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

Abstract : 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 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.
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Submitted on : Tuesday, May 19, 2020 - 8:51:29 PM
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Victor Lefèvre, Kostas Danas, Oscar Lopez-Pamis. 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, Elsevier, 2020, 119, pp.103362. ⟨10.1016/j.ijnonlinmec.2019.103362⟩. ⟨hal-02613180⟩

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