Intrinsic incremental evolution of hypoelastic discrete mechanical systems - Archive ouverte HAL
Article Dans Une Revue Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Année : 2023

Intrinsic incremental evolution of hypoelastic discrete mechanical systems

Jean Lerbet
Laboratoire de Mathématiques et Modélisation d'Evry
CV
Noël Challamel
Institut de Recherche Dupuy de Lôme
Francois Nicot
Institut des Sciences de la Terre
Félix Darve
Laboratoire sols, solides, structures - risques [Grenoble]
CV

Résumé

AbstractThis paper provides an explicit geometric and coordinate‐free formulation of incremental discrete mechanics in the framework of potentially non integrable hypoelasticity. First, the general framework is developed in order to tackle hypoelasticity as an Ehresmann connection on the cotangent bundle . Two types of incremental evolutions may be distinguished, the weak or integrable incremental evolutions and the strong or non integrable incremental evolutions, according to the nature of the hypoelastic constitutive law. The geometric structure of the double tangent bundle is fully used in order to get the geometric counterpart κ of the so‐called tangent stiffness matrix. Subject to specific conditions in , the incremental evolution is then a well‐founded question. An hypoelastic four‐grains granular system illustrates in detail these general results.

Domaines

Sciences de l'ingénieur [physics] Mathématiques [math]

Jean LERBET  : Connectez-vous pour contacter le contributeur

https://hal.science/hal-04351304

Soumis le : lundi 18 décembre 2023-17:03:49

Dernière modification le : jeudi 19 septembre 2024-16:44:04

Fichier non déposé

Dates et versions

hal-04351304 , version 1 (18-12-2023)

Identifiants

Citer

Jean Lerbet, Noël Challamel, Francois Nicot, Félix Darve. Intrinsic incremental evolution of hypoelastic discrete mechanical systems. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2023, 103 (11), ⟨10.1002/zamm.202300078⟩. ⟨hal-04351304⟩

Exporter

BibTeX XML-TEI Dublin Core DC Terms EndNote DataCite

Collections

INSU UNIV-BREST UNIV-SAVOIE UGA CNRS UNIV-EVRY OSUG 3S-R INSMI UBS ENIB ISTERRE LAMME UNIV-PARIS-SACLAY IRDL_UBS INRAE GS-LIFE-SCIENCES-HEALTH MATHNUM
43 Consultations
0 Téléchargements

Altmetric

Partager

More