. Chapter, Based on the comparison of the numerical solutions computed with the same material properties on different geometries, we show to which extent (much more than what was expected) the 'shape effect' influences the coupled behavior of an MRE-based structure. Such a result suggests that any simplification of the geometry to numerically simulate an MRE boundary value problem (in particular the magnetostriction test) doesn't provide a correct solution. The only option left in the fitting procedure is to simulate the full geometry and compare the obtained solution with experimental data, Modeling and Identification of the constitutive behavior of Magnetorheological Elastomers

F. .. Theory,

. , Form of energy density functions

F. .. Theory,

. , 2 Form of energy density functions

. , Solving a boundary value problem

. , for the perturbed magnetic vector potential A

. , Coupled magneto-mechanical patch test on an infinite medium (uniform field case), IV.5.3

. , Coupled magneto-mechanical patch test on a sphere (non-uniform field case), IV.5.4

I. V. Appendix and .. .. Complement-for-the-f-b-theory,

, Metallic materials Tensile testing Part 1: Method of test at room temperature. International Organization for Standardization, p.31, 2016.

J. E. Adkins, Symmetry relations for orthotropic and transversely isotropic materials, Archive for Rational Mechanics and Analysis, vol.4, issue.1, pp.193-213, 1959.

J. E. Adkins, Further symmetry relations for transversely isotropic materials, Archive for Rational Mechanics and Analysis, vol.5, issue.1, pp.263-274, 1960.

. Th, M. Alshuth, R. H. Ramspeck, B. Schuster, F. Halbedel et al., Magnetorheologische elastomere: Einfluss der partikelausrichtung auf die schaltbarkeit, Kautschuk Gummi Kunststoffe, p.12, 2007.

P. S. Antonel, G. Jorge, O. E. Perez, A. Butera, and A. G. Leyva, Magnetic and elastic properties of CoFe 2 O 4-polydimethylsiloxane magnetically oriented elastomer nanocomposites, Journal of Applied Physics, vol.110, issue.043920, p.12, 2011.

G. Ausanio, C. L. Hison, V. Iannotti, L. Lanotte, and L. Lanotte, Magnetopiezoresistance in elastomagnetic composites, Journal of Applied Physics, vol.110, issue.063903, pp.1-5, 2011.

G. Ausanio, V. Iannotti, E. Ricciardi, L. Lanotte, and L. Lanotte, Magnetopiezoresistance in magnetorheological elastomersfor magnetic induction gradient or position sensors, Sensors and Actuators A, vol.205, p.11, 2014.

Y. Bar-cohen, Electroactive Polymer (EAP) Actuators as Artificial Muscles: Reality, Potential, and Challenges. SPIE, the International society for Optical Engineering, vol.10, 2004.

C. Bellan and G. Bossis, Field dependence of viscoelastic properties of mr elastomers, Journal of Modern Physics B, vol.16, pp.2447-2453, 2002.

A. Bergander, J. Lozada, T. Pössinger, and S. Roselier, EP 2504607 A2. Translatably and rotably semi-active device, p.24, 2012.

I. Bica, Magnetoresistor sensor with magnetorheological elastomers, Journal of Industrial and Engineering Chemistry, vol.17, p.11, 2011.

O. Biro and K. Preis, On the use of the magnetic vector potential in the finiteelement analysis of three-dimensional eddy currents, IEEE Transactions on Magnetics, vol.25, issue.4, p.91, 1989.

A. Boczkowska and S. Awietjan, Microstructure and properties of magnetorheological elastomers, vol.29, pp.147-180, 2012.

L. Bodelot, J. Voropaieff, and T. Pössinger, Experimental investigation of the coupled magneto-mechanical response in magnetorheological elastomers, Experimental Mechanics, vol.58, issue.2, pp.207-221, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01635196

C. Bolzmacher, G. Changeon, V. Plaud, S. Roselier, J. Lozada et al., Tactile refreshable screen based on magneto-rheological fluids for map exploration and navigation tasks, SPIE Proceedings, vol.8066, p.13, 2011.

T. Borbath, S. Günther, D. Y. Borin, . Th, S. Gundermann et al., X-ray microtomographic analysis of magnetic field-induced phase transitions in magnetorheological elastomers, Smart Materials and Structures, vol.21, p.12, 2012.

