N. Auffray, F. Isola, . Eremeyev, and . Va, Analytical continuum mechanics á la Hamilton?Piola least action principle for second gradient continua and capillary fluids Math Mech Solid Epub online ahead of print 28 DOI: 101177/1081286513497616 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 [4] Rivlin, RS. Generalized mechanics of continuous media Multipolar continuum mechanics Simple force and stress multipoles Directors and multipolar displacements in continuum mechanics Micro-materials and multipolar continuum mechanics Plane traction problems for inextensible networks, Math Mech Solid. Arch Rat Mech Anal Arch Rat Mech Anal Int J Eng Sci Int J Eng Sci J Mech Appl Math, vol.20, issue.344, pp.887-928, 1964.

M. Hilgers and A. Pipkin, ELASTIC SHEETS WITH BENDING STIFFNESS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.45, issue.1, pp.57-75, 1992.
DOI : 10.1093/qjmam/45.1.57

R. Mindlin, Influence of couple-stresses on stress concentrations, Experimental Mechanics, vol.3, issue.1, pp.1-7, 1963.
DOI : 10.1007/BF02327219

R. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, vol.16, issue.1, pp.51-78, 1964.
DOI : 10.1007/BF00248490

R. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, vol.1, issue.4, pp.417-438, 1965.
DOI : 10.1016/0020-7683(65)90006-5

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

R. Mindlin, Polarization gradient in elastic dielectrics, International Journal of Solids and Structures, vol.4, issue.6, pp.637-642, 1968.
DOI : 10.1016/0020-7683(68)90079-6

R. Mindlin, Theories of Elastic Continua and Crystal Lattice Theories, 1968.
DOI : 10.1007/978-3-662-30257-6_38

R. Toupin, Theories of elasticity with couple-stress, Archive for Rational Mechanics and Analysis, vol.17, issue.2, pp.85-112, 1964.
DOI : 10.1007/BF00253050
URL : https://hal.archives-ouvertes.fr/hal-00853382

P. Casal, Theory of second gradient and capillarity, CR Hebd Sean Acad Sci Ser A, vol.274, issue.22, pp.1571-1574, 1972.

P. Casal and H. Gouin, Relation entre l'équation de l'énergie et l'équation du mouvement en théorie de Korteweg de la capillarité, CR Hebd Sean Acad Sci Ser, vol.2, issue.3007, pp.231-234, 1985.

P. Casal and H. Gouin, Invariance properties of inviscid fluids of grade n (eds) PDEs and continuum models of phase transitions, pp.85-98, 1989.

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, La méthode des puissances virtuelles en mécanique des milieux continus. Premiére partie. Théorie du second gradient, J Méc, vol.12, pp.235-274, 1973.

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

L. Landau and E. Lifshits, The classical theory of fields, 1975.

L. Landau and E. Lifshits, Quantum mechanics: Non-relativistic theory. Translation from the Russian by, 1965.

L. Sedov, MATHEMATICAL METHODS FOR CONSTRUCTING NEW MODELS OF CONTINUOUS MEDIA, Russian Mathematical Surveys, vol.20, issue.5, pp.123-182, 1965.
DOI : 10.1070/RM1965v020n05ABEH001191

. Camar-eddine and P. Seppecher, Determination of the Closure of the Set of Elasticity Functionals, Archive for Rational Mechanics and Analysis, vol.170, issue.3, pp.211-245, 2003.
DOI : 10.1007/s00205-003-0272-7

C. Pideri and P. Seppecher, A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium, Continuum Mechanics and Thermodynamics, vol.9, issue.5, pp.241-257, 1997.
DOI : 10.1007/s001610050069
URL : https://hal.archives-ouvertes.fr/hal-00527291

C. Boutin, S. Hans, and C. Chesnais, Generalized beams and continua: Dynamics of reticulated structures Mechanics of generalized continua, pp.131-141, 2010.

