L. Euler and C. Carathéodory, Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes Sive Solutio Problematis Isoperimetrici Latissimo Sensu Accepti, vol.1, 1952.

D. Bernoulli, The 26th letter to Euler, Corresp. Math. Phys, vol.2, p.1742, 1843.

J. Bernoulli, Quadratura curvae, e cujus evolutione describitur inflexae laminae curvatura. Die Werke von Jakob Bernoulli 1691, pp.223-227, 1692.

S. S. Antman and M. Renardy, Nonlinear problems of elasticity, SIAM Rev, vol.37, issue.4, p.637, 1995.

D. J. Steigmann, Finite Elasticity Theory, 2017.

K. E. Bisshopp and D. C. Drucker, Large deflection of cantilever beams, Q. Appl. Math, vol.3, issue.3, pp.272-275, 1945.

D. G. Fertis, Nonlinear Structural Engineering, 2006.

P. Ladevèze, Nonlinear Computational Structural Mechanics: New Approaches and Non-incremental Methods of Calculation, 2012.

D. J. Steigmann, Invariants of the stretch tensors and their application to finite elasticity theory, Math. Mech. Solids, vol.7, issue.4, pp.393-404, 2002.

M. Nizette and A. Goriely, Towards a classification of Euler-Kirchhoff filaments, J. Math. Phys, vol.40, issue.6, pp.2830-2866, 1999.

A. Goriely, M. Nizette, and M. Tabor, On the dynamics of elastic strips, J. Nonlinear Sci, vol.11, issue.1, pp.3-45, 2001.

A. Hamdouni and O. Millet, An asymptotic non-linear model for thin-walled rods with strongly curved open cross-section, Int. J. Non Linear Mech, vol.41, issue.3, pp.396-416, 2006.

A. Luongo and D. Zulli, Mathematical Models of Beams and Cables, 2013.

G. Piccardo, F. D'annibale, and A. Luongo, A perturbation approach to the nonlinear generalized beam theory, 4th Canadian Conference on Nonlinear Solid Mechanics, 2013.

G. Taig, G. Ranzi, and F. D'annibale, An unconstrained dynamic approach for the generalised beam theory, Contin. Mech. Thermodyn, vol.27, p.879, 2015.

G. Piccardo, G. Ranzi, and A. Luongo, A complete dynamic approach to the generalized beam theory cross-section analysis including extension and shear modes, Math. Mech. Solids, vol.19, issue.8, pp.900-924, 2014.

A. Della-corte, F. Dell'isola, R. Esposito, and M. Pulvirenti, Equilibria of a clamped euler beam (elastica) with distributed load: large deformations, Mathem. Models Methods Appl. Sci, vol.27, pp.1-31, 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.

H. Bungartz and M. Schäfer, Fluid-Structure Interaction: Modelling, Simulation, Optimisation, vol.53, 2006.

Y. Bazilevs, K. Takizawa, and T. E. Tezduyar, Computational Fluid-Structure Interaction: Methods and Applications, 2013.

G. Solaria, L. C. Pagnini, and G. Piccardo, A numerical algorithm for the aerodynamic identification of structures, J. Wind Eng. Ind. Aerodyn, vol.69, pp.719-730, 1997.

L. C. Pagnini, A numerical approach for the evaluation of wind-induced effects on inclined, slender structural elements, Eur. J. Environ. Civ. Eng, vol.21, pp.1-20, 2016.

E. Liberge, M. Pomarede, and A. Hamdouni, Reduced-order modelling by pod-multiphase approach for fluid-structure interaction, Eur. J. Comput. Mech. Revue Eur. Méc. Numér, vol.19, issue.1-3, pp.41-52, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00536642

C. Pideri and P. Seppecher, A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium, Contin. Mech. Thermodyn, vol.9, issue.5, pp.241-257, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00527291

S. Forest and R. Sievert, Nonlinear microstrain theories, Int. J. Solids Struct, vol.43, issue.24, pp.7224-7245, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00136739

A. A. Atai and D. J. Steigmann, On the nonlinear mechanics of discrete networks, Arch. Appl. Mech, vol.67, issue.5, pp.303-319, 1997.

C. Boutin, I. Giorgio, and L. Placidi, Linear pantographic sheets: asymptotic micro-macro models identification, Math. Mech. Complex Syst, vol.5, issue.2, pp.127-162, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01494280

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, issue.1, pp.1-21, 2017.