L. Borcea and O. Bruno, On the magneto-elastic properties of elastomer-ferromagnet composites, Journal of the Mechanics and Physics of Solids, vol.49, pp.2877-2919, 2001.

H. Böse, Viscoelastic properties of silicone-based magnetorheological elastomers, Journal of Modern Physics B, vol.21, issue.29, pp.4790-4797, 2007.

H. Böse, R. Rabindranath, and J. Ehrlich, Soft magnetorheological elastomers as new actuators for valves, Journal of Intelligent Material Systems and Structures, vol.23, issue.9, p.14, 2012.

G. Bossis, C. Abbo, S. Cutillas, S. Lacis, and C. Metayer, Electroactive and electrostructured elastomers, Journal of Modern Physics B, vol.15, issue.6 & 7, pp.564-573, 2001.

W. F. Brown, Magnetostatic Principles, p.31, 1962.

W. F. Brown, Magnetoelastic Interactions, 1966.

A. L. Browne and N. L. Johnson, US 0266417 A1. Active material based fasteners including cable ties and twist ties, p.14, 2012.

R. Bustamante, Mathematical modelling of non-linear magneto-and electro-active rubber-like materials, vol.25, 2007.

R. Bustamante, Transversely isotropic nonlinear magneto-active elastomers, Acta Mechanica, vol.210, pp.183-214, 2010.

R. Bustamante, A. Dorfmann, and R. W. Ogden, On variational formulations in nonlinear magnetoelastostatics, Mathematics and Mechanics of Solids, vol.13, pp.725-745, 2008.

R. Bustamante, A. Dorfmann, and R. W. Ogden, Nonlinear electroelastostatics: a variational framework, Journal of Applied Mathematics and Physics, vol.60, issue.1, pp.154-177, 2009.

J. D. Carlson, US 6296088 B1. Magnetorheological fluid seismic damper, p.24, 2001.

J. D. Carlson and M. R. Jolly, MR fluid, foam and elastomer devices, Mechatronics, vol.10, pp.555-569, 2000.
DOI : 10.1016/s0957-4158(99)00064-1

D. J. Charlton, J. Yang, and K. K. Teh, A review of methods to characterize rubber elastic behavior for use in finite element analysis. Rubber Chemistry and Technology, vol.67, p.17, 1994.

L. Chen, X. L. Gong, W. Q. Jiang, J. J. Yao, H. X. Deng et al., Investigation on magnetorheological elastomers based on natural rubber, Journal of Materials Science, vol.42, pp.5483-5489, 2007.
DOI : 10.1007/s10853-006-0975-x

URL : https://arrow.dit.ie/cgi/viewcontent.cgi?article=1003&context=cerart

L. Chen, X. L. Gong, and W. H. Li, Microstructures and viscoelastic properties of anisotropic magnetorheological elastomers, Smart Materials and Structures, vol.16, 2007.

A. Ciesielski, An introduction to rubber technology, vol.35, 1999.

E. Coquelle, Propriétés élastiques et viscoélastiques de matériaux composites adaptifs, vol.19, 2004.

E. Coquelle and G. Bossis, Magnetostriction and piezoresistivity in elastomers filled with magnetic particles, Journal of Advanced Science, vol.17, pp.132-138, 2005.

E. Coquelle and G. Bossis, Mullins effect in elastomers filled with particles aligned by a magnetic field, International Journal of Solids and Structures, vol.43, p.26, 2006.

. Chapter,

R. Corcolle, L. Daniel, and F. Bouillault, Optimal design of magnetostrictive composites: An analytical approach, IEEE Transactions on Magnetics, vol.44, issue.1, pp.17-23, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00352283

R. J. Crist, US 7584685 B2. Active vibrational damper, vol.25, 2009.

K. Danas, Effective response of classical, auxetic and chiral magnetoelastic materials by use of a new variational principle, Journal of the Mechanics and Physics of Solids, vol.105, p.120, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01627522

K. Danas, S. V. Kankanala, and N. Triantafyllidis, Experiments and modeling of ironparticle-filled magnetorheological elastomers, Journal of the Mechanics and Physics of Solids, vol.60, p.97, 2012.

