Two families of explicit models constructed from a homogenization solution for the magnetoelastic response of MREs containing iron and ferrofluid particles

• Published in: International journal of non-linear mechanics Vol. 119; p. 103362
• Main Authors: Lefèvre, Victor, Danas, Kostas, Lopez-Pamies, Oscar
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.03.2020; Elsevier BV; Elsevier
• Subjects: Boundary value problems; Computational fluid dynamics; Deformation; Elastomers; Engineering Sciences; Ferrofluid inclusions; Ferrofluids; Finite magnetoelastostatics; Homogenization; Iron; Magnetic fields; Magnetorheological elastomers; Magnetostriction; Mathematical analysis; Mechanical engineering; Mechanics; Model accuracy; Solid mechanics; Magnetostriction; Ferrofluid inclusions; Finite magnetoelastostatics; Magnetorheological elastomers
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2019.103362

This 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 WH=WH(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. •Two families of phenomenological models are put forth for isotropic MREs.•The models apply to MREs containing iron and ferrofluid particles.•Their accuracy is assessed by direct comparison with a homogenization solution.•The models are deployed to investigate the magnetostriction of spherical MRE specimens.