A. Pipkin, PLANE TRACTION PROBLEMS FOR INEXTENSIBLE NETWORKS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.34, issue.4, pp.415-429, 1981.
DOI : 10.1093/qjmam/34.4.415

R. Rivlin, Plane strain of a net formed by inextensible cords, Collected Papers of RS Rivlin, pp.511-534, 1997.

S. Forest, Mechanics of generalized continua: construction by homogenizaton, Le Journal de Physique IV, vol.08, issue.PR4, pp.4-39, 1998.
DOI : 10.1051/jp4:1998405

L. Placidi, G. Rosi, I. Giorgio, and A. Madeo, Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials, Mathematics and Mechanics of Solids, vol.19, issue.5, pp.555-578, 2014.
DOI : 10.1177/1081286512474016
URL : https://hal.archives-ouvertes.fr/hal-01167200

P. Neff, K. Che?mi?ski, and H. Alber, NOTES ON STRAIN GRADIENT PLASTICITY: FINITE STRAIN COVARIANT MODELLING AND GLOBAL EXISTENCE IN THE INFINITESIMAL RATE-INDEPENDENT CASE, Mathematical Models and Methods in Applied Sciences, vol.19, issue.02, pp.307-346, 2009.
DOI : 10.1142/S0218202509003449

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

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, Mathematics and Mechanics of Solids, vol.20, issue.8, pp.887-928, 2014.
DOI : 10.1177/1081286513509811
URL : https://hal.archives-ouvertes.fr/hal-00869677

M. Assidi, B. B. Boubaker, and J. F. Ganghoffer, Equivalent properties of monolayer fabric from mesoscopic modelling strategies, International Journal of Solids and Structures, vol.48, issue.20, pp.482920-2930, 2011.
DOI : 10.1016/j.ijsolstr.2011.06.010

F. , D. Reis, and J. F. Ganghoffer, Equivalent mechanical properties of auxetic lattices from discrete homogenization, Computational Materials Science, vol.51, pp.314-321, 2012.

F. Dell, D. Isola, and . Steigmann, A two-dimensional gradient-elasticity theory for woven fabrics, Journal of Elasticity, vol.118, issue.1, pp.113-125, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00997790

J. Altenbach, H. Altenbach, A. Victor, and . 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, 2010.
DOI : 10.1007/s00419-009-0365-3
URL : https://hal.archives-ouvertes.fr/hal-00827365

E. Garusi, A. Tralli, and A. Cazzani, AN UNSYMMETRIC STRESS FORMULATION FOR REISSNER-MINDLIN PLATES: A SIMPLE AND LOCKING-FREE RECTANGULAR ELEMENT, International Journal of Computational Engineering Science, vol.05, issue.03, pp.589-618, 2004.
DOI : 10.1142/S1465876304002587

A. Rinaldi and L. Placidi, A microscale second gradient approximation of the damage parameter of quasi-brittle heterogeneous lattices, ZAMM -Zeitschrift für Angewandte Mathematik und Mechanik, 2013.
DOI : 10.1002/zamm.201300028

S. Federico, A. Grillo, and W. Herzog, A transversely isotropic composite with a statistical distribution of spheroidal inclusions: a geometrical approach to overall properties, Journal of the Mechanics and Physics of Solids, vol.52, issue.10, pp.2309-2327, 2004.
DOI : 10.1016/j.jmps.2004.03.010

P. Neff, On material constants for micromorphic continua, Applications of Mathematics to Mechanics, STAMM Proceedings, Seeheim, pp.337-348, 2004.

C. Boutin, Microstructural effects in elastic composites, International Journal of Solids and Structures, vol.33, issue.7, pp.1023-1051, 1996.
DOI : 10.1016/0020-7683(95)00089-5
URL : https://hal.archives-ouvertes.fr/hal-00940462

S. Federico, On the linear elasticity of porous materials, International Journal of Mechanical Sciences, vol.52, issue.2, pp.175-182, 2010.
DOI : 10.1016/j.ijmecsci.2009.09.006

P. Neff, I. Ghiba, A. Madeo, L. Placidi, and G. Rosi, A unifying perspective: the relaxed linear micromorphic continuum, Continuum Mechanics and Thermodynamics, vol.44, issue.1, pp.1-43, 2013.
DOI : 10.1007/s00161-013-0322-9
URL : https://hal.archives-ouvertes.fr/hal-01167202

L. Placidi and K. Hutter, Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity, Continuum Mechanics and Thermodynamics, vol.399, issue.152, pp.409-451, 2006.
DOI : 10.1007/s00161-005-0006-1

