S. Quiligotti, . Maugin, and F. Isola, An Eshelbian approach to the nonlinear mechanics of constrained solid-fluid mixtures, Acta Mechanica, vol.160, issue.1-2, pp.45-60, 2003.
DOI : 10.1007/s00707-002-0968-z

URL : https://hal.archives-ouvertes.fr/hal-00502067

L. L. Russo and . America-dimenticata.-i-rapporti-tra-le-civiltà-e-un-errore-di-tolomeo, The forgotten revolution, 2003.
DOI : 10.1007/978-3-642-18904-3

C. Truesdell and R. Toupin, The Classical Field Theories, Handbuch der Physik Essays in the hystory of mechanics, 1960.
DOI : 10.1007/978-3-642-45943-6_2

D. Capecchi, G. Ruta, and G. Piola, Piola's contribution to continuum mechanics Memoria intorno alle equazioni fondamentali del movimento di corpi qualsivogliono considerati secondo la naturale loro forma e costituzione, Arch Hist Exact Sci, vol.618, pp.303-342, 2007.

G. Piola, Sull'applicazione de' principj della meccanica analitica del Lagrange ai principali problemi: Imp. Regia Stamperia, 1825. [9] Piola, G. La meccanica de' corpi naturalmente estesi: Trattata col calcolo delle variazioni, 1833.

G. Piola, Nuova analisi per tutte le questioni della meccanica molecolare, p.1835

G. Piola, Di un principio controverso della meccanica analitica di Lagrange e delle molteplici sue applicazioni, p.1856

E. Cosserat and F. Cosserat, Théorie des corps deformables, 1909.

A. Bedford, Hamilton???s Principle in Continuum Mechanics, Journal of Applied Mechanics, vol.53, issue.3, 1985.
DOI : 10.1115/1.3171846

V. Berdichevsky, Variational principles of continuum mechanics I: Fundamentals, 2009.

V. Berdichevsky, Variational principles of continuum mechanics II: Applications, 2009.

N. Daher and G. 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. Germain, La méthode des puissances virtuelles en mécanique des milieux continus, I: Thèorie du second gradient, J Mec, 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

E. Kroner, Mechanics of generalized continua, 1968.
DOI : 10.1007/978-3-662-30257-6

G. Maugin, The principle of virtual power: from eliminating metaphysical forces to providing an efficient modelling tool, Continuum Mechanics and Thermodynamics, vol.273, issue.18, pp.127-146, 2011.
DOI : 10.1007/s00161-011-0196-7

R. 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. 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

A. Green and R. Rivlin, Multipolar continuum mechanics, Arch Rat Mech Anal, vol.17, pp.113-147, 1964.

A. Green and R. 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

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

P. Neff, A finite-strain elastic???plastic Cosserat theory for polycrystals with grain rotations, International Journal of Engineering Science, vol.44, issue.8-9, pp.8-9, 2006.
DOI : 10.1016/j.ijengsci.2006.04.002

P. Neff, Existence of minimizers for a finite-strain micromorphic elastic solid, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.136, issue.05, pp.997-1012, 2006.
DOI : 10.1017/S0308210500004844

P. Neff and J. Jeong, A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy, ZAMM, vol.61, issue.8, pp.107-122, 2009.
DOI : 10.1002/zamm.200800156

S. Forest, Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage, Journal of Engineering Mechanics, vol.135, issue.3, pp.117-131, 2009.
DOI : 10.1061/(ASCE)0733-9399(2009)135:3(117)

URL : https://hal.archives-ouvertes.fr/hal-00368014

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. Peano, De latino sine flexione, Lingua auxiliare internationale. Rev Math, vol.8, pp.74-83, 1903.

G. Piola, Honori Amicitiaeque Vincenzij Brunacci, Articolo necrologico inserito nel Fascicolo XXX della Biblioteca Italiana, 1818.

