A geometrically exact model for thin magneto-elastic shells

TL;DR

This paper introduces a geometrically exact, reduced two-dimensional model for thin magneto-elastic shells actuated by magnetic fields, validated against 3D nonlinear models, facilitating design of magnetic structures.

Contribution

The paper develops a novel reduced magneto-elastic shell model incorporating geometrically exact strains and provides a physical interpretation of magnetic effects.

Findings

Excellent agreement with 3D nonlinear models

Identification of primary magneto-elastic mechanisms

Validation through indentation and buckling tests

Abstract

We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love assumption, we derive a reduced two-dimensional magneto-elastic energy that can be minimized through numerical analysis. In parallel, we simplify the reduced energy by expanding it up to the second-order in the displacement field and provide a physical interpretation. Our theoretical analysis allows us to identify and interpret the two primary mechanisms dictating the magneto-elastic response: a combination of equivalent magnetic pressure and forces at the first order, and distributed magnetic torques at the second order. We contrast our reduced framework against a three-dimensional nonlinear model by investigating three test cases involving the indentation and the pressure buckling of shells under magnetic loading. We find excellent agreement between the two approaches, thereby verifying our reduced model for shells undergoing nonlinear and non-axisymmetric deformations. We believe that our model for magneto-elastic shells will serve as a valuable tool for the rational design of magnetic structures, enriching the set of reduced magnetic models.