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

P. Neff and S. Forest, A Geometrically Exact Micromorphic Model for Elastic Metallic Foams Accounting for Affine Microstructure. Modelling, Existence of Minimizers, Identification of Moduli and Computational Results, Journal of Elasticity, vol.103, issue.8, pp.239-276, 2007.
DOI : 10.1007/s10659-007-9106-4
URL : https://hal.archives-ouvertes.fr/hal-00165821

R. D. Mindlin, Micro-structure in linear elasticity Archive for Rational Mechanics and Analysis, pp.51-78, 1964.

A. Misra and Y. Yang, 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. Madeo, P. Neff, L. Ghiba, G. Placidi, and . Rosi, Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps, Continuum Mechanics and Thermodynamics, vol.49, issue.3, pp.1-20, 2013.
DOI : 10.1007/s00161-013-0329-2

M. Ferretti, A. Madeo, F. Dell-'isola, and P. Boisse, Modeling the onset of shear boundary layers in fibrous composite reinforcements by second-gradient theory, Zeitschrift für angewandte Mathematik und Physik, pp.587-612, 2014.
DOI : 10.1007/s00033-013-0347-8
URL : https://hal.archives-ouvertes.fr/hal-00934569

P. Seppecher, J. Alibert, and F. D. Isola, Linear elastic trusses leading to continua with exotic mechanical interactions, Journal of Physics: Conference Series, p.12018, 2011.
DOI : 10.1088/1742-6596/319/1/012018
URL : https://hal.archives-ouvertes.fr/hal-00630098

A. Grillo, S. Federico, G. Wittum, S. Imatani, G. Giaquinta et al., Evolution of a fibre-reinforced growing mixture, Nuovo Cimento C, vol.32, issue.1, pp.97-119, 2009.

A. Grillo, G. Wittum, A. Tomic, and S. Federico, Remodelling in statistically oriented fibrereinforced materials and biological tissues Mathematics and Mechanics of Solids, pp.10-1177, 2014.

A. Grillo, S. Federico, and G. Wittum, Growth, mass transfer, and remodeling in fiber-reinforced, multi-constituent materials, International Journal of Non-Linear Mechanics, vol.47, issue.2, pp.388-401, 2012.
DOI : 10.1016/j.ijnonlinmec.2011.09.026

N. Hamila and P. Boisse, Locking in simulation of composite reinforcement deformations. Analysis and treatment, Composites Part A: Applied Science and Manufacturing, vol.53, pp.109-117, 2013.
DOI : 10.1016/j.compositesa.2013.06.001
URL : https://hal.archives-ouvertes.fr/hal-00934483

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

D. Scerrato, I. Giorgio, A. Madeo, A. Limam, and F. Darve, A simple non-linear model for internal friction in modified concrete, International Journal of Engineering Science, vol.80, pp.136-152, 2014.
DOI : 10.1016/j.ijengsci.2014.02.021
URL : https://hal.archives-ouvertes.fr/hal-00864497

C. P. Laurent, D. Durville, C. Vaquette, R. Rahouadj, and J. F. Ganghoffer, Computer-Aided Tissue Engineering: Application to the Case of Anterior Cruciate Ligament Repair, Biomechanics of Cells and Tissues, vol.9, pp.1-44, 2013.
DOI : 10.1007/978-94-007-5890-2_1
URL : https://hal.archives-ouvertes.fr/hal-00825072

C. P. Laurent, D. Durville, D. Mainard, J. Ganghoffer, and R. Rahouadj, Designing a new scaffold for anterior cruciate ligament tissue engineering, Computer Methods in Biomechanics and Biomedical Engineering, vol.13, issue.sup1, pp.184-196, 2012.
DOI : 10.1016/j.jbiomech.2009.07.019

C. P. Laurent, D. Durville, X. Wang, J. Ganghoffer, and R. Rahouadj, Designing a new scaffold for anterior cruciate ligament tissue engineering, Computer Methods in Biomechanics and Biomedical Engineering, vol.13, issue.sup1, pp.87-88, 2010.
DOI : 10.1016/j.jbiomech.2009.07.019

I. Goda, M. Assidi, S. Belouettar, and J. F. Ganghoffer, A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization, Journal of the Mechanical Behavior of Biomedical Materials, vol.16, pp.87-108, 2012.
DOI : 10.1016/j.jmbbm.2012.07.012

S. J. Hollister, Porous scaffold design for tissue engineering, Nature Materials, vol.51, issue.7, pp.518-524, 2005.
DOI : 10.1097/00006123-200209000-00024

A. Grillo and G. Wittum, Growth and Mass Transfer in Multi-Constituent Biological Materials, AIP Conference Proceedings, vol.1281, issue.1, pp.355-358, 2010.
DOI : 10.1063/1.3498474
URL : http://porto.polito.it/2499112/1/GrilloWittum_AIP.pdf