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 and A. Akay, Dissipation in a finite-size bath, Physical Review E, vol.84, issue.1, p.11121, 2011.
DOI : 10.1103/PhysRevE.84.011121

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

A. Carcaterra, A. Akay, and I. Ko, 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, 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 and A. Sestieri, ENERGY DENSITY EQUATIONS AND POWER FLOW IN STRUCTURES, Journal of Sound and Vibration, vol.188, issue.2, pp.269-282, 1995.
DOI : 10.1006/jsvi.1995.0591

F. Dell-'isola and S. Vidoli, Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping, Archive of Applied Mechanics (Ingenieur Archiv), vol.68, issue.1, pp.1-19, 1998.
DOI : 10.1007/s004190050142

URL : https://hal.archives-ouvertes.fr/hal-00495542

F. Dell-'isola and S. Vidoli, Damping of bending waves in truss beams by electrical transmission lines with PZT actuators, Archive of Applied Mechanics (Ingenieur Archiv), vol.68, issue.9, pp.626-636, 1998.
DOI : 10.1007/s004190050192

URL : https://hal.archives-ouvertes.fr/hal-00495549

C. Maurini, F. Isola, D. Vescovo, and D. , Comparison of piezoelectronic networks acting as distributed vibration absorbers, Mechanical Systems and Signal Processing, vol.18, issue.5, pp.1243-1271, 2004.
DOI : 10.1016/S0888-3270(03)00082-7

URL : https://hal.archives-ouvertes.fr/hal-00502098

C. Maurini, J. Pouget, and F. Isola, On a model of layered piezoelectric beams including transverse stress effect, International Journal of Solids and Structures, vol.41, issue.16-17, pp.4473-4502, 2004.
DOI : 10.1016/j.ijsolstr.2004.03.002

URL : https://hal.archives-ouvertes.fr/hal-00503237

T. Levi-civita, A simplified presentation of Einstein's unified field equations. Authorized translation into English, 1929.

T. Levi-civita, Caractéristiques des systèmes différentiels et propagation des ondes. Bologne: Librairie Félix Alcan, 1931.

T. Levi-civita, The absolute differential calculus (calculus of tensors), 1977.

G. Ricci-curbastro and T. Levi-civita, M???thodes de calcul diff???rentiel absolu et leurs applications, Mathematische Annalen, vol.54, issue.1-2, pp.125-201, 1900.
DOI : 10.1007/BF01454201

A. Eringen, Microcontinuum field theories I: Foundations and solids, 1999.

A. Eringen and D. Edelen, On nonlocal elasticity, International Journal of Engineering Science, vol.10, issue.3, pp.233-248, 1972.
DOI : 10.1016/0020-7225(72)90039-0

C. Polizzotto, Nonlocal elasticity and related variational principles, International Journal of Solids and Structures, vol.38, issue.42-43, pp.7359-7380, 2001.
DOI : 10.1016/S0020-7683(01)00039-7

E. Hellinger, Die allgemeinen Ansätze der Mechanik der Kontinua, Encyk Math Wiss, vol.4, issue.5, pp.601-694, 1913.

N. Auffrray, F. Isola, and V. Eremeyev, 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, 2013.
DOI : 10.1177/1081286513497616

D. Steigmann, Frame-Invariant Polyconvex Strain-Energy Functions for Some Anisotropic Solids, Mathematics and Mechanics of Solids, vol.8, issue.5, pp.497-506, 2003.
DOI : 10.1177/10812865030085004

A. Eringen, Nonlocal Continuum Field Theories, Applied Mechanics Reviews, vol.56, issue.2, 2002.
DOI : 10.1115/1.1553434

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

F. Dell-'isola, H. Gouin, and P. Seppecher, Radius and surface tension of microscopic bubbles by second gradient theory, CR Acad Sci, Ser IIb, vol.320, pp.211-216, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00308860

F. Dell-'isola, . Guarascio, and K. Hutter, 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

F. Dell-'isola and P. Seppecher, The relationship between edge contact forces, double force and interstitial working allowed by the principle of virtual power, CR Acad Sci, vol.321, pp.303-308, 1995.

P. Demmie and S. Silling, An approach to modeling extreme loading of structures using peridynamics, Journal of Mechanics of Materials and Structures, vol.2, issue.10, pp.1921-1945, 2007.
DOI : 10.2140/jomms.2007.2.1921

Q. Du, M. Gunzburger, and R. Lehoucq, A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.03, pp.493-540, 2013.
DOI : 10.1142/S0218202512500546

E. Emmrich, R. Lehoucq, and D. Puhst, Peridynamics: A Nonlocal Continuum Theory, Lecture Notes in Computational Science and Engineering, vol.89, pp.45-65, 2013.
DOI : 10.1007/978-3-642-32979-1_3

