Variational inequalities for ferroelectric constitutive modeling. (February 2021)

• Record Type: Journal Article
• Authors: Meindlhumer, Martin; Pechstein, Astrid; Humer, Alexander
• Is Part Of: Journal of intelligent material systems and structures. Volume 32:Number 3(2021)
• Page Start: 317
• Page End: 330
• Publication Date: 2021-02
• Subjects: Ferroelectricity -- variational inequalities -- mixed finite elements -- polarization; Smart materials -- Periodicals; Intelligent control systems -- Periodicals; Artificial intelligence -- Periodicals; Matériaux intelligents -- Périodiques; Commande intelligente -- Périodiques; Intelligence artificielle -- Périodiques; 620.11
• DOI: 10.1177/1045389X20951252
• Languages: English
• ISSNs: 1045-389X

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.