J. J. Alibert and A. Della-corte, Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof, Zeitschrift f??r angewandte Mathematik und Physik, vol.80, issue.4, pp.2855-2870, 2015.
DOI : 10.1007/s00033-015-0526-x

URL : https://hal.archives-ouvertes.fr/hal-01279491

J. J. Alibert and P. , Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients, Mathematics and Mechanics of Solids, vol.8, issue.1, pp.51-73, 2003.
DOI : 10.1177/1081286503008001658

URL : https://hal.archives-ouvertes.fr/hal-00497327

H. Altenbach and V. A. Eremeyev, On the linear theory of micropolar plates, ZAMM, vol.12, issue.1, pp.242-256, 2009.
DOI : 10.1002/zamm.200800207

URL : https://hal.archives-ouvertes.fr/hal-00824928

H. Altenbach, M. Bîrsan, and V. A. Eremeyev, Generalized Continua from the Theory to Engineering Applications, 2013, chap. Cosserat-Type Rods, pp.179-248
DOI : 10.1007/978-3-7091-1371-4

J. Altenbach, H. Altenbach, and V. A. Eremeyev, On generalized Cosserat-type theories of plates and shells: a short review and bibliography, Archive of Applied Mechanics, vol.31, issue.3, pp.73-92, 2009.
DOI : 10.1007/s00419-009-0365-3

URL : https://hal.archives-ouvertes.fr/hal-00827365

H. Aminpour and N. Rizzi, On the continuum modelling of carbon nano tubes, 2015.

H. Aminpour and N. Rizzi, A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis, Mathematics and Mechanics of Solids, vol.21, issue.2, pp.168-181, 2016.
DOI : 10.1177/1081286515577037

H. Aminpour, N. Rizzi, and G. Salerno, A one-dimensional beam model for single-wall carbon nano tube column buckling, 2014.

H. Aminpour and N. Rizzi, On the Modelling of Carbon Nano Tubes as Generalized Continua, pp.15-35, 2016.
DOI : 10.1007/978-3-319-31721-2_2

U. Andreaus, I. Giorgio, and T. Lekszycki, A 2-D continuum model of a mixture of bone tissue and bio-resorbable material for simulating mass density redistribution under load slowly variable in time, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.29, issue.11, pp.978-1000, 2014.
DOI : 10.1002/zamm.201200182

URL : https://hal.archives-ouvertes.fr/hal-00842604

U. Andreaus, M. Colloca, and D. Iacoviello, Optimal bone density distributions: Numerical analysis of the osteocyte spatial influence in bone remodeling, Computer Methods and Programs in Biomedicine, vol.113, issue.1, pp.80-91, 2014.
DOI : 10.1016/j.cmpb.2013.09.002

A. Skii and V. I. Ponomarev, Fundamentals of general topology: problems and exercises, 2001.

. Morrow, Remark that atrapon " road, trail, track " here takes the more specific sense of " short cut " . The Latin translation is instead by Francesco Barozzi, 1560) Copyright line will be provided by the publisher, p.57, 1970.

N. Auffray, F. Dell-'isola, V. A. Ermeyev, and G. Rosi, Analytical continuum mechanics a la Hamilton-Piola least action principle for second gradient continua and capillary fluids, Mathematics and Mechanics of Solids, vol.20, issue.4, pp.375-417, 2013.
DOI : 10.1177/1081286513497616

URL : https://hal.archives-ouvertes.fr/hal-00836085

A. Berezovski, I. Giorgio, and A. Della-corte, Interfaces in micromorphic materials: Wave transmission and reflection with numerical simulations, Mathematics and Mechanics of Solids, vol.21, issue.1, pp.37-51, 2016.
DOI : 10.1177/1081286515572244

URL : https://hal.archives-ouvertes.fr/hal-01194376

A. M. Bersani, I. Giorgio, and G. Tomassetti, Buckling of an elastic hemispherical shell with an obstacle, Continuum Mechanics and Thermodynamics, vol.38, issue.2-4, pp.443-467, 2012.
DOI : 10.1007/s00161-012-0273-6

A. Braides and M. S. Gelli, Continuum Limits of Discrete Systems without Convexity Hypotheses, Mathematics and Mechanics of Solids, vol.7, issue.1, pp.41-66, 2002.
DOI : 10.1177/1081286502007001229

A. Carcaterra, F. Dell-'isola, R. Esposito, and M. Pulvirenti, Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials, Archive for Rational Mechanics and Analysis, vol.11, issue.6, pp.1239-1262, 2015.
DOI : 10.1007/s00205-015-0879-5

URL : https://hal.archives-ouvertes.fr/hal-01155474

A. Cauchy, De la pression ou tension dans un corps solide, pp.60-78, 1827.
DOI : 10.1017/CBO9780511702662.007

C. Cercignani and L. Boltzmann, The Man Who Trusted Atoms, OUP Oxford, 2006.

F. Dell-'isola, U. Andreaus, and L. Placidi, 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. Solid, vol.20, issue.8, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00869677

F. Isola, A. Della-corte, and I. Giorgio, Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives, Math. Mech. Solid, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01256929

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, p.4722185, 2016.

