R. Abeyaratne and N. , An Investigation of Localization in a Porous Elastic Material Using Homogenization Theory, Journal of Applied Mechanics, vol.51, issue.3, pp.481-486, 1984.
DOI : 10.1115/1.3167661

E. C. 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

J. Alibert, P. Seppecher, and F. , 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

C. Banfi, A. Marzocchi, and A. Musesti, On the principle of virtual powers in continuum mechanics, Ricerche di Matematica, vol.55, issue.2, pp.299-310, 2006.
DOI : 10.1007/s11587-006-0017-7

S. Bardenhagen and N. Triantafyllidis, Derivation of higher order gradient continuum theories in 2,3-d non-linear elasticity from periodic lattice models, Journal of the Mechanics and Physics of Solids, vol.42, issue.1, pp.111-139, 1994.
DOI : 10.1016/0022-5096(94)90051-5

V. Berdichevsky, Variational Principles of Continuum Mechanics, 2009.

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

A. Carcaterra and E. Ciappi, Prediction of the compressible stage slamming force on rigid and elastic systems impacting on the water surface, Nonlinear Dynamics, vol.21, issue.2, pp.193-220, 2000.
DOI : 10.1023/A:1008338301185

A. Carcaterra, E. Ciappi, and A. Iafrati, SHOCK SPECTRAL ANALYSIS OF ELASTIC SYSTEMS IMPACTING ON THE WATER SURFACE, Journal of Sound and Vibration, vol.229, issue.3, pp.579-605, 2000.
DOI : 10.1006/jsvi.1999.2517

A. Carcaterra, Ensemble energy average and energy flow relationships for nonstationary vibrating systems, Journal of Sound and Vibration, vol.288, issue.3, pp.751-790, 2005.
DOI : 10.1016/j.jsv.2005.07.015

A. Carcaterra, A. Akay, and I. M. Koc, Near-irreversibility in a conservative linear structure with singularity points in its modal density, The Journal of the Acoustical Society of America, vol.119, issue.4, pp.2141-2149, 2006.
DOI : 10.1121/1.2179747

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

M. O. Carvalho and &. M. Zindeluk, Active control of waves in a Timoshenko beam, International Journal of Solids and Structures, vol.38, issue.10-13, pp.1749-1764, 2001.
DOI : 10.1016/S0020-7683(00)00134-7

P. Casal and &. 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, vol.300, issue.7, pp.231-235, 1985.

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.

E. Cosserat and &. F. Cosserat, Sur la théorie des corps déformables, 1909.

A. Culla, A. Sestieri, and A. Carcaterra, ENERGY FLOW UNCERTAINTIES IN VIBRATING SYSTEMS: DEFINITION OF A STATISTICAL CONFIDENCE FACTOR, Mechanical Systems and Signal Processing, vol.17, issue.3, pp.635-663, 2003.
DOI : 10.1006/mssp.2002.1487

N. Daher and G. A. Maugin, 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 Mechanica, vol.16, issue.3-4, pp.217-240, 1986.
DOI : 10.1007/BF01176354

P. G. De-gennes, Some effects of long range forces on interfacial phenomena, Journal de Physique Lettres, vol.42, issue.16, p.379, 1981.
DOI : 10.1051/jphyslet:019810042016037700
URL : https://hal.archives-ouvertes.fr/jpa-00231951

F. Dell-'isola and &. P. Seppecher, The relationship between edge contact forces, double force and interstitial working allowed by the principle of virtual power. CRAS -Serie IIb, pp.303-308, 1995.

M. Degiovanni, A. Marzocchi, and A. Musesti, 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

M. Degiovanni, A. Marzocchi, 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

F. Dellisola, H. Gouin, and P. Seppecher, Radius and Surface Tension of Microscopic Bubbles by Second Gradient Theory, CRAS IIB Mechanics, vol.320, pp.211-216, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00308860

F. Dellisola, H. Gouin, and G. Rotoli, Nucleation of Spherical Shell-Like Interfaces by Second Gradient Theory: Numerical Simulations, Eur. J. Mech., B/Fluids, vol.15, issue.4, pp.545-568, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00393974

F. Dell-'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. Dellisola, A. Madeo, and P. Seppecher, Boundary conditions at fluid-permeable interfaces in porous media: A variational approach, International Journal of Solids and Structures, vol.46, issue.17, pp.3150-3164, 2009.
DOI : 10.1016/j.ijsolstr.2009.04.008
URL : https://hal.archives-ouvertes.fr/hal-00504035

F. Dell-'isola, G. Sciarra, and S. Vidoli, Generalized Hooke's law for isotropic second gradient materials, Proc. R. Soc. A 465, pp.2177-2196, 2009.

