[Sur le contact de Boussinesq–Love et l'impact entre corps hyperélastiques]
Cet article est consacré à la modélisation de grandes déformations hyperélastiques en présence du contact et de l'impact. Une formulation en Lagrangien total est adoptée pour décrire le comportement avec non linéarités géométriques. Un schéma du premier ordre est appliqué pour intégrer les équations du mouvement. Le problème du contact est résolu à l'aide de la méthode du bi-potentiel. Pour l'implantation par éléments finis, une expression explicite de l'opérateur tangent est proposée dans le cas du modèle hyperélastique . Le problème classique du contact de Boussinesq–Love est traité numériquement. Un deuxième exemple concerne l'impact entre deux blocs hyperélastiques en trois dimensions.
This article is devoted to the modeling of finite deformations of hyperelastic bodies under contact/impact conditions. A total Lagrangian formulation is adopted to describe the geometrically nonlinear behavior. A first order algorithm is applied to integrate the equations of motion. The contact problem is solved by the bi-potential method. For the finite element implementation, an explicit expression of the tangent operator for the hyperelastic model is derived. The classical Boussinesq–Love contact problem is first investigated numerically. A second example concerns the impact between two hyperelastic bodies in three-dimension.
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Mot clés : Mécanique des solides numérique, Elasticité isotrope, Contact–impact
@article{CRMECA_2007__335_9-10_536_0,
author = {Zhi-Qiang Feng and Claude Vall\'ee},
title = {From {Boussinesq{\textendash}Love} contact to impact between hyperelastic bodies},
journal = {Comptes Rendus. M\'ecanique},
pages = {536--547},
publisher = {Elsevier},
volume = {335},
number = {9-10},
year = {2007},
doi = {10.1016/j.crme.2007.01.009},
language = {en},
}
Zhi-Qiang Feng; Claude Vallée. From Boussinesq–Love contact to impact between hyperelastic bodies. Comptes Rendus. Mécanique, Volume 335 (2007) no. 9-10, pp. 536-547. doi : 10.1016/j.crme.2007.01.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.01.009/
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