A. Carcaterra, F. Isola, and R. Esposito, 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

J. Salençon, Handbook of Continuum Mechanics: General Concepts, Thermoelasticity, Applied Mechanics Reviews, vol.55, issue.3, 2001.
DOI : 10.1115/1.1470668

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

K. Popper, The logic of scientific discovery

G. Galilei, Il saggiatore (The assayer) In: Discoveries and opinions of Galileo, 1957.

G. Piola, Intorno alle equazioni fondamentali del movimento dei corpi qualsivogliono, considerati secondo naturale loro forma e costituzione (1845) Memorie di matematica e di fisica della Società Italiana delle Scienze, pp.1-186

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

L. Sedov, Models of continuous media with internal degrees of freedom, Journal of Applied Mathematics and Mechanics, vol.32, issue.5, pp.771-785, 1968.
DOI : 10.1016/0021-8928(68)90001-4

L. Sedov, Variational methods of constructing models of continuous media Irreversible aspects of continuum mechanics and transfer of physical characteristics in moving fluids, pp.346-358, 1968.

C. Truesdell, Essays in the history of mechanics, 1968.

R. Toupin, Theory of elasticity with couple stresses, Arch Rat Mech Anal, vol.17, pp.85-112, 1964.

R. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, vol.38, issue.1, pp.385-413, 1962.
DOI : 10.1007/BF00253945
URL : https://hal.archives-ouvertes.fr/hal-00852443

F. Dell-'isola and P. Seppecher, The relationship between edge contact forces, double forces and interstitial working allowed by the principle of virtual power, CR Acad Sci Ser IIB, vol.321, pp.303-308, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00494505

F. Dell-'isola and P. Seppecher, Edge contact forces and quasi-balanced power, Mec, vol.32, issue.1, pp.33-52, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00494641

L. Schwartz, Théorie des distributions, Act Sci Indus Inst Math Uni Stras, vol.1, issue.2, 1966.

W. Rudin, Functional analysis (International Series in Pure and Applied Mathematics), 1991.

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

G. Piola, Sull'applicazione de' principj della meccanica analitica del Lagrange ai principali problemi, p.1825

E. Cosserat, C. , and F. , Sur la th??orie de l'??lasticit??. Premier m??moire, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.10, issue.3-4, pp.1-116, 1896.
DOI : 10.5802/afst.130

E. Cosserat, C. , and F. , Théorie des corps déformables Paris: Librairie Scientifique. A. Hermann et Fils (English translation by Delphenich, D 2007), reprint 2009 by Hermann Librairie Scientifique. Paris: Scientific Library A. Hermann and Sons. Available at: http://www.uni-due.de/?hm0014, Cosserat_files/Cosserat09_eng.pdf [55] Green, AE, and Rivlin, RS. Multipolar continuum mechanics, pp.113-147, 1964.

R. Rivlin, The formulation of theories in generalized continuum mechanics and their physical significance, Symp Math, vol.1, pp.357-373, 1969.

W. Noll, The foundations of classical mechanics in the light of recent advances in continuum mechanics. The Axiomatic Method, with Special Reference to Geometry and Physics, Studies in Logic and the Foundations of Mathematics, pp.266-281, 1957.

W. Noll and E. Virga, On edge interactions and surface tension, Archive for Rational Mechanics and Analysis, vol.17, issue.1, pp.1-31, 1990.
DOI : 10.1007/BF00375698

C. Truesdell and W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, 1965.

R. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, vol.1, issue.4, pp.417-438, 1965.
DOI : 10.1016/0020-7683(65)90006-5

F. Dell-'isola, L. Rosa, and C. Wo´zniakwo´zniak, A micro-structured continuum modelling compacting fluid-saturated grounds: The effects of pore-size scale parameter, Acta Mech, vol.127, pp.1-4, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00497282

A. Cecchi, R. , and N. , Heterogeneous elastic solids: a mixed homogenization-rigidification technique, International Journal of Solids and Structures, vol.38, issue.1, pp.29-36, 2001.
DOI : 10.1016/S0020-7683(00)00018-4

G. Piccardo, G. Ranzi, and A. Luongo, A direct approach for the evaluation of the conventional modes within the GBT formulation, Thin-Walled Structures, vol.74, pp.133-145, 2014.
DOI : 10.1016/j.tws.2013.09.008

R. Dendievel, S. Forest, C. , and G. , An estimation of overall properties of heterogeneous Cosserat materials European conference on mechanics of materials with intrinsic length scale: Physics, experiments, modelling and applications (EMMC-2), pp.23-26, 1998.