R. Lehoucq and S. Silling, Force flux and the peridynamic stress tensor, Journal of the Mechanics and Physics of Solids, vol.56, issue.4, pp.1566-1577, 2008.
DOI : 10.1016/j.jmps.2007.08.004

P. Selesonetal2013-seleson, S. Beneddine, and S. Prudhomme, A force-based coupling scheme for peridynamics and classical elasticity, Computational Materials Science, vol.66, pp.34-49, 2013.
DOI : 10.1016/j.commatsci.2012.05.016

S. Silling, M. Epton, and O. Weckner, Peridynamic States and Constitutive Modeling, Journal of Elasticity, vol.6, issue.2, pp.151-184, 2007.
DOI : 10.1007/s10659-007-9125-1

P. Steinmann, On boundary potential energies in deformational and configurational mechanics, Journal of the Mechanics and Physics of Solids, vol.56, issue.3, pp.772-780, 2008.
DOI : 10.1016/j.jmps.2007.07.001

P. Steinmann, A. Elizondo, and R. Sunyk, Studies of validity of the Cauchy???Born rule by direct comparison of continuum and atomistic modelling, Modelling and Simulation in Materials Science and Engineering, vol.15, issue.1, pp.271-281, 2007.
DOI : 10.1088/0965-0393/15/1/S21

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

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, 2013.
DOI : 10.1002/zamm.201200182

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

A. Madeo, D. George, and T. Lekszycki, A second gradient continuum model accounting for some effects of micro-structure on reconstructed bone remodelling, Comptes Rendus M??canique, vol.340, issue.8, pp.575-589, 2012.
DOI : 10.1016/j.crme.2012.05.003

A. Madeo, T. Lekszycki, and F. Isola, A continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery, Comptes Rendus M??canique, vol.339, issue.10, pp.625-640, 2011.
DOI : 10.1016/j.crme.2011.07.004

URL : https://hal.archives-ouvertes.fr/hal-00609793

S. Silling and R. Lehoucq, Convergence of Peridynamics to Classical Elasticity Theory, Journal of Elasticity, vol.38, issue.1, pp.13-37, 2008.
DOI : 10.1007/s10659-008-9163-3

D. Steigmann, Invariants of the Stretch Tensors and their Application to Finite Elasticity Theory, Mathematics and Mechanics of Solids, vol.7, issue.4, pp.393-404, 2002.
DOI : 10.1177/108128028481

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, pp.1119-1141, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00662376

P. Neff, A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS, Mathematical Models and Methods in Applied Sciences, vol.17, issue.03, pp.363-392, 2007.
DOI : 10.1142/S0218202507001954

P. Neff, On Korn's first inequality with non-constant coefficients, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.132, issue.01, pp.221-243, 2002.
DOI : 10.1017/S0308210500001591

P. Neff, The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric, ZAMM, vol.17, issue.1, pp.892-912, 2006.
DOI : 10.1002/zamm.200510281

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 Course and Lectures, pp.1-16, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00607746

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

L. Sedov, Models of continuous media with internal degrees of freedom, Journal of Applied Mathematics and Mechanics, vol.32, issue.5, pp.803-819, 1972.
DOI : 10.1016/0021-8928(68)90001-4

L. Sedov, Variational Methods of Constructing Models of Continuous Media, pp.346-358, 1968.
DOI : 10.1007/978-3-7091-5581-3_23

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

R. Gatignol and P. Seppecher, Modelisation of fluid-fluid interfaces with material properties, J Mec Theor Appl ; Special number, pp.225-247, 1986.

A. Madeo and S. Gavrilyuk, Propagation of acoustic waves in porous media and their reflection and transmission at a pure-fluid/porous-medium permeable interface, European Journal of Mechanics - A/Solids, vol.29, issue.5, pp.897-910, 2010.
DOI : 10.1016/j.euromechsol.2010.05.004

URL : https://hal.archives-ouvertes.fr/hal-00659527

P. Seppecher, Moving contact lines in the Cahn-Hilliard theory, International Journal of Engineering Science, vol.34, issue.9, pp.977-992, 1996.
DOI : 10.1016/0020-7225(95)00141-7