K. Danas and N. Triantafyllidis, Instability of a magnetoelastic layer resting on a nonmagnetic substrate, Journal of the Mechanics and Physics of Solids, vol.69, pp.67-83, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00995717

L. C. Davis, Model of magnetorheological elastomers, Journal of Applied Physics, vol.85, issue.6, pp.3348-3351, 1999.

M. E. Dekkers and D. Heikens, The effect of interfacial adhesion on the tensile behavior of polystyrene-glass-bead composites, Jounal of Applied Polymer Science, vol.28, p.26, 1983.

G. Diguet, Huge magnetostriction of magneto-rheological composite, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00488910

G. Diguet, E. Beaugnon, and J. Y. Cavaillé, From dipolar interactions of a random distribution of ferromagnetic particles to magnetostriction, Journal of Magnetism and Magnetic Materials, vol.321, pp.396-401, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00431389

G. Diguet, E. Beaugnon, and J. Y. Cavaillé, Shape effect in the magnetostriction of ferromagnetic composite, Journal of Magnetism and Magnetic Materials, vol.322, pp.3337-3341, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01813955

A. Dorfmann and R. W. Ogden, Magnetoelastic modelling of elastomers, European Journal of Mechanics-A/Solids, vol.22, issue.4, pp.497-507, 2003.

A. Dorfmann and R. W. Ogden, A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber, International Journal of Solids and Structures, vol.41, p.111, 2004.

A. Dorfmann and R. W. Ogden, Some problems in nonlinear magnetoelasticity, Zeitschrift für angewandte Mathematik und Physik ZAMP, vol.56, issue.4, p.73, 2005.

T. A. Duenas and G. P. Carman, Large magnetostrictive response of Terfenol-D resin composites, Journal of Applied Physics, vol.87, issue.9, pp.4696-4701, 2000.

A. , Standard test methods for tension testing of metallic materials, p.31, 2001.

L. D. Elie and J. M. Ginder, EP 0784163 B1. Variable stiffness bushing using magnetorheological elastomers, 2002.

Y. C. Fan, X. L. Gong, S. H. Xuan, W. Zhang, J. Zheng et al., Interfacial friction damping properties in magnetorheological elastomers, Smart Materials and Structures, vol.20, issue.035007, p.12, 2011.

M. Farshad and A. Benine, Magnetoactive elastomer composites, Polymer Testing, vol.23, pp.347-353, 2004.

M. Farshad and M. Le-roux, A new active noise abatement barrier system, Polymer Testing, vol.23, pp.855-860, 2004.

M. Farshad and M. Le-roux, Compression properties of magnetostrictive polymer composite gels, Polymer Testing, vol.24, p.18, 2005.

S. Y. Fu, X. Q. Feng, B. Lauke, and Y. W. Mai, Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate-polymer composites, Composites: Part B, vol.39, p.26, 2008.

E. Galipeau and P. P. Castañeda, The effect of particle shape and distribution on the macroscopic behavior of magnetoelastic composites, International Journal of Solids and Structures, vol.49, pp.1-17, 2012.

E. Galipeau and P. P. Castañeda, A finite-strain constitutive model for magnetorheological elastomers: Magnetic torques and fiber rotations, Journal of the Mechanics and Physics of Solids, vol.61, pp.1065-1090, 2013.

E. Galipeau and P. P. Castañeda, Giant field-induced strains in magnetoactive elastomer composites, Proceedings of the Royal Society A, vol.469, 2013.

E. Galipeau, S. Rudykh, G. Debotton, and P. P. Castañeda, Magnetoactive elastomers with periodic and random microstructures, International Journal of Solids and Structures, vol.51, pp.3012-3024, 2014.

A. N. Gent and B. K. Park, Failure processes in elastomers at or near a rigid spherical inclusion, Journal of Materials Science, vol.19, p.26, 1984.

. Chapter,

J. M. Ginder, S. M. Clark, W. F. Schlotter, and M. E. Nichols, Magnetostrictive phenomena in magnetorheological elastomers, Journal of Modern Physics B, vol.16, issue.17 & 18, pp.2412-2418, 2002.

J. M. Ginder, M. E. Nichols, L. D. Elie, and S. M. Clark, Controllable-stiffness components based on magnetorheological elastomers, Smart Structures and Materials, vol.3985, pp.418-425, 2000.

