Landau theory for ferro-paramagnetic phase transition in finitely-strained viscoelastic magnets

Tomáš Roubíček

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arXiv · 2302.02850

Landau theory for ferro-paramagnetic phase transition in finitely-strained viscoelastic magnets

Tomáš Roubíček

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Abstract

The thermodynamic model of visco-elastic deformable magnetic materials at finite strains is formulated in a fully Eulerian way in rates. The Landau theory applies for ferro-to-para-magnetic phase transition, the gradient theory (leading exchange energy) for magnetization with general mechanically dependent coefficient, hysteresis in magnetization evolution by Landau-Lifshitz-Gilbert equation involving objective corotational time derivative of magnetization, and demagnetizing field are considered in the model. The Kelvin-Voigt viscoelastic rheology with a higher-order viscosity (exploiting the concept of multipolar materials) is used, allowing for physically relevant frame-indifferent stored energies and for local invertibility of deformation. The model complies with energy conservation and Clausius-Duhem entropy inequality. Existence and a certain regularity of weak solutions is proved by a Faedo-Galerkin semi-discretization and a suitable regularization.

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Tomáš Roubíček. 2023-02-06. Landau theory for ferro-paramagnetic phase transition in finitely-strained viscoelastic magnets. https://arxiv.org/abs/2302.02850

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