Variational limits of problems in junction domains for ferroelectric and hyperelastic materials by reduction of dimensión = Problemas límites en la modelización de fenómenos ferro-eléctricos e hiperelásticos en la unión de dominios por reducción de dimensión.

Abstract

In this work, firstly we study the junction phenomena for two joined thin structures in two kind of context, the first: ferroelectricity, starting from a non-convex and nonlocal 3D-variational model for the electric polarization in a T−junction of two orthogonal thin wires made of ferroelectric material, and using an asymptotic process based on dimensional reduction, we obtain different 1D variational models depending of the initially boundary condition, and the second context: hyperelasticity, starting from 3D nonlinear elasticity equations and using dimensional reduction and Γ−convergence analyze junction phenomena for two orthogonal joined thin beams and we obtain a 1D variational model composed of the elastic energy of the vertical beam and the horizontal beam