A fully-coupled nonlinear magnetoelastic thin shell formulation

TL;DR

This paper introduces a comprehensive, geometrically exact 2D model for nonlinear deformation of thin magnetoelastic shells, incorporating magnetic variables into the classical shell theory for improved accuracy in design applications.

Contribution

It develops a fully-coupled nonlinear shell formulation that generalizes mechanical assumptions to magnetic variables, using a variational approach and considering the entire deformation map.

Findings

Analytical solution for an infinite cylindrical shell demonstrates model capabilities.

Discards plane stress assumption due to Maxwell stresses, ensuring physical accuracy.

Provides a new variational framework for magnetoelastic shell analysis.

Abstract

A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a consistent two-dimensional theory based on a rigorous variational approach. The general deformation map, as opposed to the mid-surface deformation, is considered as the primary variable resulting in a more accurate description of the nonlinear deformation. The commonly used plane stress assumption is discarded due to the Maxwell stress in the surrounding free-space requiring careful treatment on the upper and lower shell surfaces. The complexity arising from the boundary terms when deriving the Euler-Lagrange governing equations is addressed via a unique application of Green's theorem.The governing equations are solved analytically for the problem of an infinite cylindrical magnetoelastic shell. This clearly demonstrates the model's capabilities and provides a physical interpretation of the new variables in the modified variational approach. This novel formulation for magnetoelastic shells serves as a valuable tool for the accurate design of thin magneto-mechanically coupled devices.