M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, 1972.

K. Anoukou, R. Brenner, F. Hong, M. Pellerin, and K. Danas, Random distribution of polydisperse ellipsoidal inclusions and homogenization estimates for porous elastic materials, Comp. Struct, vol.210, pp.87-101, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01875674

M. Arroyo and M. Ortiz, Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods, International Journal for Numerical Methods in Engineering, vol.65, issue.13, pp.2167-2202, 2006.

L. Bodelot, T. Pössinger, K. Danas, N. Triantafyllidis, and C. Bolzmacher, Magnetorheological elastomers: Experimental and modeling aspects, Mechanics of Composite and Multi-functional Materials, vol.7, pp.251-256, 2016.
URL : https://hal.archives-ouvertes.fr/cea-01831842

L. Bodelot, J. Voropaieff, and T. Pössinger, Experimental investigation of the coupled magneto-mechanical response in magnetorheological elastomers, Exp Mech, vol.58, issue.2, pp.207-221, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01635196

R. Bustamante, Transversely isotropic nonlinear magneto-active elastomers, Acta Mechanica, vol.210, issue.3-4, pp.183-214, 2010.

R. Bustamante, A. Dorfmann, and R. Ogden, On variational formulations in nonlinear magnetoelastostatics, Mathematics and Mechanics of Solids, vol.13, issue.8, pp.725-745, 2008.

R. Bustamante, A. Dorfmann, and R. Ogden, Numerical solution of finite geometry boundary-value problems in nonlinear magnetoelasticity, International Journal of Solids and Structures, vol.48, issue.6, pp.874-883, 2011.

R. Bustamante and R. W. Ogden, Nonlinear magnetoelastostatics: Energy functionals and their second variations, Mathematics and Mechanics of Solids, vol.18, issue.7, pp.760-772, 2012.

K. Danas, Effective response of classical, auxetic and chiral magnetoelastic materials by use of a new variational principle, J. Mech. Phys. Solids, vol.105, pp.25-53, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01627522

K. Danas, S. Kankanala, and N. Triantafyllidis, Experiments and modeling of iron-particle-filled magnetorheological elastomers, J. Mech. Phys. Solids, vol.60, issue.1, pp.120-138, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00647544

K. Danas and N. Triantafyllidis, Instability of a magnetoelastic layer resting on a non-magnetic substrate, J. Mech. Phys. Solids, vol.69, pp.67-83, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00995717

G. Diguet, E. Beaugnon, and J. Cavaillé, Shape effect in the magnetostriction of ferromagnetic composite, J. Magn. Magn. Mater, vol.322, issue.21, pp.3337-3341, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01813955

A. Dorfmann and R. Ogden, Nonlinear magnetoelastic deformations of elastomers, Acta Mechanica, vol.167, issue.1-2, pp.13-28, 2004.

A. Dorfmann and R. W. Ogden, Some problems in nonlinear magnetoelasticity, Zeitschrift für angewandte Mathematik und Physik ZAMP, vol.56, issue.4, pp.718-745, 2005.

E. Galipeau and P. Ponte-castañeda, A finite-strain constitutive model for magnetorheological elastomers: Magnetic torques and fiber rotations, J Mech Phys Solids, vol.61, issue.4, pp.1065-1090, 2013.

E. Galipeau, S. Rudykh, G. Debotton, and P. Ponte-castañeda, Magnetoactive elastomers with periodic and random microstructures, International Journal of Solids and Structures, vol.51, issue.18, pp.3012-3024, 2014.

J. Ginder, M. Nichols, L. Elie, and J. Tardiff, Magnetorheological elastomers: properties and applications, Smart Mater Struct, vol.3675, pp.131-138, 1999.

R. K. Hankin, Numerical evaluation of the gauss hypergeometric function with the hypergeo package, The R Journal, vol.7, pp.81-88, 2015.

D. L. Henann, S. A. Chester, and K. Bertoldi, Modeling of dielectric elastomers: Design of actuators and energy harvesting devices, J Mech Phys Solids, vol.61, issue.10, pp.2047-2066, 2013.

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. Muñoz, 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, issue.6, pp.613-622, 1996.

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.102, pp.286-296, 2016.

S. V. Kankanala and N. Triantafyllidis, On finitely strained magnetorheological elastomers, J. Mech. Phys. Solids, vol.52, issue.12, pp.2869-2908, 2004.

M. Keip and M. Rambausek, A multiscale approach to the computational characterization of magnetorheological elastomers, Int J Numer Methods Eng, vol.7, pp.23-32, 2015.

M. Keip and A. Sridhar, A variationally consistent phase-field approach for micro-magnetic domain evolution at finite deformations, Journal of the Mechanics and Physics of Solids, 2018.

Y. Kim, H. Yuk, R. Zhao, S. A. Chester, and X. Zhao, Printing ferromagnetic domains for untethered fast-transforming soft materials, Nature, vol.558, issue.7709, pp.274-279, 2018.

S. Kumar, K. Danas, and D. M. Kochmann, Enhanced local maximum-entropy approximation for stable meshfree simulations, Computer Methods in Applied Mechanics and Engineering, vol.344, pp.858-886, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01917356

C. M. Landis, A new finite-element formulation for electromechanical boundary value problems, International Journal for Numerical Methods in Engineering, vol.55, issue.5, pp.613-628, 2002.

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, J. Mech. Phys. Solids, vol.107, pp.343-364, 2017.

V. Lefèvre, K. Danas, and O. Lopez-pamies, Two families of explicit models constructed from a homogenization solution for the magnetoelastic response of mres containing iron and ferrofluid particles, International Journal of Non-Linear Mechanics, 2019.