URL : https://hal.archives-ouvertes.fr/hal-00527283

G. Rosi, A. Madeo, and J. Guyader, Switch between fast and slow Biot compression waves induced by ???second gradient microstructure??? at material discontinuity surfaces in porous media, International Journal of Solids and Structures, vol.50, issue.10, pp.1721-1746, 2013.
DOI : 10.1016/j.ijsolstr.2013.01.038

URL : https://hal.archives-ouvertes.fr/hal-00926066

P. Seppecher, Etude d'une modelisation des zones capillaires fluides: Interfaces et lignes de contact, 1987.
URL : https://hal.archives-ouvertes.fr/tel-00522117

Y. Yang, W. Ching, and A. Misra, Higher-Order Continuum Theory Applied to Fracture Simulation of Nanoscale Intergranular Glassy Film, Journal of Nanomechanics and Micromechanics, vol.1, issue.2, pp.60-71, 2011.
DOI : 10.1061/(ASCE)NM.2153-5477.0000030

URL : https://hal.archives-ouvertes.fr/hal-00556184

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

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

V. Yeremeyev, . Freidin, and L. Sharipova, The stability of the equilibrium of two-phase elastic solids, Journal of Applied Mathematics and Mechanics, vol.71, issue.1, pp.61-84, 2007.
DOI : 10.1016/j.jappmathmech.2007.03.007

URL : https://hal.archives-ouvertes.fr/hal-00831678

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

P. Seppecher, Etude des conditions aux limites en théorie du second gradient: Cas de la capillarité, CR Acad Sci, vol.309, pp.497-502, 1989.

P. Seppecher, Les fluides de Cahn-Hilliard. Memoir, 1996.
URL : https://hal.archives-ouvertes.fr/tel-00522242

P. Seppecher, Line Tension Effect Upon Static Wetting, Oil & Gas Science and Technology, vol.56, issue.1, pp.77-81, 2001.
DOI : 10.2516/ogst:2001009

P. Seppecher, Second-gradient theory: Application to Cahn-Hilliard fluids In:Continuum thermomechanics (Solid Mechanics and its Applications, pp.379-388, 2002.

P. Seppecher, Thermodynamique des zones capillaires, Ann Phys, vol.13, pp.13-22, 1988.

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

A. Atai and D. Steigmann, On the nonlinear mechanics of discrete networks, Archive of Applied Mechanics (Ingenieur Archiv), vol.67, issue.5, pp.303-319, 1997.
DOI : 10.1007/s004190050119

E. Haseganu and D. Steigmann, Equilibrium analysis of finitely deformed elastic networks, Computational Mechanics, vol.335, issue.6, pp.359-373, 1996.
DOI : 10.1007/BF00363980

V. Eremeyev, A. Freidin, and L. Sharipova, Nonuniqueness and stability in problems of equilibrium of elastic two-phase bodies, Doklady Physics, vol.48, issue.7, pp.359-363, 2003.
DOI : 10.1134/1.1598247

V. Eremeyev and L. Lebedev, Existence of weak solutions in elasticity, Mathematics and Mechanics of Solids, vol.18, issue.2, pp.204-217, 2013.
DOI : 10.1177/1081286512462187

URL : https://hal.archives-ouvertes.fr/hal-00831088

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

V. Eremeyev and W. Pietraszkiewicz, Thermomechanics of shells undergoing phase transition, Journal of the Mechanics and Physics of Solids, vol.59, issue.7, pp.1395-1412, 2011.
DOI : 10.1016/j.jmps.2011.04.005

URL : https://hal.archives-ouvertes.fr/hal-00835667

A. Madeo, I. Djeran-maigre, and G. Rosi, The effect of fluid streams in porous media on acoustic compression wave propagation, transmission, and reflection, Continuum Mechanics and Thermodynamics, vol.35, issue.3, pp.2-4, 2013.
DOI : 10.1007/s00161-012-0236-y

URL : https://hal.archives-ouvertes.fr/hal-01293274

W. Pietraszkiewicz, . Eremeyev, . Va, and V. Konopinska, Extended non-linear relations of elastic shells undergoing phase transitions, ZAMM, vol.58, issue.2, pp.150-159, 2007.
DOI : 10.1002/zamm.200610309

URL : https://hal.archives-ouvertes.fr/hal-00831047

P. Neff, A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus, Continuum Mechanics and Thermodynamics, vol.36, issue.6, pp.577-628, 2004.
DOI : 10.1007/s00161-004-0182-4