C. Truesdell, An idiot's fugitive essays on science, 1984.

J. Dahler and L. Scriven, Theory of Structured Continua. I. General Consideration of Angular Momentum and Polarization, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.275, issue.1363, pp.504-527, 1963.
DOI : 10.1098/rspa.1963.0183

E. Cosserat, C. , and F. , Note sur la théorie de l'action Euclidienne, Traité de mécanique rationelle, pp.557-629, 1909.

F. Dell-'isola and L. Placidi, Variational principles are a powerful tool also for formulating field theories, Variational models and methods in solid and fluid mechanics (CISM Courses and Lectures, pp.1-15, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00607746

E. Hellinger, Die allgemeinen Ansätze der Mechanik der Kontinua, Encyklopädie der Mathematischen Wissenschaften, pp.602-694, 1914.
DOI : 10.1007/978-3-663-16028-1_9

N. Auffray, R. Bouchet, and Y. Bréchet, Derivation of anisotropic matrix for bi-dimensional strain-gradient elasticity behavior, International Journal of Solids and Structures, vol.46, issue.2, pp.440-454, 2009.
DOI : 10.1016/j.ijsolstr.2008.09.009
URL : https://hal.archives-ouvertes.fr/hal-00445238

S. Cowin and . Bone, Bone poroelasticity, Journal of Biomechanics, vol.32, issue.3, pp.217-238, 1999.
DOI : 10.1016/S0021-9290(98)00161-4

J. Ganghoffer, A contribution to the mechanics and thermodynamics of surface growth. Application to bone external remodeling, International Journal of Engineering Science, vol.50, issue.1, pp.166-191, 2012.
DOI : 10.1016/j.ijengsci.2011.08.004

I. Jasiuk and M. Ostoja-starzewski, Modeling of bone at a single lamella level, Biomechanics and Modeling in Mechanobiology, vol.6, issue.2, pp.67-74, 2004.
DOI : 10.1007/s10237-004-0048-5

T. Lekszycki and F. Isola, 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

U. Andreaus, I. Giorgio, and A. Madeo, Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids, Zeitschrift f??r angewandte Mathematik und Physik, vol.8, issue.1, pp.209-237, 2015.
DOI : 10.1007/s00033-014-0403-z
URL : https://hal.archives-ouvertes.fr/hal-00944570

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

A. Pipkin, R. , and T. , Plane Deformations of Incompressible Fiber-Reinforced Materials, Journal of Applied Mechanics, vol.38, issue.3, pp.634-640, 1971.
DOI : 10.1115/1.3408866

M. Ferretti, A. Madeo, and F. Isola, Modeling the onset of shear boundary layers in fibrous composite reinforcements by second-gradient theory, Zeitschrift f??r angewandte Mathematik und Physik, vol.16, issue.3, pp.587-612, 2014.
DOI : 10.1007/s00033-013-0347-8
URL : https://hal.archives-ouvertes.fr/hal-00934569

H. Gouin and W. Kosi´nskikosi´nski, Boundary conditions for a capillary fluid in contact with a wall, Arch Mech, vol.50, issue.5, pp.907-916, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00255841

R. Alessi, J. Marigo, and S. Vidoli, Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks, Archive for Rational Mechanics and Analysis, vol.110, issue.1, pp.575-615, 2014.
DOI : 10.1007/s00205-014-0763-8

G. Francfort and A. Garroni, A Variational View of Partial Brittle Damage Evolution, Archive for Rational Mechanics and Analysis, vol.47, issue.1, pp.125-152, 2006.
DOI : 10.1007/s00205-006-0426-5