V. Lefèvre and O. Lopez-pamies, Nonlinear electroelastic deformations of dielectric elastomer composites: I -ideal elastic dielectrics, J Mech Phys Solids, vol.99, pp.409-437, 2016.

V. Lefèvre and O. Lopez-pamies, Nonlinear electroelastic deformations of dielectric elastomer composites: II -non-gaussian elastic dielectrics, J Mech Phys Solids, vol.99, pp.438-470, 2016.

L. Liu, R. James, and P. Leo, Magnetostrictive composites in the dilute limit, J. Mech. Phys. Solids, vol.54, issue.5, pp.951-974, 2006.

O. Lopez-pamies, Elastic dielectric composites: Theory and application to particle-filled ideal dielectrics, Journal of the Mechanics and Physics of Solids, vol.64, pp.61-82, 2014.

O. Lopez-pamies, T. Goudarzi, and K. Danas, The nonlinear elastic response of suspensions of rigid inclusions in rubber: II -a simple explicit approximation for finite-concentration suspensions, J Mech Phys Solids, vol.61, issue.1, pp.19-37, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00870885

J. E. Martin, R. A. Anderson, D. Read, and G. Gulley, Magnetostriction of field-structured magnetoelastomers, Phys. Rev. E, vol.74, p.51507, 2006.

P. Metsch, K. A. Kalina, C. Spieler, and M. Kästner, A numerical study on magnetostrictive phenomena in magnetorheological elastomers, Computational Materials Science, vol.124, pp.364-374, 2016.

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, Comput Methods Appl Mech Eng, vol.300, pp.294-346, 2016.

D. Mukherjee and K. Danas, An evolving switching surface model for ferromagnetic hysteresis, Journal of Applied Physics, vol.125, issue.3, p.33902, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02394300

M. Otténio, M. Destrade, and R. W. Ogden, Incremental magnetoelastic deformations, with application to surface instability, Journal of Elasticity, vol.90, issue.1, pp.19-42, 2007.

W. F. Perger, A. Bhalla, and M. Nardin, A numerical evaluator for the generalized hypergeometric series, Computer physics communications, vol.77, issue.2, pp.249-254, 1993.

P. Castañeda, P. Galipeau, and E. , Homogenization-based constitutive models for magnetorheological elastomers at finite strain, Journal of the Mechanics and Physics of Solids, vol.59, issue.2, pp.194-215, 2011.

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

E. Psarra, L. Bodelot, and K. Danas, Wrinkling to crinkling transitions and curvature localization in a magnetoelastic film bonded to a non-magnetic substrate, Journal of the Mechanics and Physics of Solids, vol.133, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02321677

M. D. Rintoul and S. Torquato, Reconstruction of the structure of dispersions, Journal of Colloid and Interface Science, vol.186, issue.2, pp.467-476, 1997.

P. A. Sánchez, T. Gundermann, A. Dobroserdova, S. S. Kantorovich, and S. Odenbach, Importance of matrix inelastic deformations in the initial response of magnetic elastomers, Soft Matter, 2018.

P. Saxena, M. Hossain, and P. Steinmann, A theory of finite deformation magneto-viscoelasticity, International Journal of Solids and Structures, vol.50, issue.24, pp.3886-3897, 2013.

P. Saxena, J. Pelteret, and P. Steinmann, Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure, European Journal of Mechanics -A/Solids, vol.50, pp.132-151, 2015.

M. Schümann, D. Borin, S. Huang, G. Auernhammer, R. Müller et al., A characterisation of the magnetically induced movement of ndfeb-particles in magnetorheological elastomers, Smart Materials and Structures, vol.26, issue.9, 2017.

J. Segurado and J. Llorca, A numerical approximation to the elastic properties of sphere-reinforced composites, Journal of the Mechanics and Physics of Solids, vol.50, issue.10, pp.2107-2121, 2002.

A. S. Semisalova, N. S. Perov, G. V. Stepanov, E. Y. Kramarenko, and A. R. Khokhlov, Strong magnetodielectric effects in magnetorheological elastomers, Soft Matter, vol.9, issue.47, 2013.

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.

C. Spieler, M. Kästner, J. Goldmann, J. Brummund, and V. Ulbricht, Xfem modeling and homogenization of magnetoactive composites, Acta Mechanica, vol.224, issue.11, pp.2453-2469, 2013.

C. Spieler, P. Metsch, M. Kästner, and V. Ulbricht, Microscale modeling of magnetoactive composites undergoing large deformations, Technische Mechanik, vol.34, issue.1, pp.39-50, 2014.

M. Tarantino, O. Zerhouni, and K. Danas, Random 3D-printed isotropic composites with high volume fraction of pore-like polydisperse inclusions and near-optimal elastic stiffness, Acta Materialia, vol.175, pp.331-340, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02167837

O. Zerhouni, M. Tarantino, and K. Danas, Numerically-aided 3D printed random isotropic porous materials approaching the hashinshtrikman bounds, Composites Part B: Engineering, vol.156, pp.344-354, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01875669

R. Zhao, Y. Kim, S. A. Chester, P. Sharma, and X. Zhao, Mechanics of hard-magnetic soft materials, Journal of the Mechanics and Physics of Solids, vol.124, pp.244-263, 2019.

G. Zurlo, M. Destrade, and T. Lu, Fine tuning the electro-mechanical response of dielectric elastomers, Applied Physics Letters, vol.113, issue.16, p.162902, 2018.