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

Victor Lefèvre*, Kostas Danas, Oscar Lopez-Pamies

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Scopus citations

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 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.

Original languageEnglish (US)
Article number103362
JournalInternational Journal of Non-Linear Mechanics
Volume119
DOIs
StatePublished - Mar 2020

Keywords

  • Ferrofluid inclusions
  • Finite magnetoelastostatics
  • Magnetorheological elastomers
  • Magnetostriction

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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