F. Isola, A. Madeo, and P. Seppecher, Cauchy tetrahedron argument applied to higher contact interactions, Arch. Ration. Mech. An, vol.219, issue.3, pp.1305-1341, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01060548

F. Dell-'isola, G. Maier, U. Perego, U. Andreaus, R. Esposito et al., The complete works of Gabrio Piola: Volume I: Commented English Translation, 38 in Advanced Structured Materials, 2014.

F. Dell-'isola, P. Seppecher, and A. Della-corte, The postulations à la D'Alembert and à la Cauchy for higher gradient continuum theories are equivalent: a review of existing results, pp.471-2183, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01226235

F. Isola and P. Seppecher, hypertractions and hyperstresses convey the same mechanical information Continuum Mech, Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories, pp.163-176, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00495800

F. Isola and P. Seppecher, Edge contact forces and quasi-balanced power, Meccanica, vol.32, issue.1, pp.33-52, 1997.
DOI : 10.1023/A:1004214032721

URL : https://hal.archives-ouvertes.fr/hal-00494641

F. Dell-'isola, P. Seppecher, and A. Madeo, How contact interactions may depend on the shape of Cauchy cuts in nth gradient continua: approach " à la D'Alembert, Z. Angew. Math. Phys, vol.63, issue.6, pp.1119-1141, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00662376

V. A. Eremeyev and L. P. Lebedev, Existence theorems in the linear theory of micropolar shells, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.85, issue.2, pp.468-476, 2011.
DOI : 10.1002/zamm.201000204

URL : https://hal.archives-ouvertes.fr/hal-00831156

V. A. Eremeyev and H. Altenbach, Equilibrium of a second-gradient fluid and an elastic solid with surface stresses, Meccanica, vol.95, issue.2069, pp.2635-2643, 2013.
DOI : 10.1007/s11012-013-9851-3

E. Fried and M. E. Gurtin, Tractions, Balances, and Boundary Conditions for Nonsimple Materials with Application to Liquid Flow at Small-Length Scales, Archive for Rational Mechanics and Analysis, vol.34, issue.3, pp.513-554, 2006.
DOI : 10.1007/s00205-006-0015-7

R. N. Gabrieles, A one-dimensional nonlinear thin walled beam model derived from koiter shell theory, 2014.

N. Gabriele, V. Rizzi, and . Varano, On the imperfection sensitivity of thin-walled frames, Proceedings of the Eleventh International Conference on Computational Structures Technology, 2012.

N. Gabriele, V. Rizzi, and . Varano, A 1D nonlinear TWB model accounting for in plane cross-section deformation, International Journal of Solids and Structures, vol.94, issue.95, pp.94-95, 2016.
DOI : 10.1016/j.ijsolstr.2016.04.017

P. Germain, La méthodes des puissances virtuelles en mécanique des milieux continus -1ère partie, théorie du second gradient, Journal de Mécanique, vol.12, pp.235-274, 1973.

P. Germain, The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure, SIAM Journal on Applied Mathematics, vol.25, issue.3, pp.556-575, 1973.
DOI : 10.1137/0125053

P. Germain, Functional concepts in continuum mechanics, Meccanica, vol.33, issue.5, pp.433-444, 1998.
DOI : 10.1023/A:1004304224398

I. Giorgio, U. Andreaus, D. Scerrato, and P. Braidotti, Modeling of a non-local stimulus for bone remodeling process under cyclic load: Application to a dental implant using a bioresorbable porous material, Mathematics and Mechanics of Solids, 2016.
DOI : 10.1177/1081286516644867

URL : https://hal.archives-ouvertes.fr/hal-01306436

I. Giorgio, U. Andreaus, T. Lekszycki, and A. Della-corte, The influence of different geometries of matrix/scaffold on the remodeling process of a bone and bioresorbable material mixture with voids, Mathematics and Mechanics of Solids, 2015.
DOI : 10.1177/1081286515616052

I. Giorgio, U. Andreaus, and A. Madeo, The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids, Continuum Mechanics and Thermodynamics, vol.71, issue.1, pp.21-40, 2014.
DOI : 10.1007/s00161-014-0397-y

URL : https://hal.archives-ouvertes.fr/hal-01094868

I. Giorgio and D. Scerrato, Multi-scale concrete model with rate-dependent internal friction, Eur, J. Environ. Civil Eng. pp, pp.1-19, 2016.

