Evaluation of External Magnetic Flux Density in Piezo-Flexomagnetic Nanobeams Using a Hybrid 1D-2D Finite Element Framework

TL;DR

This paper presents a hybrid finite element framework to evaluate external magnetic flux in piezo-flexomagnetic nanobeams, highlighting the significance of external magnetic fields in sensor design.

Contribution

It introduces a coupled 1D-2D finite element model that accounts for external magnetic flux, which is often neglected in prior studies.

Findings

External magnetic flux is significant even without piezomagnetic coupling.

The framework is verified against analytical solutions.

Material parameters strongly influence magnetic flux density.

Abstract

This study numerically evaluates the external magnetic flux density generated in air by the bending of a piezo-flexomagnetic nanobeam. In several classes of non-contact sensors, the magnetic field induced in the surrounding medium is often more useful than the internal magnetic response. However, most theoretical studies on piezo-flexomagnetic nanostructures neglect the external magnetic domain. The proposed framework employs a coupled hybrid finite element formulation combining a 1D Timoshenko beam model with a 2D magnetostatic problem encompassing both the beam body and the surrounding air domain. The formulation is verified against analytical solutions of magnetically isolated piezo-flexomagnetic beams. The results demonstrate the presence of a significant external magnetic flux distribution in free-standing structures, even in the absence of piezomagnetic coupling. A systematic sensitivity analysis further identifies the material parameters most strongly influencing the external transverse magnetic flux density. These findings provide insight into the design of nanoscale non-contact magnetoelastic sensing systems.