Energetical and multiscale approaches for the definition of an equivalent stress for magneto-elastic couplings

A main limitation of most models describing the effect of stress on the magnetic behavior is that they are restricted to uniaxial - tensile or compressive - stress. Nevertheless, stress is multiaxial in most of industrial applications. An idea to overcome the strong limitation of models is to define a fictive uniaxial stress, the equivalent stress, that would change the magnetic behavior in a similar manner than a multiaxial stress. A first definition of equivalent stress, called the deviatoric equivalent stress, is proposed. It is based on an equivalence in magneto-elastic energy. This formulation is first derived for isotropic materials under specific assumptions. An extension to orthotropic media under disoriented magneto-mechanical loading is made. A new equivalent stress expression, called generalized equivalent stress, is then proposed. It is based on an equivalence in magnetization. Inverse identification of equivalent stress is made possible thanks to a strong simplification of the description of the material seen as an assembly of elementary magnetic domains. It is shown that this second proposal is a generalization of the deviatoric expression. Equivalent stress proposals are compared to former proposals and validated using experimental results carried out on an iron-cobalt sheet submitted to biaxial mechanical loading. These results are compared to the predictions obtained thanks to the equivalent stress formulations. The generalized equivalent stress is shown to be a tool able to foresee the magnetic behavior of a large panel of materials submitted to multiaxial stress. (C) 2011 Elsevier B.V. All rights reserved.