F. Isola and P. Seppecher, Commentary about the paper Hypertractions and hyperstresses convey the same mechanical information Continuum Mech Thermodyn 22:163176 " by Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories, Continuum Mechanics and Thermodynamics, vol.22, pp.163-175, 2010.

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

V. I. Erofeyev, Wave Processes in Solids with Microstructure, 2003.
DOI : 10.1142/5157

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. Chan, and G. H. Paulino, 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. L. Gavrilyuk and S. M. Shugrin, Media with state equations that depend on the derivatives. (Russian) Prikl, Mekh. Tekhn. Fiz. translation in J. Appl. Mech. Tech. Phys, vol.37, issue.372, pp.35-49, 1996.

S. Gavrilyuk and H. Gouin, Symmetric form of governing equations for capillary fluids Trends in applications of mathematics to mechanics (Nice, Surv. Pure Appl. Math, vol.106, pp.306-311, 1998.

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.

P. Germain, La méthode des puissances virtuelles en mécanique des milieux continus Premiere partie: Théorie du second gradient, J. Mécanique, vol.12, issue.2, pp.235-274, 1973.

P. Germain-microstructure and S. I. , The method of virtual power in continuum mechanics Part 2, J. Appl. Math, vol.25, issue.3, pp.556-575, 1973.

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, Multipolar continuum mechanics, Arch. Rational Mech. Anal, vol.17, pp.113-147, 1964.

A. E. Green and R. S. Rivlin, 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

J. Guyader, Vibration in Continuous Media, ISTE Ltd, 2006.
DOI : 10.1002/9780470612453
URL : https://hal.archives-ouvertes.fr/hal-00414874

J. G. Harris, Linear Elastic Waves, 2004.

N. Kirchner and P. Steinmann, A unifying treatise on variational principles for gradient and micromorphic continua, Philosophical Magazine, vol.16, issue.33-35, pp.33-35, 2005.
DOI : 10.1002/nme.1620372006

R. Larsson and S. Diebels, A second-order homogenization procedure for multi-scale analysis based on micropolar kinematics, International Journal for Numerical Methods in Engineering, vol.2, issue.12, pp.2485-2512, 2007.
DOI : 10.1002/nme.1854

M. Lazar and G. A. Maugin, Defects in gradient micropolar elasticity?I: screw dislocation, Journal of the Mechanics and Physics of Solids, vol.52, issue.10, pp.2263-2284, 2004.
DOI : 10.1016/j.jmps.2004.04.003

M. Lazar and G. A. Maugin, Defects in gradient micropolar elasticity?II: edge dislocation and wedge disclination, Journal of the Mechanics and Physics of Solids, vol.52, issue.10, pp.2285-2307, 2004.
DOI : 10.1016/j.jmps.2004.04.002

M. Lazar and G. A. Maugin, Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity, International Journal of Engineering Science, vol.43, issue.13-14, pp.1157-1184, 2005.
DOI : 10.1016/j.ijengsci.2005.01.006

M. Lazar, G. A. Maugin, and E. C. , On dislocations in a special class of generalized elasticity, physica status solidi (b), vol.17, issue.12, pp.2365-2390, 2005.
DOI : 10.1002/pssb.200540078

M. Lazar and G. A. Maugin, A note on line forces in gradient elasticity, Mechanics Research Communications, vol.33, issue.5, pp.674-680, 2006.
DOI : 10.1016/j.mechrescom.2005.08.004

M. Lazar, G. A. Maugin, and E. C. , Dislocations in second strain gradient elasticity, International Journal of Solids and Structures, vol.43, issue.6, pp.1787-1817, 2006.
DOI : 10.1016/j.ijsolstr.2005.07.005

M. Lucchesi, M. Silhav´ysilhav´y, and N. Zani, 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. Dellisola, 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, p.607625, 2008.
DOI : 10.2140/jomms.2008.3.607
URL : https://hal.archives-ouvertes.fr/hal-00499567

O. Marangos, A. Misra, P. Spencer, J. L. Katz, and J. L. , Scanning acoustic microscopy investigation of frequency-dependent reflectance of acid- etched human dentin using homotopic measurements, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.58, issue.3, 2011.
DOI : 10.1109/TUFFC.2011.1841
URL : https://hal.archives-ouvertes.fr/hal-00555784

G. A. Maugin and A. C. Eringen, On the equations of the electrodynamics of deformable bodies of finite extent, J. Mécanique, vol.16, issue.1, pp.101-147, 1977.

