Violation of the Complementing Condition and Local Bifurcation in Nonlinear Elasticity

Autor:	Errol L. Montes-Pizarro, Pablo V. Negrón-Marrero
Rok vydání:	2011
Předmět:	Mechanical Engineering Isotropy Mathematical analysis Rotational symmetry Geometry Differential operator Cylinder (engine) law.invention Mechanics of Materials law Compatibility (mechanics) Principal part General Materials Science Algebraic number Bifurcation Mathematics
Zdroj:	Journal of Elasticity. 107:151-178
ISSN:	1573-2681 0374-3535
DOI:	10.1007/s10659-011-9349-y
Popis:	The complementing condition (CC) is an algebraic compatibility requirement between the principal part of a linear elliptic differential operator and the principal part of the corresponding boundary operators. We study the implications of failure of the CC in the context of nonlinear elasticity. In particular we show that for axisymmetric deformations of cylinders and for any homogeneous isotropic material, failure of the CC is equivalent to the existence of sequences of possible bifurcation points accumulating at the point where the CC fails. For non axisymmetric deformations and for Hadamard–Green type materials, we show for axial compressions of the cylinder that the CC fails on a full interval of values of the loading parameter, and for the lateral compression problem it fails at least once.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::10051610ec93a8c4adb92fa88ff8505c https://doi.org/10.1007/s10659-011-9349-y Zobrazit plný text záznamu Full text from SpringerLink