https://hal-polytechnique.archives-ouvertes.fr/hal-02613180Lefèvre, VictorVictorLefèvreNorthwestern University [Evanston]Danas, KostasKostasDanasLMS - Laboratoire de mécanique des solides - X - École polytechnique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueLopez-Pamis, OscarOscarLopez-PamisTwo families of explicit models constructed from a homogenization solution for the magnetoelastic response of MREs containing iron and ferrofluid particlesHAL CCSD2020Magnetorheological elastomersFerrofluid inclusionsMagnetostrictionFinite magnetoelastostatics[SPI.MECA.GEME] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph][SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]Danas, Kostas2020-05-19 20:51:292023-02-08 17:11:122020-05-25 10:56:39enJournal articleshttps://hal-polytechnique.archives-ouvertes.fr/hal-02613180/document10.1016/j.ijnonlinmec.2019.103362application/pdf1This work puts forth two families of fully explicit continuum or phenomenological models that are constructed by approximating an analytical (but implicit) homogenization solution recently derived for the free-energy function describing the macroscopic magnetoelastic response of two classes of MREs comprised of an isotropic incompressible elastomer filled with a random isotropic distribution of: i) spherical iron particles and ii) spherical ferrofluid particles. Both families are given in terms of free-energy functions W H = W H (F, H) that depend on the deformation gradient F and the Lagrangian magnetic field H and are constructed so as to agree identically with the homogenization solution for small and large applied magnetic fields, this for arbitrary finite deformations and arbitrary volume fractions c of particles in the entire physical range c ∈ [0, 1]. The accuracy of the proposed phenomenological models is assessed inter alia via the direct comparison of their predictions with that of the homogenization solution for a boundary-value problem of both fundamental and practical significance: the magnetostriction response of a spherical MRE specimen subject to a remotely applied uniform magnetic field.