Stability of quasi-static crack evolution through dimensional reduction

Jean-François Babadjian (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

This paper deals with quasi-static crack growth in thin films. We show that, when the thickness of the film tends to zero, any three-dimensional quasi-static crack evolution converges to a two-dimensional one, in a sense related to the Gamma-convergence of the associated total energy. We extend the prior analysis of [2] by adding conservative body and surface forces which allow us to remove the boundedness assumption on the deformation field

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Babadjian. Stability of quasi-static crack evolution through dimensional reduction. IUTAM symposium on variational concepts with applications to the mechanics of materials, Sep 2008, Bochum, Germany. pp.1-13, ⟨10.1007/978-90-481-9195-6_1⟩. ⟨hal-00797538⟩