R. K. Abeyaratne, N. Triantafyllidis, ]. R. Abraham, J. E. Marsden, and T. Ratiu, Abu Al-Rub Modeling the interfacial effect on the yield strength and flow stress of thin metal films on substrates Mechanics Research Communications An investigation of localization in a porous elastic material using homogenization theory, Manifolds,Tensor Analysis, and Applications', Applied Mathematical Sciences, pp.65-72, 1984.

J. Alibert, P. Seppecher, and F. Dell-'isola, Truss modular beams with deformation energy depending on higher displacement gradients [5] V.I. Arnold, Mathematical Methods of Classical Mechanics Marzocchi and A. Musesti On the principle of virtual powers in continuum mechanics Triantafyllidis Derivation of higher order gradient continuum theories in 2,3-D nonlinear elasticity from periodic lattice models, Benvenuto La scienza delle costruzioni e il suo sviluppo storico Sansoni Berdichevsky, Variational Principles of Continuum Mechanics, pp.51-73, 1979.

J. L. Bleustein, A note on the boundary conditions of toupin's strain-gradient theory, International Journal of Solids and Structures, vol.3, issue.6, pp.1053-1057, 1967.
DOI : 10.1016/0020-7683(67)90029-7

B. Bourdin, G. A. Francfort, and J. Marigo, The variational approach to fracture, J. Elasticity, vol.91, pp.1-3, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00551079

J. L. Borges, Pierre Menard Author of the Quixote (translation by

P. Casal and E. H. Gouin, Relation entre l'´ equation de l'´ energie et l'´ equation du mouvement en théorie de Korteweg de la capillaritè, C. R. Acad. Sci. Paris, t, vol.300, issue.7, pp.231-233, 1985.

]. P. Casal, La théorie du second gradient et la capillarité, C. R, issue.14

. Acad and . Sci, Paris, t. 274, Série A, pp.1571-1574, 1972.

P. Casal and E. H. Gouin, Relation entre l'´ equation de l'´ energie et l'´ equation du mouvement en théorie de Korteweg de la capillarité, C. R. Acad. Sci. Paris, t, vol.300, issue.7, pp.231-233, 1985.

A. Carcaterra, A. Akay, and I. M. , Koc Near-irreversibility in a conservative linear structure with singularity points in its modal density, Journal of the Acoustical Society of America, vol.119, pp.4-2141, 2006.

F. Collin, R. Chambon, and R. Charlier, A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models, International Journal for Numerical Methods in Engineering, vol.51, issue.11, pp.1749-1772, 2006.
DOI : 10.1002/nme.1515

E. Cosserat and F. , Cosserat Note sur la théorie de l'action euclidienne, 1908.

N. Daher and G. A. , Virtual power and thermodynamics for electromagnetic continua with interfaces, Journal of Mathematical Physics, vol.27, issue.12, pp.3022-3035, 1986.
DOI : 10.1063/1.527231

N. Daher and G. A. , Maugin The method of virtual power in continuum mechanics. Application to media presenting singular surfaces and interfaces, Acta Mech, vol.60, pp.3-4, 1986.

F. Isola and W. Kosinski, Deduction of thermodynamic balance laws for bidimensional nonmaterial directed continua modelling interphase layers, Archives of Mechanics, vol.45, pp.333-359, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00502045

F. Isola and P. Seppecher, The relationship between edge contact forces, double force and interstitial working allowed by the principle of virtual power, Comptes Rendus de l'Academie de Sciences -Serie IIb: Mecanique, Physique, Chimie, Astronomie, pp.303-308, 1995.

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, G. Sciarra, and S. Vidoli, Generalized Hooke's law for isotropic second gradient materials, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.34, issue.2107, pp.2177-2196, 2009.
DOI : 10.1098/rspa.2008.0530

F. Dell-'isola, G. Sciarra, and R. C. Batra, Static Deformations of a Linear Elastic Porous Body Filled with an Inviscid Fluid, Journal of Elasticity, vol.72, issue.1-3, pp.99-120, 2003.
DOI : 10.1023/B:ELAS.0000018765.68432.bb

URL : https://hal.archives-ouvertes.fr/hal-01362142

F. Isola, M. Guarascio, and K. , A variational approach for the deformation of a saturated porous solid. A second-gradient theory extending Terzaghi's effective stress principle, Archive of Applied Mechanics (Ingenieur Archiv), vol.70, issue.5, pp.323-337, 2000.
DOI : 10.1007/s004199900020

URL : https://hal.archives-ouvertes.fr/hal-00502003

A. , D. Carlo-e, and A. , Tatone (Iper-)Tensioni & Equi-Potenza AIMETA'01 XV Congresso AIMETA di Meccanica Teorica e Applicata, 2001.