C. Glocker, Set-Valued Force Laws, Dynamics of Non-Smooth Systems, Lecture Notes in Applied Mechanics, vol.1, 2001.

A. E. Green and R. S. Rivlin, Multipolar continuum mechanics, Arch. Ration. Mech. An, vol.17, issue.2, pp.113-147, 1964.
DOI : 10.1007/bf00253051

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.469.5709

M. E. Gurtin, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, Journal of the Mechanics and Physics of Solids, vol.50, issue.1, pp.5-32, 2002.
DOI : 10.1016/S0022-5096(01)00104-1

T. Heath, The Method of Archimedes, Recently Discovered by Heiberg: A Supplement to the Works of Archimedes, 2007.

T. S. Kuhn, The Structure of Scientific Revolutions, 1962.

L. P. Lebedev, M. J. Cloud, and V. A. Eremeyev, Tensor analysis with applications in mechanics, 2010.
DOI : 10.1142/7826

L. P. Lebedev, M. J. Cloud, and V. A. Eremeyev, Advanced Engineering Analysis: The Calculus of Variations and Functional Analysis with Applications in Mechanics, 2012.
DOI : 10.1142/8401

T. Lekszycki and F. , A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.14, issue.12, pp.426-444, 2012.
DOI : 10.1002/zamm.201100082

URL : https://hal.archives-ouvertes.fr/hal-00935587

A. Luongo and D. Zulli, A non-linear one-dimensional model of cross-deformable tubular beam, 4th Canadian Conference on Non-linear Solid Mechanics, pp.33-42, 2014.
DOI : 10.1016/j.ijnonlinmec.2014.03.008

E. Mach, The Science of Mechanics: A Critical and Historical Account of Its Development (Open court publishing Company, 1919.
DOI : 10.1017/CBO9781107338401

A. Madeo, M. Ferretti, F. Isola, and P. Boisse, Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks, Zeitschrift f??r angewandte Mathematik und Physik, vol.6, issue.6, pp.2041-2060, 2015.
DOI : 10.1007/s00033-015-0496-z

URL : https://hal.archives-ouvertes.fr/hal-01144230

G. A. Maugin and A. V. Metrikine, Mechanics of generalized continua, Advances in mechanics and mathematics 21, 2010.

H. Meissner, Topics in operator theory: Ernst D. Hellinger memorial volume, Operator theory, advances and applications, pp.43-46, 1990.

A. Misra and P. Poorsolhjouy, Granular micromechanics based micromorphic model predicts frequency band gaps, Continuum Mechanics and Thermodynamics, vol.80, issue.3, pp.215-234, 2015.
DOI : 10.1007/s00161-015-0420-y

A. Misra and P. Poorsolhjouy, Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics, Mathematics and Mechanics of Solids, 2015.
DOI : 10.1177/1081286515576821

A. Misra and P. Poorsolhjouy, Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics, Mathematics and Mechanics of Complex Systems, vol.3, issue.3, pp.285-308, 2015.
DOI : 10.2140/memocs.2015.3.285

A. Misra and P. Poorsolhjouy, Elastic Behavior of 2D Grain Packing Modeled as Micromorphic Media Based on Granular Micromechanics, Journal of Engineering Mechanics, vol.143, issue.1, 2016.
DOI : 10.1061/(ASCE)EM.1943-7889.0001060

A. W. Moore and N. , The Method of Exhaustion as a Model for the Calculus, pp.139-148, 1993.
DOI : 10.1007/978-94-011-1662-6_12

R. Netz and W. Noel, The Archimedes Codex: Revealing The Secrets Of The World's Greatest Palimpsest, Hachette UK, 2011.

M. Owen and I. Gildenhard, Tacitus Annals 15, Latin Text, Study Aids with Vocabulary, and Commentary, pp.20-23, 2013.

L. Pagnini, A. Freda, and G. Piccardo, Uncertainties in the evaluation of one degree-of-freedom galloping onset, European Journal of Environmental and Civil Engineering, vol.80, issue.4, pp.1-21, 2016.
DOI : 10.1016/j.ijengsci.2013.11.008

G. Peano, De latino sine flexione. lingua auxiliare internationale, Revista de Mathematica, vol.8, 1903.

G. Piccardo, F. Tubino, and A. Luongo, A shear???shear torsional beam model for nonlinear aeroelastic analysis of tower buildings, Zeitschrift f??r angewandte Mathematik und Physik, vol.99, issue.6???7, pp.1895-1913, 2014.
DOI : 10.1007/s00033-014-0456-z

G. Piccardo, G. Ranzi, and A. Luongo, A direct approach for the evaluation of the conventional modes within the GBT formulation , Thin Wall, Struct, vol.74, pp.133-145, 2014.

