Effective Theories for Incompressible Magnetoelastic Shallow Shells.

Abstract

We characterize the asymptotic behaviour, in the sense of $\Gamma$ -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.