M. Degiovanni and A. , Edge-force densities and second-order powers, Annali di Matematica Pura ed Applicata, vol.84, issue.1, pp.81-103, 2006.
DOI : 10.1007/s10231-004-0129-1

M. Degiovanni, A. Marzocchi, A. Musesti, and A. , Cauchy Fluxes Associated with Tensor Fields Having Divergence Measure, Archive for Rational Mechanics and Analysis, vol.147, issue.3, pp.197-223, 1999.
DOI : 10.1007/s002050050149

J. E. Dunn and J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal, vol.88, issue.2, pp.95-133, 1985.

J. E. Dunn, Interstitial working and a non classical continuum thermodynamics New Perspectives in Thermodynamics, pp.187-222, 1986.

G. E. Exadaktylos and I. Vardoulakis, Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics, Tectonophysics, vol.335, issue.1-2, pp.81-109, 2001.
DOI : 10.1016/S0040-1951(01)00047-6

A. C. Fannjiang, Y. S. Chan, and G. H. , Strain Gradient Elasticity for Antiplane Shear Cracks: A Hypersingular Integrodifferential Equation Approach, SIAM Journal on Applied Mathematics, vol.62, issue.3, pp.1066-1091, 2001.
DOI : 10.1137/S0036139900380487

S. Forest, Mechanics of generalized continua: construction by homogenizaton, Le Journal de Physique IV, vol.08, issue.PR4, 1998.
DOI : 10.1051/jp4:1998405

S. Forest and M. Amestoy, Mécanique des milieux continus, 2004.

S. Forest, Milieux continus généralisés et matériaux hétérogènes, 2004.

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

E. Fried and M. E. Gurtin, A continuum mechanical theory for turbulence: a generalized Navier???Stokes-?? equation with boundary conditions, Theoretical and Computational Fluid Dynamics, vol.49, issue.6, pp.513-554, 2008.
DOI : 10.1007/s00162-008-0083-4

P. Germain, Cours de M` ecanique des Milieux Continus, 1973.

P. Germain, La méthode des puissances virtuelles en mécanique des milieux continus.Premì ere partie. Théorie du second gradient, J. 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, Sur l'application de la méthode des puissances virtuelles en mécanique des milieux continus, C. R. Acad. Sci. Paris Série A-B, vol.274, pp.1051-1055, 1972.

A. E. Green and R. S. Rivlin, Simple force and stress multipoles, Arch. Rational Mech. Anal, vol.16, pp.325-353, 1964.

A. E. Green and R. S. Rivlin, On cauchy's equations of motion, Zeitschrift f??r angewandte Mathematik und Physik ZAMP, vol.15, issue.3, pp.290-292, 1964.
DOI : 10.1007/BF01607019

A. E. Green and R. S. , Multipolar Continuum Mechanics: Functional Theory I, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.284, issue.1398, pp.303-324, 1965.
DOI : 10.1098/rspa.1965.0065

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.809-819, 2002.
DOI : 10.1016/S0022-5096(01)00104-1

N. Kirchner and P. Steinmann, On the material setting of gradient hyperelasticity. (English summary) Math, Mech. Solids, vol.12, 2007.

W. Kosinski, R. Larsson, and S. Diebels, Field Singularities and Wave Analysis in Continuum Mechanics Ellis Horwood Series: Mathematics and Its Applications Second-order homogenization procedure for multi-scale analysis based on micropolar kinematics, Internat. J. Numer. Methods Engrg, vol.69, issue.12, pp.2485-2512, 1986.

M. Lazar and G. A. , Maugin A note on line forces in gradient elasticity Mechanics Research Communications, pp.674-680, 2006.

M. Lucchesi, ·. Silhav´ysilhav´y, and ·. , On the Balance Equation for Stresses Concentrated on Curves, Journal of Elasticity, vol.75, issue.2, pp.209-223, 2008.
DOI : 10.1007/s10659-007-9139-8

A. Madeo, F. Dell-'isola, N. Ianiro, and G. Sciarra, A second gradient poroelastic model of consolidation, SIMAI, pp.15-19, 2008.

A. Madeo, F. Dell-'isola, N. Ianiro, and G. Sciarra, A variational deduction of second gradient poroelasticity II: an application to the consolidation problem, Journal of Mechanics of Materials and Structures, vol.3, issue.4, pp.607-625, 2008.
DOI : 10.2140/jomms.2008.3.607

URL : https://hal.archives-ouvertes.fr/hal-00499567

A. Marzocchi and A. Musesti, Balanced virtual powers in Continuum Mechanics, Meccanica, vol.38, issue.3, pp.369-389, 2003.
DOI : 10.1023/A:1023301303945

A. Marzocchi and A. Musesti, Decomposition and integral representation of Cauchy interactions associated with measures, Continuum Mechanics and Thermodynamics, vol.13, issue.3, pp.149-169, 2001.
DOI : 10.1007/s001610100046

G. M. Mathreview and M. , 99e:73005) on the paper G. Capriz and G. Mazzini Invariance and balance in continuum mechanics .Nonlinear analysis and continuum mechanics, pp.27-35, 1992.

G. A. Maugin and A. V. , Metrikine Editors Mechanics of Generalized Continua, One Hundred Years After the Cosserats, 2010.

R. D. 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. D. Mindlin, Micro-structure in linear elasticity Complex representation of displacements and stresses in plane strain with couple-stresses, Proc. Internat. Sympos ., Tbilisi), pp.51-78, 1963.

