Magneto-elasticity on the disk
Sandra Carillo, Michel Chipot, Vanda Valente, Giorgio Vergara, Caffarelli
TL;DR
This paper investigates the magneto-elastic energy minimization in a 2D circular disk, proving existence of minimizers, analyzing their dependence on eigenvalues, and identifying bifurcation points for specific parameter values.
Contribution
It introduces a simplified 2D model for magneto-elastic bodies, proves the existence of minimizers, and explores bifurcation phenomena related to parameter variations.
Findings
Existence of minimizers for the magneto-elastic energy functional.
Dependence of minimizers on eigenvalues of the problem.
Bifurcation points identified at specific parameter values.
Abstract
A model problem of magneto-elastic body is considered. Specifically, the case of a two dimensional circular disk is studied. The functional which represents the magneto-elastic energy is introduced. Then, the minimisation problem, referring to the simplified two-dimensional model under investigation, is analysed. The existence of a minimiser is proved and its dependence on the eigenvalues of the problem is investigated. A bifurcation result is obtained corresponding to special values of the parameters.
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Taxonomy
TopicsElasticity and Wave Propagation · Contact Mechanics and Variational Inequalities · Elasticity and Material Modeling