P. Neff and K. Che?mi´nskiche?mi´nski, A geometrically exact Cosserat shell-model for defective elastic crystals. Justification via ??-convergence, Interfaces and Free Boundaries, vol.9, issue.4, pp.455-492, 2007.
DOI : 10.4171/IFB/173

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

A. Mcbride, A. Javili, and P. Steinmann, Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion, Journal of the Mechanics and Physics of Solids, vol.59, issue.10, pp.2116-2133, 2011.
DOI : 10.1016/j.jmps.2011.06.002

A. Mcbride, J. Mergheim, and A. Javili, Micro-to-macro transitions for heterogeneous material layers accounting for in-plane stretch, Journal of the Mechanics and Physics of Solids, vol.60, issue.6, pp.1221-1239, 2012.
DOI : 10.1016/j.jmps.2012.01.003

L. Placidi, G. Rosi, and I. Giorgio, Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials. Math Mech Solids. Epub ahead of print 4, pp.10-1177, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01167200

H. Steeb and S. Diebels, Modeling thin films applying an extended continuum theory based on a scalar-valued order parameter., International Journal of Solids and Structures, vol.41, issue.18-19, pp.5071-5085, 2004.
DOI : 10.1016/j.ijsolstr.2004.03.013

D. Steigmann, A Concise Derivation of Membrane Theory from??Three-Dimensional Nonlinear Elasticity, Journal of Elasticity, vol.54, issue.79, pp.97-101, 2009.
DOI : 10.1007/s10659-009-9209-1

URL : https://hal.archives-ouvertes.fr/hal-00773265

D. Steigmann and R. Ogden, Elastic surface--substrate interactions, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.455, issue.1982, pp.437-474, 1982.
DOI : 10.1098/rspa.1999.0320

D. Steigmann and R. Ogden, Plane deformations of elastic solids with intrinsic boundary elasticity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.453, issue.1959, pp.853-877, 1959.
DOI : 10.1098/rspa.1997.0047

A. Luongo, D. Egidio, and A. , Bifurcation Equations Through Multiple-Scales Analysis for a Continuous Model of a Planar Beam, Nonlinear Dynamics, vol.77, issue.1, pp.171-190, 2005.
DOI : 10.1007/s11071-005-2804-1

URL : https://hal.archives-ouvertes.fr/hal-00790794

A. Luongo, R. , and F. , A Transfer-Matrix-Perturbation Approach to the Dynamics of Chains of Nonlinear Sliding Beams, Journal of Vibration and Acoustics, vol.128, issue.2, pp.190-196, 2006.
DOI : 10.1115/1.2159034

URL : https://hal.archives-ouvertes.fr/hal-00790182

A. Luongo, . Zulli, and G. Piccardo, On the effect of twist angle on nonlinear galloping of suspended cables, Computers & Structures, vol.87, issue.15-16, pp.1003-1014, 2009.
DOI : 10.1016/j.compstruc.2008.04.014

URL : https://hal.archives-ouvertes.fr/hal-00788461

D. Steigmann, Equilibrium of prestressed networks, IMA Journal of Applied Mathematics, vol.48, issue.2, pp.195-215, 1992.
DOI : 10.1093/imamat/48.2.195

D. Steigmann, The variational structure of a nonlinear theory for spatial lattices, Meccanica, vol.32, issue.4, pp.441-455, 1996.
DOI : 10.1007/BF00429932

URL : https://hal.archives-ouvertes.fr/hal-00782160

D. Steigmann and M. Faulkner, Variational theory for spatial rods, Journal of Elasticity, vol.61, issue.1, pp.1-26, 1993.
DOI : 10.1007/BF00042633

URL : https://hal.archives-ouvertes.fr/hal-00782186

C. Boutin, S. Hans, C. , and C. , Generalized Beams and Continua. Dynamics??of??Reticulated Structures, Advances in Mechanics and Mathematics, vol.21, pp.131-141, 2011.
DOI : 10.1007/978-1-4419-5695-8_14

URL : https://hal.archives-ouvertes.fr/hal-00941153

C. Boutin, H. , and S. , Homogenisation of periodic discrete medium: Application to dynamics of framed structures, Computers and Geotechnics, vol.30, issue.4, pp.303-320, 2003.
DOI : 10.1016/S0266-352X(03)00005-3

