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Constitutive Models for Magnetorheological Elastomers at Finite Strains: Dipolar Interactions versus Magnetic Torques

le 23 mai 2013

P. Ponte Castañeda Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania

Pedro Ponte Castaneda

Pedro Ponte Castaneda

This presentation is concerned with the application of a finite-strain homogenization framework to develop constitutive models for magnetorheological elastomers (MREs) consisting of initially aligned, rigid magnetic particles distributed randomly in an elastomeric matrix. For this purpose, a novel strategy is proposed to partially decouple the mechanical and magnetostatic effects in the composite. Thus, the effective electro-elastic energy of the composite is written in terms of a purely mechanical component, together with a magnetostatic component evaluated in the deformed configuration of the composite, as estimated by means of the purely mechanical solution of the problem. It is argued that the resulting constitutive model for the material, which can account for the initial volume fraction, average shape, orientation and distribution of the generally anisotropic and non-spherical particles, should be accurate when the matrix is stiff compared to the magnetic forces and torques on the particles. The theory predicts the existence of certain extra stressesarising in the composite beyond the purely mechanical and magnetic (Maxwell) stresseswhich can be directly linked to changes in the effective magnetic permittivity of the composite with the deformation. For the special case of isotropic distributions of magnetically isotropic, spherical particles, the extra stresses are due to changes in the particle two-point distribution function with the deformation, and are of order volume fraction squared, arising from dipole interactions between the particles. On the other hand, for the case of aligned, ellipsoidal particles, the effect can be of order volume fraction, when changes are induced in the orientation of the particles, as a consequence of magnetic torques on individual particles. The theory is capable of handling the strongly nonlinear effects associated with finite strains and magnetic saturation of the particles at sufficiently high deformations and magnetic fields, respectively. It will be shown that particle rotations can be used to produce relatively large magnetostrictive strains and actuation stresses, as well as to control the instantaneous stiffness of the material. Time permitting, related results will also be presented for dielectric elastomer composites, which is another class of technologically important active materials.
Type :
Séminaires - conférences
Lieu(x) :
Campus de Cachan
Amphi e-média
Bâtiment Léonard De Vinci de - ENS Cachan
61, avenue du Président Wilson 94230 Cachan
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