R. D. Mindlin and H. F. Tiersten, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, vol.190, issue.1, pp.415-448, 1962.
DOI : 10.1007/BF00253946

R. D. Mindlin and N. N. , 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. D. Mindlin, Stress functions for a Cosserat continuum, International Journal of Solids and Structures, vol.1, issue.3, pp.265-271, 1965.
DOI : 10.1016/0020-7683(65)90033-8

M. Muntersbjom, Francis Bacon's Philosophy of Science: Machina intellectus and Forma indita Philosophy of Science, pp.1137-1148, 2003.

W. Noll and E. G. 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

W. Noll, The foundations of classical mechanics in the light of recent advances in continuum mechanics' Proceeding of the Berkeley Symposium on the Axiomatic Method, pp.226-281, 1959.

W. Noll, Lectures on the foundations of continuum mechanics and thermodynamics', Arch. Rational Mech. Anal, pp.62-92, 1973.

W. Noll, The geometry of contact, separation, and reformation of continuous bodies, Archive for Rational Mechanics and Analysis, vol.102, issue.3, pp.197-212, 1993.
DOI : 10.1007/BF00380254

C. Pideri and P. , 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

P. Podio-guidugli, Contact interactions, stress, and material symmetry, for nonsimple elastic materials. (English, Serbo- Croatian summary) Issue dedicated to the memory of Professor Rastko Stojanovic, Theoret. Appl. Mech, vol.28, pp.29-261, 2002.

P. Podio-guidugli and M. , Vianello Hypertractions and hyperstresses convey the same mechanical information Continuum Mech, Thermodyn, vol.22, pp.163-176, 2010.

C. Polizzotto, Strain-gradient elastic-plastic material models and assessment of the higher order boundary conditions, European Journal of Mechanics - A/Solids, vol.26, issue.2
DOI : 10.1016/j.euromechsol.2006.07.005

C. Rorres, Completing Book II of Archimedes's On Floating Bodies THE MATHEMATICAL INTELLIGENCER 26, pp.32-42, 2004.

J. Salençon-mécanique-des-milieux-continus and E. , Handbook of Continuum Mechanics Ed) Mécanique des milieux continus, Ellipses, 1988.

G. Sciarra and F. Dell, Second gradient poromechanics, International Journal of Solids and Structures, vol.44, issue.20, pp.6607-6629, 2007.
DOI : 10.1016/j.ijsolstr.2007.03.003

URL : https://hal.archives-ouvertes.fr/hal-01362157

G. Sciarra, F. Isola, and K. Hutter, A solid-fluid mixture model allowing for solid dilatation under external pressure, Continuum Mechanics and Thermodynamics, vol.13, issue.5, pp.287-306, 2001.
DOI : 10.1007/s001610100053

URL : https://hal.archives-ouvertes.fr/hal-00499418

G. Sciarra, F. Dell-'isola, N. Ianiro, and A. Madeo, A variational deduction of second gradient poroelasticity I: general theory, Journal of Mechanics of Materials and Structures, vol.3, issue.3, pp.507-526, 2008.
DOI : 10.2140/jomms.2008.3.507

URL : https://hal.archives-ouvertes.fr/hal-01362159

P. Seppecher, Etude des conditions aux limites en théorie du second gradient: cas de la capillarité, C. R. Acad. Sci. Paris, t, vol.309, pp.497-502, 1989.

P. Seppecher, Etude d'une Modélisation des Zones Capillaires Fluides: Interfaces et Lignes de Contact, Thèse de l, 1987.

M. ?. Silhav´ysilhav´y, The existence of the flux vector and the divergence theorem for general Cauchy fluxes, Archive for Rational Mechanics and Analysis, vol.3, issue.3, pp.195-211, 1985.
DOI : 10.1007/BF00251730

M. Spivak, A comprehensive introduction to differential geometry . Voll. I and II, 1979.

A. S. Suiker and C. S. Chang, Application of higher-order tensor theory for formulating enhanced continuum models, Acta Mechanica, vol.33, issue.1-4, pp.223-234, 2000.
DOI : 10.1007/BF01190020

R. A. 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

N. Triantafyllidis and S. Bardenhagen, On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models, Journal of Elasticity, vol.29, issue.3
DOI : 10.1007/BF00043251

N. Triantafyllidis and S. Bardenhagen, The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models, Journal of the Mechanics and Physics of Solids, vol.44, issue.11, pp.1891-1928, 1996.
DOI : 10.1016/0022-5096(96)00047-6

N. Triantafyllidis and E. C. , A gradient approach to localization of deformation. I. Hyperelastic materials, Journal of Elasticity, vol.5, issue.3, pp.225-237, 1986.
DOI : 10.1007/BF00040814

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

Y. Yang, W. Y. Ching, and A. Misra, Higher-order continuum theory applied to fracture simulation of nano-scale intergranular glassy film, Journal of Nanomechanics and Micromechanics, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00556184

G. Vailati, Il principio dei lavori virtuali da Aristotele a Erone d'Alessandria, Scritti (Bologna, Forni, pp.113-128, 1897.