M. Ablowitz and P. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, lecture note series, 1991.
DOI : 10.1017/CBO9780511623998

M. Ablowitz and H. Segur, Solitons and the inverse scattering transform. SIAM, Philadelphia Aifantis EC (1992) On the role of gradients in the localization of deformation and fracture, Int J Engng Sci, vol.30, issue.10, pp.1279-1299, 1981.

E. Aifantis, Update on a class of gradient theories, Mechanics of Materials, vol.35, issue.3-6, pp.259-280, 2003.
DOI : 10.1016/S0167-6636(02)00278-8

E. Aifantis, Gradient material mechanics: Perspectives and Prospects, Acta Mechanica, vol.40, issue.4-5, pp.4-5999, 2014.
DOI : 10.1107/S0021889807016299

H. Askes and E. Aifantis, Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, International Journal of Solids and Structures, vol.48, issue.13, pp.1962-1990, 2011.
DOI : 10.1016/j.ijsolstr.2011.03.006

H. Askes and I. Gitman, Reducible and irreducible forms of stabilised gradient elasticity in dynamics, Mathematics and Mechanics of Complex Systems, vol.16, issue.1, pp.1-17, 2017.
DOI : 10.1016/S0165-2125(02)00037-9

A. Bertram, Gradient materials with internal constraints, Mathematics and Mechanics of Complex Systems, vol.27, issue.1, pp.1-15, 2016.
DOI : 10.1007/s10659-013-9435-4

URL : http://msp.org/memocs/2016/4-1/memocs-v4-n1-p01-s.pdf

C. Boutin, F. Isola, I. Giorgio, and L. Placidi, Linear pantographic sheets: Asymptotic micro-macro models identification, Mathematics and Mechanics of Complex Systems, vol.38, issue.2, pp.127-162, 2017.
DOI : 10.1061/(ASCE)NM.2153-5477.0000030

URL : https://hal.archives-ouvertes.fr/hal-01494280

S. Chandrasekhar, G. Chatzigeorgiou, F. Meraghni, and A. Javili, Liquid Crystals Generalized interfacial energy and size effects in composites, J Mech Phys Solids, vol.106, pp.257-282, 1977.

N. Cordero, S. Forest, and E. Busso, Second strain gradient elasticity of nano-objects, Journal of the Mechanics and Physics of Solids, vol.97, pp.92-124, 2016.
DOI : 10.1016/j.jmps.2015.07.012

URL : https://hal.archives-ouvertes.fr/hal-01424985

M. Agostino, I. Giorgio, L. Greco, A. Madeo, and P. Boisse, Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements, International Journal of Solids and Structures, vol.59, pp.1-17, 2015.
DOI : 10.1016/j.ijsolstr.2014.12.014

F. Isola and D. Steigmann, A two-dimensional gradient-elasticity theory for woven fabrics, J Elast, vol.118, issue.1, pp.113-125, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00997790

F. Isola, G. I. Pawlikowski, M. Rizzi, and N. , Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenisation, experimental and numerical examples of equilibrium, Proc Roy Soc London A, p.47220150790, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01228588

F. Dell-'isola, D. Steigmann, and A. Della-corte, Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response, Applied Mechanics Reviews, vol.67, issue.6, pp.60804-060804, 2016.
DOI : 10.1115/1.4032206

URL : https://hal.archives-ouvertes.fr/hal-01284511

F. Dell-'isola, D. Corte, A. Giorgio, and I. , Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives, Math Mech Solids, vol.22, issue.4, pp.852-872, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01256929

J. Eastham and J. Peterson, The finite element method in anisotropic sobolev spaces, Computers & Mathematics with Applications, vol.47, issue.10-11, pp.1775-1786, 2004.
DOI : 10.1016/j.camwa.2004.06.020

J. Engelbrecht and A. Berezovski, Reflections on mathematical models of deformation waves in elastic microstructured solids, Mathematics and Mechanics of Complex Systems, vol.58, issue.1, pp.43-82, 2015.
DOI : 10.2172/811184

URL : https://hal.archives-ouvertes.fr/hal-01152448

V. Eremeyev and W. Pietraszkiewicz, Local Symmetry Group in the General Theory of Elastic Shells, Journal of Elasticity, vol.386, issue.2, pp.125-152, 2006.
DOI : 10.1007/978-1-4612-5206-1

URL : https://hal.archives-ouvertes.fr/hal-00835610

V. Eremeyev and W. Pietraszkiewicz, Material symmetry group of the non-linear polar-elastic continuum, International Journal of Solids and Structures, vol.49, issue.14, pp.1993-2005, 2012.
DOI : 10.1016/j.ijsolstr.2012.04.007

URL : https://hal.archives-ouvertes.fr/hal-00835636

V. Eremeyev and W. Pietraszkiewicz, Material symmetry group and constitutive equations of micropolar anisotropic elastic solids, Mathematics and Mechanics of Solids, vol.65, issue.2, pp.210-221, 2016.
DOI : 10.1016/0020-7225(93)90054-X

V. Eremeyev, F. Isola, C. Boutin, and D. Steigmann, Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions, Journal of Elasticity, vol.68, issue.110, pp.10659-10676, 1007.
DOI : 10.1002/1521-3773(20000703)39:13<2255::AID-ANIE2255>3.0.CO;2-L

URL : https://hal.archives-ouvertes.fr/hal-01466979

S. Forest, N. Cordero, and E. Busso, First vs. second gradient of strain theory for capillarity effects in an elastic fluid at small length scales, Computational Materials Science, vol.50, issue.4, pp.1299-1304, 2011.
DOI : 10.1016/j.commatsci.2010.03.048

URL : https://hal.archives-ouvertes.fr/hal-00569981

G. P. De-gennes, J. Prost, I. Giorgio, N. Rizzi, and E. Turco, The Physics of Liquid Crystals Continuum modelling of pantographic sheets for outof-plane bifurcation and vibrational analysis, Proc Roy Soc A, vol.473, 1993.