C. Chesnais, . Boutin, and S. Hans, Effects of the local resonance on the wave propagation in periodic frame structures: Generalized Newtonian mechanics, The Journal of the Acoustical Society of America, vol.132, issue.4, pp.2873-2886, 2012.
DOI : 10.1121/1.4744975

URL : https://hal.archives-ouvertes.fr/hal-00853842

L. Contrafatto and M. Cuomo, A framework of elastic???plastic damaging model for concrete under multiaxial stress states, International Journal of Plasticity, vol.22, issue.12, pp.2272-2300, 2006.
DOI : 10.1016/j.ijplas.2006.03.011

URL : https://hal.archives-ouvertes.fr/hal-00878684

L. Contrafatto and M. Cuomo, A globally convergent numerical algorithm for damaging elasto-plasticity based on the Multiplier method, International Journal for Numerical Methods in Engineering, vol.28, issue.8, pp.1089-1125, 2005.
DOI : 10.1002/nme.1235

URL : https://hal.archives-ouvertes.fr/hal-00878215

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

M. Cuomo, C. , and L. , Stress rate formulation for elastoplastic models with internal variables based on augmented Lagrangian regularisation, International Journal of Solids and Structures, vol.37, issue.29, pp.3935-3964, 2000.
DOI : 10.1016/S0020-7683(99)00163-8

URL : https://hal.archives-ouvertes.fr/hal-00913269

M. Cuomo and G. Ventura, Complementary energy approach to contact problems based on consistent augmented Lagrangian formulation, Mathematical and Computer Modelling, vol.28, issue.4-8, pp.185-204, 1998.
DOI : 10.1016/S0895-7177(98)00117-4

URL : https://hal.archives-ouvertes.fr/hal-00913282

A. Misra, C. , and C. , 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

A. Misra, C. , and W. , Theoretical nonlinear response of complex single crystal under multi-axial tensile loading, Scientific Reports, vol.77, p.1488, 2013.
DOI : 10.1038/srep01488

A. Misra and V. Singh, Micromechanical model for viscoelastic materials undergoing damage, Continuum Mechanics and Thermodynamics, vol.22, issue.2, pp.1-16, 2013.
DOI : 10.1007/s00161-012-0262-9

A. Misra, Y. , and Y. , Micromechanical model for cohesive materials based upon pseudo-granular structure, International Journal of Solids and Structures, vol.47, issue.21, pp.2970-2981, 2010.
DOI : 10.1016/j.ijsolstr.2010.07.002

URL : https://hal.archives-ouvertes.fr/hal-00556078

A. Rinaldi, L. , and Y. , Statistical damage theory of 2D lattices: Energetics and physical foundations of damage parameter, International Journal of Plasticity, vol.23, issue.10-11, pp.1796-1825, 2007.
DOI : 10.1016/j.ijplas.2007.03.005

A. Rinaldi, D. Krajcinovic, and P. Peralta, Lattice models of polycrystalline microstructures: A quantitative approach, Mechanics of Materials, vol.40, issue.1-2, pp.17-36, 2008.
DOI : 10.1016/j.mechmat.2007.02.005

B. Nadler, . Papadopoulos, and D. Steigmann, Multiscale constitutive modeling and numerical simulation of fabric material, International Journal of Solids and Structures, vol.43, issue.2, pp.206-221, 2006.
DOI : 10.1016/j.ijsolstr.2005.05.020

M. Epstein, The geometrical language of continuum mechanics, 2010.
DOI : 10.1017/CBO9780511762673

M. Epstein and R. Segev, Differentiable manifolds and the principle of virtual work in continuum mechanics, Journal of Mathematical Physics, vol.21, issue.5, pp.1243-1245, 1980.
DOI : 10.1063/1.524516

R. Segev, Forces and the existence of stresses in invariant continuum mechanics, Journal of Mathematical Physics, vol.27, issue.1, pp.163-170, 1986.
DOI : 10.1063/1.527406

URL : https://hal.archives-ouvertes.fr/hal-00957447

R. Segev, The Geometry of Cauchy's Fluxes, Archive for Rational Mechanics and Analysis, vol.154, issue.3, pp.183-198, 2000.
DOI : 10.1007/s002050000089

M. Spivak, A comprehensive introduction to differential geometry, 1979.

M. Spivak, A comprehensive introduction to differential geometry, 1979.