TY - JOUR

T1 - Two families of explicit models constructed from a homogenization solution for the magnetoelastic response of MREs containing iron and ferrofluid particles

AU - Lefèvre, Victor

AU - Danas, Kostas

AU - Lopez-Pamies, Oscar

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

KW - Ferrofluid inclusions

KW - Finite magnetoelastostatics

KW - Magnetorheological elastomers

KW - Magnetostriction

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U2 - 10.1016/j.ijnonlinmec.2019.103362

DO - 10.1016/j.ijnonlinmec.2019.103362

M3 - Article

AN - SCOPUS:85076440591

VL - 119

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

M1 - 103362

ER -