G. Grimmett, Correlation inequalities for the Potts model, Mathematics and Mechanics of Complex Systems, vol.4, issue.3-4, pp.327-334, 2016.
DOI : 10.1007/BF01982711

P. Harrison, Modelling the forming mechanics of engineering fabrics using a mutually constrained pantographic beam and membrane mesh, Composites Part A: Applied Science and Manufacturing, vol.81, pp.145-157, 2016.
DOI : 10.1016/j.compositesa.2015.11.005

T. Healey and S. Krömer, Injective weak solutions in second-gradient nonlinear elasticity. ESAIM: Control, Optimisation and Calculus of Variations, pp.863-871, 2009.

B. Kadomtsev and V. Petviashvili, On the stability of solitary waves in weakly dispersing media, Sov Phys Doklady, vol.15, issue.6, pp.539-541, 1970.

L. Lebedev, M. Cloud, and V. Eremeyev, Tensor Analysis with Applications in Mechanics Global continuation in second-gradient nonlinear elasticity, World Scientific SIAM J Math Analysis, vol.38, issue.1, pp.103-115, 2006.

A. De-masi, I. Merola, E. Presutti, and Y. Vignaud, Potts Models in the Continuum. Uniqueness and??Exponential Decay in the Restricted Ensembles, Journal of Statistical Physics, vol.18, issue.5???6, pp.281-345, 2008.
DOI : 10.1007/s10955-008-9603-2

A. De-masi, I. Merola, E. Presutti, and Y. Vignaud, Coexistence of Ordered and Disordered Phases in??Potts??Models in the Continuum, Journal of Statistical Physics, vol.18, issue.4, pp.243-306, 2009.
DOI : 10.1007/s10955-008-9677-x

G. Maugin, Nonlinear Waves in Elastic Crystals Generalized continuum mechanics: what do we mean by that?, Mechanics of Generalized Continua. One Hundred Years after the Cosserats, pp.3-13, 1999.

G. Maugin, A Historical Perspective of Generalized Continuum Mechanics, Mechanics of Generalized Continua. From the Micromechanical Basics to Engineering Applications, pp.3-19, 2011.
DOI : 10.1007/978-3-642-19219-7_1

G. Maugin, Generalized Continuum Mechanics: Various Paths, pp.223-241, 2013.
DOI : 10.1007/978-94-007-6353-1_13

G. Maugin, Continuum Mechanics Through Ages. From the Renaissance to the Twentieth Century Cham Maugin GA (2017) Non-Classical Continuum Mechanics: A Dictionary Micro-structure in linear elasticity, Singapore Mindlin RD Arch Ration Mech Analysis, vol.16, issue.1, pp.51-78, 1964.

R. Mindlin and N. Eshel, On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures, vol.4, issue.1, pp.109-124, 1968.
DOI : 10.1016/0020-7683(68)90036-X

A. Misra and C. Chang, Effective elastic moduli of heterogeneous granular solids, International Journal of Solids and Structures, vol.30, issue.18, pp.2547-2566, 1993.
DOI : 10.1016/0020-7683(93)90165-4

P. Oswald, P. Peds, G. Gray, A. Goodby, and . Fukuda, Smectic and Columnar Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments. The Liquid Crystals Book Series, 2006.
DOI : 10.1201/9781420036343

L. Placidi, E. Barchiesi, E. Turco, and N. Rizzi, A review on 2D models for the description of pantographic fabrics, Zeitschrift f??r angewandte Mathematik und Physik, vol.38, issue.8, p.121, 2016.
DOI : 10.1016/j.compositesa.2007.04.009

L. Placidi, U. Andreaus, and G. I. , Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model, Journal of Engineering Mathematics, vol.97, issue.1, pp.1-21, 2017.
DOI : 10.1016/j.ijengsci.2015.10.003

J. Pouget, Non-linear lattice models: complex dynamics, pattern formation and aspects of chaos, Philosophical Magazine, vol.7, issue.33-35, pp.33-354067, 2005.
DOI : 10.1007/BF01557077

Y. Rahali, I. Giorgio, J. Ganghoffer, and F. Isola, Homogenization ?? la Piola produces second gradient continuum models for linear pantographic lattices, International Journal of Engineering Science, vol.97, pp.148-172, 2015.
DOI : 10.1016/j.ijengsci.2015.10.003

URL : https://hal.archives-ouvertes.fr/hal-01223794

J. Simmonds, A Brief on Tensor Analysis, 1994.

J. Soubestre and C. Boutin, Non-local dynamic behavior of linear fiber reinforced materials, Mechanics of Materials, vol.55, pp.16-32, 2012.
DOI : 10.1016/j.mechmat.2012.06.005

URL : https://hal.archives-ouvertes.fr/hal-00943749

S. Timoshenko and S. Woinowsky-krieger, Theory of Plates and Shells Elastic materials with couple-stresses, Arch Ration Mech Analysis, vol.11, issue.1, pp.385-414, 1962.

H. Wood and J. Morton, Onsager's pancake approximation for the fluid dynamics of a gas centrifuge, Journal of Fluid Mechanics, vol.78, issue.01, pp.1-31, 1980.
DOI : 10.1017/S0022112080001504