J. M. Ginder, M. E. Nichols, L. D. Elie, and J. L. Tardiff, Magnetorheological elastomers: properties and applications, SPIE Proceedings, vol.3675, pp.131-138, 1999.

X. L. Gong, L. Chen, and J. F. Li, Study of utilizable magnetorheological elastomers, Journal of Modern Physics B, vol.21, issue.29, pp.4875-4882, 2007.

X. L. Gong, X. Z. Zhang, and P. Q. Zhang, Fabrication and characterization of isotropic magnetorheological elastomers, Polymer Testing, vol.24, pp.669-676, 2005.

S. R. Gorodkin, R. O. James, and W. I. Kordonski, Magnetic properties of carbonyl iron particles in magnetorheological fluids, Journal of Physics: Conference Series, vol.149, pp.1-4, 2009.

A. Green and J. E. Adkins, Large Elastic Deformations, vol.85, 1970.

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, p.41, 2005.

X. C. Guan, X. F. Dong, and J. P. Ou, Magnetostrictive effect of magnetorheological elastomer, Journal of Magnetism and Magnetic Materials, vol.320, pp.158-163, 2008.

D. Günther, D. Y. Borin, S. Günther, and S. Odenbach, X-ray micro-tomographic characterization of field-structured magnetorheological elastomers, Smart Materials and Structures, vol.21, pp.1-7, 2012.

M. Guyot, Mesure des paramètres magnétiques fondamentaux des matériaux ferromagnétiques ou ferrimagnétiques, chapter Rappels sur les paramètres fondamentaux du magnétisme, vol.12, pp.5-24, 1994.

E. H. Hall, On a new action of the magnet on electric currents, American Journal of Mathematics, vol.2, issue.3, p.42, 1879.

B. Hamrock, Mechanical Engineers' Handbook: Materials and Mechanical Design, p.24, 2006.

Y. Han, A. Mohla, X. Huang, W. Hong, and L. E. Faidley, Magnetostriction and field stiffening of magneto-active elastomers, International Journal of Applied Mechanics, vol.7, p.53, 2015.

J. A. Harvey, Smart Materials, Mechanical Engineers' Handbook, vol.1, 2006.

Z. Hashin, Analysis of composite materials, Journal of Applied Mechanics, vol.50, pp.481-505, 1983.

W. M. Haynes, CRC Handbook of Chemistry and Physics, vol.38, 2013.

Y. Hu, Y. L. Wang, X. L. Gong, X. Q. Gong, X. Z. Zhang et al., New magnetorheological elastomers based on polyurethane/si-rubber hybrid, Polymer Testing, vol.24, issue.3, p.11, 2005.

D. Ivaneyko, V. Toshchevikov, D. Borin, M. Saphiannikova, and G. Heinrich, Mechanical properties of magneto-sensitive elastomers in a homogeneous magnetic field: Theory and experiment, Macromolecular Symposia, vol.338, issue.1, p.64, 2014.

Y. Jansen, T. Karrer, and J. Borchers, Mudpad: tactile feedback and haptic texture overlay for touch surfaces, Proceedings of the ACM International Conference on Interactive Tabletops and Surfaces, p.13, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01404492

A. Javili, G. Chatzigeorgiou, and P. Steinmann, Computational homogenization in magneto-mechanics, International Journal of Solids and Structures, vol.50, pp.4197-4216, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01500815

M. R. Jolly, J. D. Carlson, B. C. Munoz, and T. A. Bullions, The magnetoviscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix, Journal of Intelligent Material Systems and Structures, vol.7, pp.613-622, 1996.

J. P. Joule, On the effects of magnetism upon the dimensions of iron and steel bars. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol.30, p.27, 1847.

J. Kaleta, M. Krolewicz, and D. Lewandowski, Magnetomechanical properties of anisotropic and isotropic magnetorheological composites with thermoplastic elastomer matrices, Smart Materials and Structures, vol.20, issue.085006, p.11, 2011.

K. A. Kalina, P. Metsch, and M. Kästner, Microscale modeling and simulation of magnetorheological elastomers at finite strains: A study on the influence of mechanical preloads, International Journal of Solids and Structures, vol.120, pp.286-296, 2016.

