Quasistatic evolution of magnetoelastic thin films via dimension reduction

TL;DR

This paper develops a mathematical model for the slow, rate-independent evolution of magnetoelastic thin films by reducing the three-dimensional problem to a two-dimensional one through dimension reduction techniques.

Contribution

It introduces a novel dimension reduction approach for quasistatic magnetoelastic thin films and proves the existence of energetic solutions for the resulting nonlinear evolution system.

Findings

Successful derivation of a 2D model from 3D magnetoelastic systems.

Establishment of existence results for energetic solutions.

Framework for analyzing quasistatic evolution in thin film magnetoelasticity.

Abstract

A rate-independent model for the quasistatic evolution of a magnetoelastic thin film is advanced and analyzed. Starting from the three-dimensional setting, we present an evolutionary $\Gamma$-convergence argument in order to pass to the limit in one of the material dimensions. By taking into account both conservative and dissipative actions, a nonlinear evolution system of rate-independent type is obtained. The existence of so-called {\it energetic solutions} to such system is proved via approximation.