G. A. Maugin, Die Methode der virtuallen Leistung in der Kontinuumsmechanik: Anwendung auf gekoppelte Felder, Acta Mechanica, vol.15, issue.No. 2, pp.1-70, 1980.
DOI : 10.1007/BF01190057

G. A. Maugin, A relativistic version of the principle of virtual power, International Journal of Engineering Science, vol.19, issue.12, pp.1719-1730, 1981.
DOI : 10.1016/0020-7225(81)90162-2

G. A. Maugin and A. V. Metrikine, Mechanics of generalized continua One hundred years after the Cosserats, Metrikine. Advances in Mechanics and Mathematics, vol.510, issue.21, pp.13-16, 2009.

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

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. Menzel and P. , Steinm'ann, On the Formulation of Higher Gradient Single and Polycrystal Plasticity, Le Journal de Physique IV Nr. Pr, vol.088, pp.239-247, 1998.

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 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

A. Misra, Mechanistic Model for Contact between Rough Surfaces, Journal of Engineering Mechanics, vol.123, issue.5, pp.475-484, 1997.
DOI : 10.1061/(ASCE)0733-9399(1997)123:5(475)

A. Misra, Effect of asperity damage on shear behavior of single fracture, Engineering Fracture Mechanics, vol.69, issue.17, pp.1997-2014, 2002.
DOI : 10.1016/S0013-7944(02)00073-5
URL : https://hal.archives-ouvertes.fr/hal-00555547

A. Misra and O. Marangos, 3D-2 Application of a Micromechanical Model to Wave Propagation Through Nonlinear Rough Interfaces Under Stress, 2006 IEEE Ultrasonics Symposium, pp.309-312, 2006.
DOI : 10.1109/ULTSYM.2006.90

A. Misra and O. Marangos, PARAMETRIC STUDIES OF WAVE PROPAGATION THROUGH IMPERFECT INTERFACES USING MICROMECHANICS BASED EFFECTIVE STIFFNESS, AIP Conference Proceedings, pp.1074-1081, 2008.
DOI : 10.1063/1.2902551
URL : https://hal.archives-ouvertes.fr/hal-00556109

A. Misra and O. Marangos, Abstract, Acta Geophysica, vol.56, issue.4, pp.1109-1128, 2008.
DOI : 10.2478/s11600-008-0050-x

A. Misra and O. Marangos, EFFECT OF CONTACT VISCOSITY AND ROUGHNESS ON INTERFACE STIFFNESS AND WAVE PROPAGATION, AIP Conference Proceedings, pp.105-112, 2009.
DOI : 10.1063/1.3114071
URL : https://hal.archives-ouvertes.fr/hal-00555518

A. Misra and S. Huang, Micromechanics based stress-displacement relationships of rough contacts: Numerical implementation under combined normal and shear loading, Computer Modeling in Engineering and Sciences, vol.52, issue.2, pp.197-215, 2009.

A. Misra and O. Marangos, Rock-Joint Micromechanics: Relationship of Roughness to Closure and Wave Propagation, International Journal of Geomechanics, vol.11, issue.6, 2011.
DOI : 10.1061/(ASCE)GM.1943-5622.0000021

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

M. Ouisse and J. Guyader, Vibration sensitive behaviour of a connecting angle. Case of coupled beams and plates, Journal of Sound and Vibration, vol.267, issue.4, pp.809-850, 2003.
DOI : 10.1016/S0022-460X(03)00179-2

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. 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, pp.189-211, 2007.
DOI : 10.1016/j.euromechsol.2006.07.005

G. Sciarra, F. Dell-'isola, and O. Coussy, 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. 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

J. Salençon, Mécanique des milieux continus Ed Handbook of Continuum Mechanics Ed Mécanique des milieux continus, Ellipses, 1988.

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

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

P. Seppecher, Equilibrium of a Cahn-Hilliard fluid on a wall: influence of the wetting properties of the fluid upon the stability of a thin liquid film, European J. Mech. B Fluids, vol.12, issue.1, pp.69-84, 1993.

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. Sokolowski, Theory of couple-stresses in bodies with constrained rotations, CISM courses and lectures, 1970.
DOI : 10.1007/978-3-7091-2943-2

P. Steinmann and E. A. Stein, A unifying treatise of variational principles for two types of micropolar continua, Acta Mechanica, vol.33, issue.1-4, pp.215-232, 1997.
DOI : 10.1007/BF01262533

R. Sunyk and P. Steinmann, On higher gradients in continuum-atomistic modelling, International Journal of Solids and Structures, vol.40, issue.24, pp.6877-6896, 2003.
DOI : 10.1016/j.ijsolstr.2003.07.001

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

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

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

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, p.33, 1993.
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

Y. Yang and A. Misra, Higher-Order Stress-Strain Theory for Damage Modeling Implemented in an Element-free Galerkin Formulation, CMES, vol.1549, 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