M. Pignataro, G. Ruta, N. Rizzi, and V. Varano, Effects of Warping Constraints and Lateral Restraint on the Buckling of Thin-Walled Frames, Volume 10: Mechanical Systems and Control, Parts A and B, pp.803-810, 2009.
DOI : 10.1115/IMECE2009-12254

L. Placidi, U. Andreaus, and I. Giorgio, Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model, Journal of Engineering Mathematics, vol.97, issue.1, 2016.
DOI : 10.1177/1081286515616043

L. Placidi, I. Giorgio, A. Della-corte, and D. Scerrato, : A review of presentations and discussions, Mathematics and Mechanics of Solids, vol.123, issue.3, 2015.
DOI : 10.1016/j.jsv.2011.01.016

F. Pradel and K. Sab, Homogenization of discrete media, Le Journal de Physique IV, vol.08, issue.PR8, pp.8-317, 1998.
DOI : 10.1051/jp4:1998839

M. M. Ricci and T. Levi-civita, M???thodes de calcul diff???rentiel absolu et leurs applications, Méthodes de calcul différentiel absolu et leurs applications, pp.125-201, 1901.
DOI : 10.1007/BF01454201

N. Rizzi and V. Varano, On the postbuckling analysis of thin-walled frames, Thirteenth international conference on civil, structural and environmental engineering computing, 2011.

N. L. Rizzi, V. Varano, and S. Gabriele, Initial postbuckling behavior of thin-walled frames under mode interaction, Thin Wall, Struct, vol.68, pp.124-134, 2013.

L. Russo, The forgotten revolution: How science was born in 300 BC and why it had to be reborn, 2004.
DOI : 10.1007/978-3-642-18904-3

G. Ruta, M. Pignataro, and N. Rizzi, A direct one-dimensional beam model for the flexural-torsional buckling of thin-walled beams, Journal of Mechanics of Materials and Structures, vol.1, issue.8, pp.1479-1496, 2006.
DOI : 10.2140/jomms.2006.1.1479

J. Salençon, Handbook of Continuum Mechanics: General Concepts, Thermoelasticity, Physics and Astronomy Online Library, 2001.
DOI : 10.1007/978-3-642-56542-7

J. Salençon, Mécanique des milieux continus: Concepts généraux, Mécanique des milieux continus, 2005.

D. Scerrato, I. Giorgio, and N. L. Rizzi, Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations, Zeitschrift f??r angewandte Mathematik und Physik, vol.64, issue.1, pp.1-19, 2016.
DOI : 10.1142/S0219455415400076

URL : https://hal.archives-ouvertes.fr/hal-01305927

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 - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.1, issue.2, 2016.
DOI : 10.1002/zamm.201600066

P. Seppecher and J. J. , Linear elastic trusses leading to continua with exotic mechanical interactions, Journal of Physics: Conference Series, vol.319, issue.1, p.12018, 2011.
DOI : 10.1088/1742-6596/319/1/012018

URL : https://hal.archives-ouvertes.fr/hal-00630098

G. Taig, G. Ranzi, and F. D. Annibale, An unconstrained dynamic approach for the Generalised Beam Theory, Continuum Mechanics and Thermodynamics, vol.46, issue.5, pp.879-904, 2014.
DOI : 10.1007/s00161-014-0358-5

R. A. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, vol.38, issue.1, pp.385-414, 1962.
DOI : 10.1007/BF00253945

URL : https://hal.archives-ouvertes.fr/hal-00852443

C. Truesdell and R. Toupin, The Classical Field Theories, Encyclopedia of Physics, vol.1, 1960.
DOI : 10.1007/978-3-642-45943-6_2

F. Waquet, J. Howe, . Latin, and . Or, The Empire of a Sign: From the Sixteenth to the Twentieth Centuries, Translated from the French by John Howe, 2002.

T. N. Winter, The mechanical problems in the corpus of aristotle, Faculty Publications, Classics and Religious Studies Department p, p.68, 2007.

Y. Yang and A. Misra, Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity, International Journal of Solids and Structures, vol.49, issue.18, pp.2500-2514, 2012.
DOI : 10.1016/j.ijsolstr.2012.05.024