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 -Zeitschrift für Angewandte Mathematik und Mechanik, pp.94978-1000, 2014.
DOI : 10.1002/zamm.201200182
URL : https://hal.archives-ouvertes.fr/hal-00842604

I. Giorgio, U. Andreaus, and A. Madeo, The influence of different loads on the remodeling process of a bone and bio-resorbable material mixture with voids. Continuum Mechanics and Thermodynamics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01094868

F. Dell-'isola, M. D. Agostino, A. Madeo, P. Boisse, and D. Steigmann, Minimization of shear energy in two dimensional continua with two orthogonal families of inextensible fibers: the case of standard bias extension test, Journal of Elasticity, pp.10-1007, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01176313

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, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00607746

L. Placidi, A variational approach for a nonlinear one-dimensional damage-elasto-plastic secondgradient continuum model, Continuum Mechanics and Thermodynamics, p.23

L. Placidi, A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Continuum Mechanics and Thermodynamics, Published online, 2014.

M. John and . Ball, Convexity conditions and existence theorems in nonlinear elasticity Archive for rational mechanics and Analysis, pp.337-403, 1976.

A. Victor, . Eremeyev, P. Leonid, and . Lebedev, Existence of weak solutions in elasticity, Mathematics and Mechanics of Solids, vol.18, issue.2, pp.204-217, 2013.

S. Federico, Volumetric-Distortional Decomposition of Deformation and Elasticity Tensor, Mathematics and Mechanics of Solids, vol.15, issue.6, pp.672-690, 2010.
DOI : 10.1177/1081286509105591

S. Federico, A. Grillo, and S. Imatani, The linear elasticity tensor of

V. A. Yeremeyev, A. B. Freidin, and L. 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

W. Pietraszkiewicz, V. Eremeyev, and V. Konopi?ska, Extended non-linear relations of elastic shells undergoing phase transitions, ZAMM -Zeitschrift für Angewandte Mathematik und Mechanik, pp.150-159, 2007.
DOI : 10.1002/zamm.200610309
URL : https://hal.archives-ouvertes.fr/hal-00831047

V. A. Eremeyev and W. Pietraszkiewicz, Phase transitions in thermoelastic and thermoviscoelastic shells, Archives of Mechanics, vol.61, issue.1, pp.41-67, 2009.
DOI : 10.1007/978-94-007-2739-7_915
URL : https://hal.archives-ouvertes.fr/hal-00826796

V. A. 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. Luongo, Perturbation methods for nonlinear autonomous discrete-time dynamical systems, Nonlinear Dynamics, vol.7, issue.3, pp.317-331, 1996.
DOI : 10.1007/BF00045480

E. Turco and P. Caracciolo, Elasto-plastic analysis of Kirchhoff plates by high simplicity finite elements, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.5-7, pp.5-7691, 2000.
DOI : 10.1016/S0045-7825(99)00438-7

A. Cazzani, M. Malagù, and E. Turco, Isogeometric analysis of plane-curved beams Mathematics and Mechanics of Solids, pp.10-1177, 2014.

L. Greco, N. Impollonia, and M. Cuomo, A procedure for the static analysis of cable structures following elastic catenary theory, International Journal of Solids and Structures, vol.51, issue.7-8, pp.1521-1533, 2014.
DOI : 10.1016/j.ijsolstr.2014.01.001
URL : https://hal.archives-ouvertes.fr/hal-00954208

L. Carassale and G. Piccardo, Non-linear discrete models for the stochastic analysis of cables in turbulent wind, International Journal of Non-Linear Mechanics, vol.45, issue.3, pp.219-231, 2010.
DOI : 10.1016/j.ijnonlinmec.2009.11.002

A. Cazzani and M. Rovati, Sensitivity analysis and optimum design of elastic-plastic structural systems, Meccanica, vol.81, issue.1?3, pp.173-178, 1991.
DOI : 10.1007/BF00429886

B. Descamps, Computational Design of Lightweight Structures: Form Finding and Optimization, 2014.
DOI : 10.1002/9781118908860

U. Andreaus and M. Colloca, Prediction of micromotion initiation of an implanted femur under physiological loads and constraints using the finite element method, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, vol.59, issue.5, pp.589-605, 2009.
DOI : 10.1243/09544119JEIM559

L. Greco and M. Cuomo, B-Spline interpolation of Kirchhoff-Love space rods, Computer Methods in Applied Mechanics and Engineering, vol.256, issue.0, pp.251-269, 2013.
DOI : 10.1016/j.cma.2012.11.017
URL : https://hal.archives-ouvertes.fr/hal-00874611