A. Cazzani and M. Rovati, Sensitivity analysis and optimum design of elastic-plastic structural systems, Meccanica, vol.81, issue.1?3, pp.2-3, 1991.
DOI : 10.1007/BF00429886

L. Contrafatto and M. Cuomo, A new thermodynamically consistent continuum model for hardening plasticity coupled with damage, International Journal of Solids and Structures, vol.39, issue.25, pp.6241-6271, 2002.
DOI : 10.1016/S0020-7683(02)00470-5
URL : https://hal.archives-ouvertes.fr/hal-00878757

E. Turco, C. , and P. , Elasto-plastic analysis of Kirchhoff plates by high simplicity finite elements, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.5-7, pp.5-7, 2000.
DOI : 10.1016/S0045-7825(99)00438-7

A. Rinaldi and L. Placidi, A microscale second gradient approximation of the damage parameter of quasi-brittle heterogeneous lattices, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.45, issue.1, pp.862-877, 2014.
DOI : 10.1002/zamm.201300028

V. Eremeyev and L. Zubov, On the stability of equilibrium of nonlinear elastic bodies with phase transformations, Proc USSR Acad Sci Mech Solid, vol.2, pp.56-65, 1991.

V. Eremeyev and W. Pietraszkiewicz, On tension of a two-phase elastic tube, Shell Struct Theor Appl, vol.2, pp.63-66, 2010.

V. Eremeyev and W. Pietraszkiewicz, The Nonlinear Theory of Elastic Shells with Phase Transitions, Journal of Elasticity, vol.74, issue.1, pp.67-86, 2004.
DOI : 10.1023/B:ELAS.0000026106.09385.8c
URL : https://hal.archives-ouvertes.fr/hal-00831721

G. Francfort and J. Marigo, Cracks in fracture mechanics: A time indexed family of energy minimizers In: IUTAM symposium on variations of domain and free-boundary problems in solid mechanics, pp.197-202, 1999.

A. Madeo, L. Placidi, R. , and G. , Towards the Design of Metamaterials with Enhanced Damage Sensitivity: Second Gradient Porous Materials, Research in Nondestructive Evaluation, vol.138, issue.4, pp.99-124, 2014.
DOI : 10.1007/s00161-012-0266-5
URL : https://hal.archives-ouvertes.fr/hal-01167198

L. Placidi, A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Contin Mech Thermodyn. Epub online ahead of print 23, pp.101007-00161, 2014.

F. Dell-'isola, P. Seppecher, D. Corte, and A. , The postulations à la D'Alembert and a' la Cauchy for higher gradient continuum theories are equivalent: A review of existing results, Proc Math Phys Eng Sci, vol.471, p.20150415, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01226235

F. Dell-'isola, D. Steigmann, D. Corte, and A. , Synthesis of complex structures. Designing micro-structure to deliver targeted macro-scale response. Appl Mech Rev. Epub online ahead of print 9, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01284511

L. Placidi, A variational approach for a nonlinear 1-dimensional second gradient continuum damage model, Continuum Mechanics and Thermodynamics, vol.1, issue.2, pp.623-638, 2015.
DOI : 10.1007/s00161-014-0338-9

Y. Yang and A. Misra, Higher-order stress-strain theory for damage modeling implemented in an element-free Galerkin formulation, Comput Model Eng Sci, vol.64, issue.1, pp.1-36, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00556175

A. Carcaterra and A. Akay, Theoretical foundations of apparent-damping phenomena and nearly irreversible energy exchange in linear conservative systems, The Journal of the Acoustical Society of America, vol.121, issue.4, pp.1971-1982, 2007.
DOI : 10.1121/1.2697030

C. Boutin, P. Royer, and J. Auriault, Acoustic absorption of porous surfacing with dual porosity, International Journal of Solids and Structures, vol.35, issue.34-35, pp.4709-4737, 1998.
DOI : 10.1016/S0020-7683(98)00091-2

D. Steigmann, E. Baesu, and R. Rudd, On the variational theory of cell-membrane equilibria, Interfaces and Free Boundaries, vol.5, issue.4, pp.357-366, 2003.
DOI : 10.4171/IFB/83