[Instabilités en coin dans un cylindre mince non linéairement élastique : solutions analytiques mécanisme déformation]
Dans cette Note, on étudie les instabilités « en coin » dans un cylindre mince formé d'un matériau non linéairement élastique. Partant des équations nonlinéaires tri-dimensionnelle, nous obtenons par une méthode nouvelle un système dynamique singulier. On montre que ce système retient les instabilités en coin. Nous obtenons également les expressions analytiques des solutions. On met aussi en évidence le fait que l'effet de couplage entre la nonlinéarité du matériau et la longueur caractéristique est le mécanisme qui provoque l'apparition de coins.
In this Note, we study the corner instabilities in a slender cylinder constituted by a nonlinearly elastic material. Starting from the three-dimensional nonlinear field equations, we derive, through a novel method, a singular dynamical system as the normal form equation. It is shown that this system can capture the corner instabilities. We are also able to obtain analytical expressions of the solutions. The mechanism that causes corner formations is also found.
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@article{CRMATH_2007__345_1_55_0,
author = {Hui-Hui Dai and Fan-Fan Wang},
title = {Corner instabilities in a slender nonlinearly elastic cylinder: analytical solutions and formation mechanism},
journal = {Comptes Rendus. Math\'ematique},
pages = {55--58},
publisher = {Elsevier},
volume = {345},
number = {1},
year = {2007},
doi = {10.1016/j.crma.2007.05.020},
language = {en},
}
TY - JOUR AU - Hui-Hui Dai AU - Fan-Fan Wang TI - Corner instabilities in a slender nonlinearly elastic cylinder: analytical solutions and formation mechanism JO - Comptes Rendus. Mathématique PY - 2007 SP - 55 EP - 58 VL - 345 IS - 1 PB - Elsevier DO - 10.1016/j.crma.2007.05.020 LA - en ID - CRMATH_2007__345_1_55_0 ER -
Hui-Hui Dai; Fan-Fan Wang. Corner instabilities in a slender nonlinearly elastic cylinder: analytical solutions and formation mechanism. Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 55-58. doi : 10.1016/j.crma.2007.05.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.020/
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