Universal relations for non-linear magnetoelastic solids

摘要

In the light of recent and growing interest in the applications of magneto-sensitive elastomers and the corresponding theoretical analysis of their properties, this paper is devoted to the derivation of universal relations for these materials, that is connections between the components of a stress tensor and the components of the magnetic (induction) field vector that hold independently of the choice of constitutive law within a considered class of such laws. Here, attention is focussed on isotropic magnetoelastic materials. In particular, within this framework, it is shown that in general there is only one possible universal relation for these materials, but for particular classes of constitutive laws or for special deformations there can be more than one. The theory is exemplified by application to the problem of homogeneous triaxial deformation combined with a simple shear.