Artjom Avakian

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

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.

An extended constitutive model for nonlinear reversible ferromagnetic behaviour under magnetomechanical multiaxial loading conditions

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.

Microstructured Multiferroic Materials: Modelling Approaches Towards Efficiency and Durability

Magnetoelectric composites are investigated by numerical simulation. Nonlinear material models describing the magneto-ferroelectric or electro-ferromagnetic behaviors of the two constituents are presented. The ferroelectric model additionally accounts for damage evolution due to micro crack growth. The constitutive equations and weak forms of balance equations have been implemented within a finite element framework. A so-called condensed approach is also elaborated towards multiferroic compounds. Numerical simulations focus on the prediction of local domain orientation, the overall constitutive behaviors, the calculation of magnetoelectric coupling coefficients, and the investigation of damage processes, predominantly during magneto-electric poling, as well as mutual interactions of these aspects. A particle and a laminated composite are compared as examples.

Nonlinear modeling of ferroelectric-ferromagnetic composites based on condensed and finite element approaches (Presentation Video)

Magnetoelectric (ME) coupling is an inherent property of only a few crystals exhibiting very low coupling coefficients at low temperatures. On the other hand, these materials are desirable due to many promising applications, e.g. as efficient data storage devices or medical or geophysical sensors. Efficient coupling of magnetic and electric fields in materials can only be achieved in composite structures. Here, ferromagnetic (FM) and ferroelectric (FE) phases are combined e.g. including FM particles in a FE matrix or embedding fibers of the one phase into a matrix of the other. The ME coupling is then accomplished indirectly via strain fields exploiting magnetostrictive and piezoelectric effects. This requires a poling of the composite, where the structure is exposed to both large magnetic and electric fields. The efficiency of ME coupling will strongly depend on the poling process. Besides the alignment of local polarization and magnetization, it is going along with cracking, also being decisive for the coupling properties. Nonlinear ferroelectric and ferromagnetic constitutive equations have been developed and implemented within the framework of a multifield, two-scale FE approach. The models are microphysically motivated, accounting for domain and Bloch wall motions. A second, so called condensed approach is presented which doesn’t require the implementation of a spatial discretisation scheme, however still considering grain interactions and residual stresses. A micromechanically motivated continuum damage model is established to simulate degradation processes. The goal of the simulation tools is to predict the different constitutive behaviors, ME coupling properties and lifetime of smart magnetoelectric devices.

Modeling of ferroelectric-ferromagnetic composites to improve magnetoelectric coupling and durability

The coupling of magnetic and electric fields due to the constitutive behavior of a material is commonly denoted as ME-effect. The latter is only observed in a few crystal classes exhibiting a very weak coupling which can hardly be exploited for technical applications. Much larger coupling coefficients are obtained in so called multiferroic composite materials, where ferroelectric and ferromagnetic constituents are embedded in a matrix. The MEeffect is then induced by the strain of the matrix converting electrical and magnetic energies based on the ferroelectric and magnetostrictive effects. In this paper, the theoretical background of nonlinear constitutive multifield behavior as well as the Finite Element implementation are presented. Nonlinear material models describing the magneto-ferroelectric behavior are presented. On this basis, the poling process in the ferroelectric phase is simulated and resulting effects are analyzed. Numerical simulations in general focus on the prediction of ME coupling coefficients and residual stresses going along with the poling process. Numerical homogenization, here, is a useful means to supply effective properties.