. Chapter,

M. Kallio, The elastic and damping properties of magnetorheological elastomers, vol.12, p.25, 2005.

S. V. Kankanala, On finitely strained magnetoelastic solids, 2007.

S. V. Kankanala and N. Triantafyllidis, On finitely strained magnetorheological elastomers, Journal of the Mechanics and Physics of Solids, vol.52, pp.2869-2908, 2004.

S. V. Kankanala and N. Triantafyllidis, Magnetoelastic buckling of a rectangular block in plane strain, Journal of the Mechanics and Physics of Solids, vol.56, pp.1147-1169, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00870865

L. Kari, Magneto-sensitive elastomers-theory and applications, chapter Constitutive Models for Rubber VIII Chapter, vol.16, pp.13-18, 2013.

M. Keip and M. Rambausek, A multiscale approach to the computational characterization of magnetorheological elastomers, International Journal of Numerical Methods in Engineering, vol.107, issue.4, pp.338-360, 2016.

M. Keip and M. Rambausek, Computational and analytical investigations of shape effects in the experimental characterization of magnetorheological elastomers, International Journal of Solids and Structures, vol.121, pp.1-20, 2017.

M. S. Kim, K. M. Yang, S. H. Lee, J. H. Yoon, U. C. Jeong et al., US 8844914 B2. Variable differential mount apparatus using magnetorheological elastomer, 2014.

J. H. Koo, A. Dawson, and H. J. Jung, Characterization of actuation properties of magnetorheological elastomers with embedded hard magnetic particles, Journal of Intelligent Material Systems and Structures, vol.23, issue.9, p.12, 2012.

A. Kovetz, Electromagnetic Theory, vol.120, 2000.

K. U. Kyung, J. U. Lee, S. Park, H. Prahlad, and P. Von-guggenberg, Flexible visiohaptic display. Haptics: Perception, Devices, Mobility, and Communication, vol.7283, p.13, 2012.

C. H. Lee and M. G. Jang, Virtual surface characteristics of a tactile display using magneto-rheological fluids, Sensors, vol.11, issue.3, p.13, 2011.

V. Lefèvre, K. Danas, and O. Lopez-pamies, A general result for the magnetoelastic response of isotropic suspensions of iron and ferrofluid particles in rubber, with applications to spherical and cylindrical specimens, Journal of the Mechanics and Physics of Solids, vol.107, pp.343-364, 2017.

M. Lokander, Performance of magnetorheological rubber materials, vol.12, 2004.

M. Lokander and B. Stenberg, Performance of isotropic magnetorheological rubber materials, Polymer Testing, vol.22, pp.245-251, 2003.

O. Lopez-pamies, A new i1-based hyperelastic model for rubber elastic materials, Comptes Rendus Mecanique, vol.338, issue.1, pp.3-11, 2009.

J. Maas and D. Uhlenbusch, Experimental and theoretical analysis of the actuation behavior of magnetoactive elastomers, Smart Materials and Structures, vol.25, issue.10, p.104002, 2016.

J. E. Martin, R. A. Anderson, D. Read, and G. Gulley, Magnetostriction of fieldstructured magnetoelastomers, Physical Review E, vol.74, pp.1-17, 2006.

J. E. Martin, R. A. Anderson, and C. P. Tigges, Simulation of the athermal coarsening of composites structured by a uniaxial field, Journal of Chemical Physics, vol.108, issue.9, p.11, 1998.

J. E. Martin, E. Venturini, G. L. Gulley, and J. Williamson, Using triaxial magnetic fields to create high susceptibility particle composites, Physical Review E, vol.69, p.11, 2004.

J. E. Martin, E. Venturini, J. Odinek, and R. A. Anderson, Anisotropic magnetism in field-structured composites, Physical Review E, vol.61, issue.3, p.11, 2000.

P. R. Marur, US 0087985 A1. Magneto-rheological elastomer-based vehicule suspension, 2013.

G. Maugin and A. Eringen, A continuum theory of deformable ferrimagnetic bodies. i. field equations, Journal of Mathematical Physics, vol.13, issue.9, pp.143-155, 1972.

G. Maugin and A. Eringen, A continuum theory of deformable ferrimagnetic bodies. ii. thermodynamics, constitutive theory, Journal of Mathematical Physics, vol.13, issue.9, pp.1334-1347, 1972.

