Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave

Abstract : The interactions between linear elastic waves and a nonlinear crack with finite compressibility are studied in the one-dimensional context. Numerical studies on a hyperbolic model of contact with sinusoidal forcing have shown that the mean values of the scattered elastic displacements are discontinuous across the crack. The mean dilatation of the crack also increases with the amplitude of the forcing levels. The aim of the present theoretical study is to analyse these nonlinear processes under a larger range of nonlinear jump conditions. For this purpose, the problem is reduced to a nonlinear differential equation. The dependence of the periodic solution on the forcing amplitude is quantified under sinusoidal forcing conditions. Bounds for the mean, maximum and minimum values of the solution are presented. Lastly, periodic forcing with a null mean value is addressed. In that case, a result about the mean dilatation of the crack is obtained.
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00339279
Contributeur : Bruno Lombard <>
Soumis le : mardi 24 mars 2009 - 15:40:47
Dernière modification le : vendredi 29 avril 2016 - 15:49:07
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 11:49:37

Fichiers

JuLo08V2.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00339279, version 2
  • ARXIV : 0811.2737

Citation

Stéphane Junca, Bruno Lombard. Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2009, 70 (3), pp.735-761. <hal-00339279v2>

Partager

Métriques

Consultations de
la notice

247

Téléchargements du document

128