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Related Experiment Video

Updated: Jul 7, 2026

Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System

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Published on: August 7, 2018

Effective Theories for Incompressible Magnetoelastic Shallow Shells.

Emanuele Tasso¹, Tobias Unterberger¹

¹Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.

Milan Journal of Mathematics

|July 6, 2026

Summary

This study analyzes the asymptotic behavior of thin magnetoelastic shallow shells using Gamma-convergence. It incorporates geometric effects from vanishing curvature, generalizing previous work.

Keywords:

Dimension reduction Magnetoelasticity

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Published on: April 25, 2019

Area of Science:

Solid Mechanics
Continuum Mechanics
Mathematical Physics

Background:

Magnetoelasticity describes the interplay between magnetic fields and mechanical deformation in materials.
Shallow shell theory simplifies the analysis of thin structures with small deflections.
Gamma-convergence is a mathematical tool for analyzing the limiting behavior of energies.

Purpose of the Study:

To characterize the asymptotic behavior of thin magnetoelastic shallow shells using Gamma-convergence.
To incorporate the effects of vanishing curvature in the shell's geometry.
To generalize existing models by including these novel geometric considerations.

Main Methods:

Utilizing Gamma-convergence to analyze the asymptotic behavior.
Employing approximations by rigid movements for deformations.
Carefully considering the geometry of the deformed domain for magnetizations.

Main Results:

Establishing compactness up to rigid motions for the shell's behavior.
Demonstrating the influence of vanishing curvature on the shell's properties.
Providing a generalized framework for magnetoelastic shallow shell analysis.

Conclusions:

The analysis successfully incorporates geometric effects due to vanishing curvature.
The study offers a generalized understanding of thin magnetoelastic shallow shell behavior.
This work advances the mathematical modeling of magnetoelastic materials.