D. C. Meeker, FEMM-finite element method magnetics version 4.2, p.19, 2013.

C. Miehe and J. Keck, Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation, Journal of the Mechanics and Physics of Solids, vol.48, pp.323-365, 2000.

. Chapter,

C. Miehe, D. Vallicotti, and S. Teichtmeister, Homogenization and multiscale stability analysis in finite magneto-electro-elasticity. application to soft matter ee, me and mee composites, Computer Methods in Applied Mechanics and Engineering, vol.300, pp.294-346, 2016.

F. C. Moon and Y. H. Pao, Magnetoelastic buckling of a thin plate, Journal of Applied Mechanics, vol.35, issue.1, p.48, 1968.

. Msc-software and . Whitepaper, Nonlinear finite element analysis of elastomers, 2010.

L. Mullins, Effect of stretching on the properties of rubber, Rubber Chemistry and Technology, vol.21, p.26, 1948.

L. Mullins and N. R. Tobin, Theoretical model for the elastic behavior of filler-reinforced vulcanized rubbers. Rubber Chemistry and Technology, vol.30, p.26, 1957.

R. W. Ogden, Mechanics and electrodynamics of magneto-and electro-elastic materials, chapter Magnetostatics: from basic principles to nonlinear interactions in deformable media, vol.527, pp.107-152, 2011.

J. A. Osborne, Demagnetizing factors of the general ellipsoid, Physical Review, vol.67, issue.11&12, p.31, 1945.

Y. Pao, Electromagnetic forces in deformable continua, Mechanics today, vol.4, pp.209-305, 1978.

Y. Pao and C. Yeh, A linear theory for soft ferromagnetic elastic solids, International Journal for Engineering Science, vol.11, issue.4, pp.415-436, 1973.

A. C. Pipkin and R. S. Rivlin, The formulation of constitutive equations in continuum physics. I. Archive for Rational Mechanics and Analysis, vol.4, pp.129-144, 1959.

P. , P. Castañeda, and E. Galipeau, Homogenization-based constitutive models for magnetorheological elastomers at finite strain, Journal of the Mechanics and Physics of Solids, vol.59, pp.194-215, 2011.

T. Pössinger, Experimental Characterization, Modeling and Simulation of

M. Elastomers, , 2015.

T. Pössinger, C. Bolzmacher, L. Bodelot, and N. Triantafyllidis, Influence of interfacial adhesion on the mechanical response of magneto-rheological elastomers at high strain. Microsystem technologies, vol.20, p.35, 2014.

E. Psarra, L. Bodelot, and K. Danas, Two-field surface pattern control via marginally stable magnetorheological elastomers, Soft Matter, vol.13, issue.37, pp.6576-6584, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01627525

J. Rabinow, The magnetic fluid clutch, Transactions of the American Institute of Electrical Engineers, vol.67, issue.2, p.24, 1948.

Y. L. Raikher, O. V. Stolbov, and G. V. Stepanov, Deformation of a circular ferroelastic membrane in a uniform magnetic field, Technical Physics, vol.53, issue.9, pp.1169-1176, 2008.

Z. Rigbi and L. Jilken, The response of an elastomer filled with soft ferrite to mechanical and magnetic influences, Journal of Magnetism and Magnetic Materials, vol.37, p.24, 1983.

A. J. , Saint-Venant. Mémoire sur la torsion des prismes, Mémoires Divers Savants, vol.14, p.31, 1855.

P. Saxena, M. Hossain, and P. Steinmann, A theory of finite deformation magnetoviscoelasticity, International Journal of Solids and Structures, vol.50, pp.3886-3897, 2013.

N. Scheerbaum, D. Hinz, O. Gutfleisch, K. H. Müller, and L. Schultz, Textured polymer bonded composites with Ni-Mn-Ga magnetic shape memory particles, Acta Materialia, vol.55, p.12, 2007.

G. Schubert, Manufacture, characterisation and modelling of magneto-rheological elastomers, vol.12, p.27, 2014.

G. Schubert and P. Harrison, Large-strain behaviour of magneto-rheological elastomers tested under uniaxial compression and tension, and pure shear deformations, Polymer Testing, vol.42, pp.122-134, 2015.

G. Schubert and P. Harrison, Equi-biaxial tension tests on magneto-rheological elastomers, Smart Materials and Structures, vol.25, 2016.

