Constitutive modeling of nonlinear reversible and irreversible ferromagnetic behaviors and application to multiferroic composites

Abstract

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.

Multiscale modeling of ferroelectrics with stochastic grain size distribution

“…where σ ij and D i denote the associated variables mechanical stress and electric displacement. In equations (2) and (3) the material properties of a grain have been assumed constant in incremental changes of state and are determined as weighted averages, see for example, Avakian and Ricoeur (2016) or Huber et al (1999),…”

Direct and converse nonlinear magnetoelectric coupling in multiferroic composites with ferromagnetic and ferroelectric phases

“…More specifically, Lu et al [35] established a model by using thermodynamic theory combined with the Eshelby's inclusion theory to study the electric, magnetic and ME properties of the nano-structured multiferroic composites. Avakian et al [36,37] applied the physically motivated constitutive models for ferromagnetic and ferroelectric phases and investigated the ME coupling coefficients in multifunctional composite consisting of a ferromagnetic inclusion in a ferroelectric matrix. Xu et al [38] proposed a new probabilistic domain switching function considering the surface FM anisotropy and the interface chargemediated effect and investigated the size-dependent electric tuning magnetization behaviour for the ME laminates at nanoscale.…”

“…In order to simultaneously consider the influence of nonlinear characteristics of ferroelectric materials and ferromagnetic materials on the ME effect for ME composites, some studies have been carried out [35][36][37][38]. More specifically, Lu et al [35] established a model by using thermodynamic theory combined with the Eshelby's inclusion theory to study the electric, magnetic and ME properties of the nano-structured multiferroic composites.…”

Vibration suppression of a rotating cantilever beam under magnetic excitations by applying the magnetostrictive material

“…To utilize the full potential of GMM, based on this nonlinear and coupled constitutive model, some extended investigations have been carried out and the coupling behavior of Terfenol-D rods was studied (Sun and Zheng, 2006), In addition, the active vibration control of Terfenol-D rods and laminated composite beams was investigated (Zhou et al, 2006; Zhou and Zhou, 2007). The constitutive model for multiferroic composites based on the nonlinear reversible and irreversible ferromagnetic behaviors was established (Avakian and Ricoeur, 2016).…”