Modeling of Cracks with Nonlinear Effects at the Tip Zones and the Generalized Energy Criterion

Autor:	Serguei A. Nazarov, Maria Specovius-Neugebauer
Rok vydání:	2011
Předmět:	Nonlinear system Mathematics (miscellaneous) Classical mechanics Homogeneous Mechanical Engineering Mathematical analysis Complex system A domain Elastic energy Elasticity (economics) Anisotropy Analysis Mathematics
Zdroj:	Archive for Rational Mechanics and Analysis. 202:1019-1057
ISSN:	1432-0673 0003-9527
DOI:	10.1007/s00205-011-0444-9
Popis:	Starting with a plane anisotropic homogeneous elasticity problem in a domain with an interior crack, we develop a mathematical frame where nonlinear effects in the tip zones like crack kinking or plastic zones can be modeled in an enlarged state space with the help of additional conditions at the crack tips. Using generalized Green’s formulae, we show that the solutions to these problems turn out to minimize energy functionals which contain terms additional to the classical elastic energy and work of external forces. They can be interpreted as performed work and energy stored in the crack tips. Within the theory of matched asymptotic expansions, the general type of these energy functionals can be characterized in a form applicable to mechanical problems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b20d61bdb1e412ba898d06ba0a9f2a28 https://doi.org/10.1007/s00205-011-0444-9 Zobrazit plný text záznamu Plný text ve formátu PDF