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The coupling of magnetic and mechanical fields due to the constitutive behavior of a material is commonly denoted as magnetostrictive effect. The latter is only observed with large coupling coefficients in ferromagnetic materials, where coupling is caused by the rotation of the domains as a result of magnetic (Joule effect) or mechanical (Villari effect) loads. However, only a few elements (e.g. Fe, Ni, Co, and Mn) and their compositions exhibit such a behavior. In this article, the constitutive modeling of nonlinear ferromagnetic behavior under combined magnetomechanical loading as well as the finite element implementation is presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of principally different nonlinear magnetostrictive behaviors. On this basis, magnetization, strain, and stress are predicted, and the resulting effects are analyzed. The phenomenological approach covers reversible nonlinear behavior as it is observed, for example, in cobalt ferrite. Numerical simulations based on the physically motivated model focus on the calculation of hysteresis loops and the prediction of local domain orientations and residual stress going along with the magnetization process. Finally, a model for ferroelectric materials is applied in connection with the physically based ferromagnetic approach, in order to predict magnetoelectric coupling coefficients in multifunctional composite.

A constitutive modelling of ferromagnetic materials under combined magnetomechanical multiaxial loading with different boundary conditions and a finite element implementation are presented. The phenomenologically motivated model is capable of predicting magnetisation, strain, and stress and is thus suitable, e.g., for applications in multiferroic composites. The approach covers a reversible nonlinear behaviour as it is observed, e.g., in cobalt ferrite and other soft magnetic alloys. Various examples demonstrate the suitability of the model and its numerical implementation and give an insight into the behaviour of soft magnets, exposed to different boundary conditions or being embedded into other compliant materials.

In this paper, the constitutive modeling of nonlinear multifield behavior as well as the finite element implementation are presented. Nonlinear material models describing the magneto‐ferroelectric or electro‐ferromagnetic behaviors are presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of principally different nonlinear magnetostrictive behaviors. Further, the nonlinear ferroelectric behavior is based on a physically motivated constitutive model. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic and magnetostrictive phases, respectively, are simulated and the resulting effects analyzed. Numerical simulations focus on the calculation of magnetoelectric coupling and on the prediction of local domain orientations going along with the poling process, thus supplying information on favorable electric‐magnetic loading sequences. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)