Session: 02-01: Multiferroics

Paper Number: 91058

91058 - Multiscale Modeling of Mangetostriction; a Probabilistic Approach to Magnetic Domain Structures 

An accurate and computationally efficient non-linear magnetostrictive constitutive model is required to properly develop novel magnetostrictive technologies. Models built using statistical mechanics are theoretically capable of capturing the full non-linear saturating behavior and magneto-mechanical coupling of magnetostrictive materials. However, accurately solving these equations can require computationally expensive numerical integration which greatly restricts their use in numerical simulations like FEA. To reduce the complexity of the requisite integrals macroscale models often resort to oversimplifications. One such simplification is to ignore the effects of exchange interaction, which reduces the complexity of the model but restricts its predictions to paramagnetic behavior (i.e., cannot predict hysteresis). In the literature, mean-field theory has often been used to reintroduce the effects of exchange through a curve fitting parameter. The focus of this research is to develop a method of introducing exchange into a one-dimensional model of magnetostriction through the use of statistical mechanics.

It was previously shown that an accurate analytical model of the average magnetization and magnetostriction of a paramagnetic material could be derived by reducing the problem to one dimension. This method will use the probabilistic directions of magnetization predicted by the paramagnetic model at a given energy state to create of representative volume element (RVE) of the materials domain structure. The exchange interaction between the magnetic domains within the RVE will then be calculated using a form of the quantum Heisenberg model. The calculated exchange energy will then be used to update the initial prediction of the paramagnetic model until a new equilibrium state is achieved. The complexity and applicability of this approach will then be compared to models from the literature that use mean-field theory. Furthermore, the model will be compared to experimental data, and it will be examined how the inclusion of exchange effects with this approach affect its predictive capabilities. We will close by examining the how this approximation method can be adapted to predict hysteretic behavior.

Presenting Author: John Domann Virginia Tech