Unified magnetomechanical homogenization framework with application to magnetorheological elastomers

Abstract

The aim of this work is to present a general homogenization framework with application to magnetorheological elastomers under large deformation processes. The macroscale and microscale magnetomechanical responses of the composite in the material and spatial description are presented and the conditions for a well-established homogenization problem in Lagrangian description are identified. The connection between the macroscopic magnetomechanical field variables and the volume averaging of the corresponding microscopic variables in the Eulerian description is examined for several types of boundary conditions. It is shown that the use of kinematic and magnetic field potentials instead of kinetic field and magnetic induction potentials provides a more appropriate homogenization process.

Limit points in the free inflation of a magnetoelastic toroidal membrane

“…By appropriately considering the micromechanical constitution of magnetoelastic polymers, formulations for coupled field equations using homogenisation techniques have been proposed by Castañeda and Galipeau (2011);Galipeau and Castañeda (2013) and Chatzigeorgiou et al (2014), among others. Phenomenon of energydissipation due to viscoelasticity has been modelled by Saxena et al (2013), Ethiraj and Miehe (2016), and Haldar et al (2016); and anisotropic structure of magnetoelastic polymers has been accounted in the models by Bustamante (2010), Danas et al (2012a), and Saxena et al (2014).…”

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

“…In this section, fundamental definitions and concepts of the theory of computational homogenization are briefly addressed in order for this paper to be self-contained. In this contribution, all relations are represented only in Lagrangian description, considering that it is straightforward to formulate the problem in Eulerian description [206,402,408,458]. Furthermore, it is possible to establish the homogenization theory based on Green-Lagrange strain and Piola-Kirchhoff stress as alternatively suitable strain and stress measures [459,460].…”

“…[398][399][400][401][402][403][404][405] for thermomechanical problems, Refs. [406][407][408][409] for magnetomechanical problems, Refs. [410][411][412][413][414][415][416] for electromechanical problems, and Refs.…”

Effective properties of multiphase composites made of elastic materials with hierarchical structure

“…It is known that finite element analysis (FEA) methods are not sufficient to solve heterogeneous problems, since heterogeneities impose restrictions on the size of elements and make too expensive the discretization of heterogeneous structures (Bensoussan et al, 1978;Guedes & Kikuchi, 1990;Hollister & Kikuchi, 1992), unless they are combined with micromechanical and/or analytical methods (Hashin, 1983;Kalamkarov & Kolpakov, 1997;Nemat-Nasser & Hori, 1999;Aboudi et al, 1999;Nemat-Nasser, 1999;Guinovart-Diaz et al, 2005;Chatzigeorgiou & Charalambakis, 2005;Love & Batra, 2006;Chatzigeorgiou et al, 2007;Kalamkarov et al, 2009;Nie et al, 2011;Wu et al, 2014;Chatzigeorgiou et al, 2014;Berrehili, 2014;Abd-Alla et al, 2014;Tu & Pindera, 2014;Savvas et al, 2014;Mahmoud et al, 2014).…”