G. Schubert, P. Harrison, and Z. Guo, The behaviour of magneto-rheological elastomers under equi-biaxial tension, 19th International Conference on Composite Materials, vol.20, 2013.

Y. Shen, M. F. Golnaraghi, and G. R. Heppler, Experimental research and modeling of magnetorheological elastomers, Journal of Intelligent Material Systems and Structures, vol.15, pp.27-35, 2004.

T. Shiga, A. Okada, and T. Kurauchi, Magnetroviscoelastic behavior of composite gels, Journal of Applied Polymer Science, vol.58, issue.4, pp.787-792, 1995.

. Chapter,

G. V. Stepanov, S. S. Abramchuk, D. A. Grishin, L. V. Nikitin, E. Y. Kramarenko et al., Effect of a homogeneous magnetic field on the viscoelastic behavior of magnetic elastomers, Polymer, vol.48, p.29, 2007.

G. V. Stepanov, E. Y. Kramarenko, and D. A. Semerenko, Magnetodeformational effect of the magnetoactive elastomer and its possible applications, Journal of Physics: Conference Series, vol.412, pp.1-4, 2013.

O. V. Stolbov, Y. L. Raikher, and M. Balasoiu, Modelling of magnetodipolar striction in soft magnetic elastomers, Soft Matter, vol.7, p.28, 2011.

M. Tejedor, H. Rubio, L. Elbaile, and R. Iglesias, External fields created by uniformly magnetized ellipsoids and spheroids, IEEE Transactions on Magnetics, vol.31, issue.1, p.67, 1995.

F. Thorsteinsson, I. Gudmundsson, and C. Lecomte, US 0060349 A1. Prosthetic and orthotic devices having magnetorheological elastomer spring with controllable stiffness, 2013.

H. F. Tiersten, Coupled magnetomechanical equations for magnetically saturated insulators, Journal of Mathematical Physics, vol.5, p.65, 1964.

H. F. Tiersten, Variational principle for saturated magnetoelastic insulators, Journal of Mathematical Physics, vol.6, issue.5, p.65, 1965.

C. Truesdell and R. Toupin, The Classical Field Theories, Handbuch der Physik, p.65, 1960.

Z. Varga, G. Filipcsei, and M. Zrinyi, Smart composites with controlled anisotropy. Polymer, vol.46, pp.7779-7787, 2005.

Z. Varga, G. Filipcsei, and M. Zrinyi, Magnetic field sensitive functional elastomers with tunable elastic modulus, Polymer, vol.47, pp.227-233, 2006.

F. Vidal-verdu and M. Hafez, Graphical tactile displays for visually-impaired people, IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol.15, issue.1, p.13, 2007.

B. Wei, X. L. Gong, and W. Q. Jiang, Influence of polyurethane properties on mechanical performances of magnetorheological elastomers, Journal of Applied Polymer Science, vol.116, p.11, 2010.

F. Xin, X. Bai, and L. Qian, Modeling and experimental verification of frequency, amplitude-, and magneto-dependent viscoelasticity of magnetorheological elastomers, Smart Materials and Structures, vol.25, issue.10, p.64, 2016.

H. M. Yin, L. Z. Sun, and J. S. Chen, Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles, Journal of the Mechanics and Physics of Solids, vol.54, pp.975-1003, 2006.

G. Zhou and Z. Jiang, Deformation in magnetorheological elastomer and elastomerferromagnet composite driven by a magnetic field, Smart Materials and Structures, vol.13, issue.2, p.29, 2004.

M. Zrinyi, L. Barsi, and A. Büki, Deformation of ferrogels induced by nonuniform magnetic fields, J. Chem. Physics, vol.104, issue.21, pp.8750-8756, 1996.

M. Zrinyi, L. Barsi, and A. Büki, Ferrogel: a new magneto-controlled elastic medium, Polymer Gels and Networks, vol.5, pp.415-427, 1997.

A. Y. Zubarev, On the theory of the magnetic deformation of ferrogels, Soft Matter, vol.8, pp.3174-3179, 2012.

G. Zurlo, M. Destrade, D. Detommasi, and G. Puglisi, Catastrophic thinning of dielectric elastomers, PHYSICAL REVIEW LETTERS, vol.118, p.121, 2017.