Effective Theories for Incompressible Magnetoelastic Shallow Shells

Abstract We characterize the asymptotic behaviour, in the sense of $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -convergence, of a thin magnetoelastic shallow shell. The compactness is achieved up to rigid motions. For deformations, it relies on an approximation by rigid movements, whereas for magnetizations it is based on a careful consideration of the geometry of the deformed domain. This result is a generalization of [1] by incorporating geometric effects due to vanishing curvature, which constitute the main novelty of the analysis.