Seppecher, J. J. Alibert, T. Lekszycki, R. Grygoruk et al., , p.585

, Pantographic metamaterials: an example of mathematically driven design and of its technological challenges, Continuum Mechanics and Thermodynamics, vol.31, issue.4, p.851884, 2019.

M. Spagnuolo, P. Peyre, and C. Dupuy, Phenomenological aspects of quasiperfect pivots in metallic pantographic structures, Mechanics Research, vol.590
URL : https://hal.archives-ouvertes.fr/hal-02457782

, Communications, 2019.

F. Isola, E. Turco, A. Misra, Z. Vangelatos, C. Grigoropoulos et al., Forcedisplacement relationship in micro-metric pantographs: Experiments and numerical simulations, Comptes Rendus Mécanique, vol.347, issue.5, p.397405, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02269992

M. Golaszewski, R. Grygoruk, I. Giorgio, M. Laudato, and F. D. Cosmo, Metamaterials with relative displacements in their microstructure: technological challenges in 3d printing, experiments and numerical predictions, Continuum Mechanics and Thermodynamics, p.120, 2018.

H. Yang and W. H. Müller, Computation and experimental comparison of 600 the deformation behavior of pantographic structures with dierent microgeometry under shear and torsion, Journal of Theoretical and Applied Mechanics, vol.57, 2019.

H. Yang, G. Ganzosch, I. Giorgio, and B. E. Abali, , p.605

, Zeitschrift für angewandte Mathematik und Physik, vol.69, issue.4, p.105, 2018.

A. Misra and V. Singh, Micromechanical model for viscoelastic materials undergoing damage, Continuum Mechanics and Thermodynamics, p.116, 2013.

A. Misra and P. Poorsolhjouy, Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics, Mathematics and Mechanics of Solids, 2015.

A. Misra and V. Singh, Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model, Continuum 615 Mechanics and Thermodynamics, vol.27, issue.4-5, p.787, 2015.

M. Angelo, M. Spagnuolo, F. , A. Pfa, K. Hoschke et al., The macroscopic behavior of pantographic sheets depends mainly on their microstructure: experimental evidence and qualitative analysis of damage in metallic 620 specimens, Continuum Mechanics and Thermodynamics, p.123, 2019.

N. Engheta, R. Ziolkowski, and M. , Physics and Engineering Explorations, 2006.

A. Misra, T. Lekszycki, I. Giorgio, G. Ganzosch, W. H. Müller et al., Pantographic metamaterials show atypical poynting eect reversal

, Res. Commun, vol.89, p.610, 2018.

M. Spagnuolo, K. Barcz, A. Pfa, F. Isola, and P. Franciosi, Qualitative pivot damage analysis in aluminum printed pantographic sheets: numerics and experiments, Mechanics Research Communications, vol.83, p.4752, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01529257

E. Turco, A. Misra, M. Pawlikowski, F. Isola, and F. Hild, , p.630

, Piola-Hencky discrete models for pantographic sheets with pivots without deformation energy: Numerics and experiments, International Journal of Solids and Structures, vol.147, p.94109, 2018.

F. Isola, P. Seppecher, J. Alibert, T. Lekszycki, R. Grygoruk et al., , p.635

M. Golaszewski, N. Rizzi, C. Boutin, V. Eremeyev, A. Misra et al., Pantographic metamaterials: an example of mathematically driven 640 design and of its technological challenges, Continuum Mechanics and Thermodynamics, vol.31, issue.4, p.851884, 2019.

F. Isola, P. Seppecher, M. Spagnuolo, E. Barchiesi, F. Hild et al.,

A. Misra, M. Angelo, F. D'annibale, A. Bouterf, X. Pinelli et al., , p.650

P. Harrison, R. Drobnicki, L. Igumnov, F. Alzahrani, and T. Hayat, Advances in Pantographic Structures: Design, Manufacturing, Models, Experiments and Image Analyses, vol.31, p.12311282, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02156824

P. Seppecher, J. Alibert, and F. D. Isola, Linear elastic trusses leading 655 to continua with exotic mechanical interactions, Journal of Physics: Conference Series, vol.319, p.12018, 2011.

M. B. Buljac, M. Shakoor, P. Bouchard, T. Morgeneyer, and F. Hild, Numerical validation framework for micromechanical simulations based on synchrotron 3D imaging, Comput. Mech, vol.59, issue.3, p.419441, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01480980

M. Shakoor, A. Buljac, J. Neggers, F. Hild, T. Morgeneyer et al., On the choice of boundary conditions for micromechanical simulations based on 3D imaging, International Journal of Solids and Structures, vol.112, p.8396, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01471645

F. Hild, A. Misra, and F. , Multiscale DIC applied to Pantographic, vol.665

. Structures, Experimental Mechanics, 2020.

