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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.
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.
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