The mathematics of thin structures

This article offers various mathematical contributions to the behavior of thin films. The common thread is view film as variational limit a three-dimensional domain with related when thickness that vanishes. After short review in Section 1 regimes can arise such an asymptotic process performed classical elastic case, giving rise well-known models plate theory (membrane, bending, Von Karmann, etc…), other sections address extensions those initial results. 2 adds brittleness and delamination investigates brittle membrane regime. Sections 4 5 focus on micromagnetics, rather than elasticity, this once again regime discuss magnetic skyrmions walls, respectively. Finally, 3 revisits setting non-Euclidean induced by presence pre-strain model.