G. Broggiato, Adaptive image correlation technique for full-eld strain measurement, 12th Int. Conf, p.420421, 2004.

Y. Sun, J. Pang, C. Wong, and F. Su, Finite-element formulation for a digital 670 image correlation method, Appl. Optics, vol.44, issue.34, p.73577363, 2005.

G. Besnard, F. Hild, and S. Roux, Finite-element displacement elds analysis from digital images: Application to Portevin-Le Chatelier bands, Exp. Mech, vol.46, p.789803, 2006.

E. Barchiesi, Synthesis of second gradient architectured meta-675 materials: Micro-to-macro approaches, numerical investigations, additive manufacturing and experimental validation, 2019.

N. Auray, F. Isola, V. Eremeyev, A. Madeo, and G. Rosi, Analytical continuum mechanics à la HamiltonPiola least action principle for second 680 gradient continua and capillary uids, Mathematics and Mechanics of Solids, vol.20, issue.4, p.375417, 2015.

D. Cooper, A bias extension test, Textile Research Journal, vol.33, issue.4, p.315317, 1963.

P. Boisse, N. Hamila, E. Maldonado, A. Madeo, and G. Hivet, , p.685

F. , The bias-extension test for the analysis of in-plane shear properties of textile composite reinforcements and prepregs: a review, International Journal of Material Forming, vol.10, issue.4, p.473492, 2017.

M. Sutton, S. Mcneill, J. Helm, and Y. Chao, Advances in Two-Dimensional and Three-Dimensional Computer Vision, vol.77, p.690

M. Sutton, Computer vision-based, noncontacting deformation measurements in mechanics: A generational transformation

, Mech. Rev, vol.65, p.50802, 2013.

W. Peters and W. Ranson, Digital imaging techniques in experimental stress 695 analysis, vol.21, p.427431, 1982.

M. Sutton, W. Wolters, W. Peters, W. Ranson, and S. Mcneill, Determination of displacements using an improved digital correlation method

. Comp, , vol.1, p.133139, 1983.

T. Chu, W. Ranson, M. Sutton, and W. Peters, Applications of digital-image-700 correlation techniques to experimental mechanics, Exp. Mech, vol.3, issue.25, p.232244, 1985.

F. Hild and S. Roux, Comparison of local and global approaches to digital image correlation, Exp. Mech, vol.52, issue.9, p.15031519, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00750756

F. Hild and S. Roux, Digital image correlation, p.705

, Optical Methods for Solid Mechanics. A Full-Field Approach, p.183228, 2012.

M. Sutton, J. Orteu, and H. Schreier, Image correlation for shape, motion and deformation measurements: Basic Concepts, Theory and Applications, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01729219

H. Leclerc, J. Périé, S. Roux, and F. Hild, Integrated digital image correlation for the identication of mechanical properties

, MIRAGE 2009, vol.5496, p.161171, 2009.

J. Réthoré, S. Roux, and F. Hild, An extended and integrated digital image 715 correlation technique applied to the analysis fractured samples, Eur. J. Comput. Mech, vol.18, p.285306, 2009.

Z. Tomi£evi¢, F. Hild, and S. Roux, Mechanics-aided digital image correlation, J. Strain Analysis, vol.48, p.330343, 2013.

A. Tikhonov, V. Arsenin, Solutions of ill-posed problems, New, vol.720
URL : https://hal.archives-ouvertes.fr/hal-02283587

(. York and . Usa, , 1977.

D. Claire, F. Hild, and S. Roux, A nite element formulation to identify damage elds: The equilibrium gap method, Int. J. Num. Meth. Engng, vol.61, issue.2, p.189208, 2004.

A. Mendoza, J. Neggers, F. Hild, and S. Roux, Complete Mechanical, vol.725

, Computer Methods in Applied Mechanics and Engineering, vol.Correlation, p.27, 2019.

, Full-Field Measurements and Identication in Solid Mechanics, 2012.

A. Carpiuc-prisacari, M. Poncelet, K. Kazymyrenko, F. Hild, and H. Leclerc, Comparison between experimental and numerical results of mixed-mode crack propagation in concrete: Inuence of boundary conditions choice, Cement and Concrete Research, vol.100, p.329340, 2017.

F. Mathieu, H. Leclerc, F. Hild, and S. Roux, Estimation of elastoplastic 735 parameters via weighted FEMU and integrated-DIC, Exp. Mech, vol.55, issue.1, p.105119, 2015.

A. Tarantola, Inverse Problems Theory. Methods for Data Fitting and Model Parameter Estimation, 1987.