L. Greco and M. Cuomo, An implicit multi patch B-spline interpolation for Kirchhoff???Love space rod, Computer Methods in Applied Mechanics and Engineering, vol.269, issue.0, pp.173-197, 2014.
DOI : 10.1016/j.cma.2013.09.018
URL : https://hal.archives-ouvertes.fr/hal-00874299

A. Javili and P. Steinmann, A finite element framework for continua with boundary energies. Part I: The two-dimensional case, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.27-29, pp.2198-2208, 2009.
DOI : 10.1016/j.cma.2009.02.008

A. Javili and P. Steinmann, A finite element framework for continua with boundary energies. Part II: The three-dimensional case, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.9-12, pp.755-765, 2010.
DOI : 10.1016/j.cma.2009.11.003

A. Berezovski, I. Giorgio, and A. D. Corte, Interfaces in micromorphic materials: Wave transmission and reflection with numerical simulations, Mathematics and Mechanics of Solids, vol.21, issue.1, pp.10-1177, 2015.
DOI : 10.1177/1081286515572244
URL : https://hal.archives-ouvertes.fr/hal-01194376

U. Andreaus, M. Colloca, and D. Iacoviello, Modeling of Trabecular Architecture as Result of an Optimal Control Procedure, Lecture Notes in Computational Vision and Biomechanics, vol.4
DOI : 10.1007/978-94-007-4270-3_2

U. Andreaus, M. Colloca, and D. Iacoviello, An optimal control procedure for bone adaptation under mechanical stimulus, Control Engineering Practice, vol.20, issue.6, pp.575-583, 2012.
DOI : 10.1016/j.conengprac.2012.02.002

U. Andreaus, M. Colloca, D. Iacoviello, and M. Pignataro, Optimal-tuning pid control of adaptive materials for structural efficiency. Structural and Multidisciplinary Optimization, pp.43-59, 2011.

V. Eremeyev, Nonlinear micropolar shells: theory and applications. Shell structures: Theory and applications, pp.11-18, 2005.

V. Eremeyev and N. Morozov, The effective stiffness of a nanoporous rod, Doklady Physics, pp.279-282, 2010.
DOI : 10.1134/S102833581006008X
URL : https://hal.archives-ouvertes.fr/hal-00831244

. Holm-altenbach, A. Victor, N. F. Eremeyev, and . Morozov, Mechanical Properties of Materials Considering Surface Effects, IUTAM Symposium on Surface Effects in the Mechanics of Nanomaterials and Heterostructures, pp.105-115, 2013.
DOI : 10.1007/978-94-007-4911-5_9

M. Bîrsan, H. Altenbach, T. Sadowski, D. Va-eremeyev, and . Pietras, Deformation analysis of functionally graded beams by the direct approach, Composites Part B: Engineering, vol.43, issue.3, pp.1315-1328, 2012.
DOI : 10.1016/j.compositesb.2011.09.003

G. Piccardo, G. Ranzi, and A. Luongo, A complete dynamic approach to the Generalized Beam Theory cross-section analysis including extension and shear modes, Mathematics and Mechanics of Solids, vol.19, issue.8, pp.900-924, 2014.
DOI : 10.1177/1081286513493107

G. Piccardo and F. Tubino, Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads, Structural Engineering and Mechanics, vol.44, issue.5, pp.681-704, 2012.
DOI : 10.12989/sem.2012.44.5.681

C. Boutin, S. Hans, and C. Chesnais, Generalized Beams and Continua. Dynamics??of??Reticulated Structures, Mechanics of Generalized Continua, pp.131-141, 2010.
DOI : 10.1007/978-1-4419-5695-8_14
URL : https://hal.archives-ouvertes.fr/hal-00941153

I. Giorgio, A. Culla, and D. D. Vescovo, Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network, Archive of Applied Mechanics, vol.15, issue.5, pp.859-879, 2009.
DOI : 10.1007/s00419-008-0258-x
URL : https://hal.archives-ouvertes.fr/hal-00798627

D. , D. Vescovo, and I. Giorgio, Dynamic problems for metamaterials: review of existing models and ideas for further research, International Journal of Engineering Science, vol.80, pp.153-172, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00947477

A. Luongo, D. Zulli, and G. Piccardo, A linear curved-beam model for the analysis of galloping in suspended cables, Journal of Mechanics of Materials and Structures, vol.2, issue.4, pp.675-694, 2007.
DOI : 10.2140/jomms.2007.2.675
URL : https://hal.archives-ouvertes.fr/hal-00789166

G. Piccardo, L. C. Pagnini, and F. Tubino, Some research perspectives in galloping phenomena: critical conditions and post-critical behavior, Continuum Mechanics and Thermodynamics, vol.61, issue.11, pp.261-285, 2015.
DOI : 10.1007/s00161-014-0374-5