A magnetomechanically coupled FE-framework based on energy-minimising microstructure evolution

Thorsten Bartel, TU Dortmund University, Dortmund, Germany
Bjoern Kiefer, Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, Germany
Andreas Menzel, Institute of Mechanics, TU Dortmund, Dortmund, Germany

In this contribution, we present a variational framework which is suitable for canonical finite element implementations of material models for multiferroic materials. The specific material model builds on a micromechanically motivated parametrisation of the underlying microstructure and the modelling of its evolution in terms of reorientation processes and domain wall motion. Therefore, additional variables are introduced which also define the material's magnetisation. The difficulty of implementing such constitutive models into FE codes lies in the fact that the magnetostatic energy stored in the demagnetisation field is non-local in nature. In other words, the microstructure evolution at a material point depends on the solution of the boundary value problem in the entire domain. To address this, the aforementioned variables are spatially fully resolved and discretised with respect to the global FE framework. Numerical examples in terms of magnetomechanically coupled boundary value problems highlight the capabilitites of the proposed framework e.g. in terms of the prediction of inhomogeneous magnetisation fields for arbitrarily shaped specimen geometries.

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