D. Scerrato, I. Giorgio, and N. L. Rizzi, Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations, Z. Angew. Math. Phys, vol.67, issue.3, p.53, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01305927

E. Turco, M. Golaszewski, A. Cazzani, and 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, vol.76, pp.51-56, 2016.

E. Turco, M. Golaszewski, I. Giorgio, and F. D'annibale, Pantographic lattices with non-orthogonal fibres: experiments and their numerical simulations, Compos. Part B Eng, vol.118, pp.1-14, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01443679

E. Turco, M. Golaszewski, I. Giorgio, and L. Placidi, Can a Hencky-type model predict the mechanical behaviour of pantographic lattices? In: Dell'lsola, F. (ed.) Mathematical Modelling in Solid Mechanics, pp.285-311, 2017.

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

S. Kalpakjian, K. S. Vijai-sekar, and S. R. Schmid, , 2014.

A. Misra, L. Placidi, and D. Scerrato, A review of presentations and discussions of the workshop computational mechanics of generalized continua and applications to materials with microstructure that was held in Catania 29-31, Math. Mech. Solids, vol.9, pp.1891-1904, 2015.

M. Nase, M. Rennert, K. Naumenko, and V. A. Eremeyev, Identifying tractionseparation behavior of self-adhesive polymeric films from in situ digital images under t-peeling, J. Mech. Phys. Solids, vol.91, pp.40-55, 2016.

M. G. Faulkner, A. W. Lipsett, and V. Tam, On the use of a segmental shooting technique for multiple solutions of planar elastica problems, Comput. Methods Appl. Mech. Eng, vol.110, issue.3-4, pp.221-236, 1993.

D. W. Raboud, M. G. Faulkner, and A. W. Lipsett, Multiple three-dimensional equilibrium solutions for cantilever beams loaded by dead tip and uniform distributed loads, Int. J. Non Linear Mech, vol.31, issue.3, pp.297-311, 1996.

S. P. Timoshenko and . Lxvi, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Lond. Edinb. Dublin Philos. Mag. J. Sci, vol.41, issue.245, pp.744-746, 1921.

S. P. Timoshenko, On the transverse vibrations of bars of uniform cross-section, Lond. Edinb. Dublin Philos. Mag. J. Sci, vol.43, issue.253, pp.125-131, 1922.

E. Cosserat and F. Cosserat, Théorie des corps déformables. A. Hermann et fils, 1909.

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

J. Altenbach, H. Altenbach, and V. A. Eremeyev, On generalized cosserat-type theories of plates and shells: a short review and bibliography, Arch. Appl. Mech, vol.80, issue.1, pp.73-92, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00827365

V. Balobanov and J. Niiranen, Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity, Comput. Methods Appl. Mech. Eng, vol.339, pp.137-159, 2018.

L. Beirao-da-veiga, T. J. Hughes, J. Kiendl, C. Lovadina, J. Niiranen et al., A locking-free model for Reissner-Mindlin plates: analysis and isogeometric implementation via nurbs and triangular nurps, Math. Models Methods Appl. Sci, vol.25, pp.1519-1551, 2015.

G. Capobianco and S. R. Eugster, Time finite element based Moreau-type integrators, Int. J. Numer. Methods Eng, vol.114, issue.3, pp.215-231, 2018.

S. R. Eugster, C. Hesch, P. Betsch, and C. Glocker, Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates, Int. J. Numer. Methods Eng, vol.97, issue.2, pp.111-129, 2014.

S. R. Eugster, Geometric Continuum Mechanics and Induced Beam Theories, vol.75, 2015.

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, issue.2, p.42, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02185404

M. Bîrsan, H. Altenbach, T. Sadowski, V. A. Eremeyev, and D. Pietras, Deformation analysis of functionally graded beams by the direct approach, Compos. Part B Eng, vol.43, pp.1315-1328, 2012.

J. Chró?cielewski, R. Schmidt, and V. A. Eremeyev, Nonlinear finite element modeling of vibration control of plane rodtype structural members with integrated piezoelectric patches, Contin. Mech. Thermodyn, vol.31, pp.1-42, 2018.

A. Javili, A. Mcbride, and P. Steinmann, Thermomechanics of solids with lower-dimensional energetics: on the importance of surface, interface, and curve structures at the nanoscale. a unifying review, Appl. Mech. Rev, vol.65, p.10802, 2013.

A. Della-corte, A. Battista, F. Isola, and P. Seppecher-m&mocs,