Explicit phase diagram for a one-dimensional blister model

Ghada Chmaycem (1, 2) , Mustapha Jazar (2) , Régis Monneau (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 Mathematics Department

In this article, we consider a simple one-dimensional variational model, describing the delamination of thin films under cooling. We characterize the global minimizers, which correspond to films of three possible types: non delaminated, partially delaminated (called blisters), or fully delaminated. Two parameters play an important role: the length of the film and the cooling parameter. In the phase plane of those two parameters, we classify all the minimizers. As a consequence of our analysis, we identify explicitly the smallest possible blisters for this model.

Mots clés: blister; thin film; fracture; delimitation; buckling; Föppel-von Kármán; variational model; phase diagram

Domaines: Mathématiques générales [math.GM]; Physique mathématique [math-ph]

Ghada Chmaycem, Mustapha Jazar, Régis Monneau. Explicit phase diagram for a one-dimensional blister model. 2014. ⟨hal-00947515⟩