Abstract
This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of free energy as well as switching and saturation conditions in form of inequalities. Thermodynamically consistent models naturally lead to variational formulations. We propose to use the concept of variational inequalities. We aim at combining the different phenomenological conditions into one variational inequality. In our formulation we use one Lagrange multiplier for each condition (the onset of domain switching and saturation), each satisfying Karush-Kuhn-Tucker conditions. An update for reversible and remanent quantities is then computed within one, in general nonlinear, iteration.
Highlights
In the current work we aim at describing the process of polarziation in ferroelectric media
Polarization has been described as a dissipative process in a thermodynamically consistent framework based on the Helmholtz free energy in a series of papers by Bassiouny et al (1988a, 1988b) and Bassiouny and Maugin (1989a, 1989b)
The evolution of the internal variables is based on inequality constraints, such as the so-called switching condition
Summary
In the current work we aim at describing the process of polarziation in ferroelectric media. The internal variables are the polarization vector in McMeeking and Landis (2002), and an independent polarization strain is added in Landis (2002) They specified non-linear free energy functions that account for the saturation phenomenon. Elhadrouz et al (2005) implemented a material model including different switching functions for polarization and polarization strain, similar as proposed by Kamlah and Tsakmakis (1999). We will follow Kamlah’s approach, but formulate the theory in the framework of variational inequalities These inequalities arise naturally from energy-based constitutive models with dissipation, see Miehe et al (2011) for the application to ferroelectric and ferromagnetic materials.
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