Journal article
Modeling of Cracks with Nonlinear Effects at the Tip Zones and the Generalized Energy Criterion
Publication Details
Authors: | Specovius-Neugebauer, M. |
Publication year: | 2011 |
Journal: | Archive for Rational Mechanics and Analysis |
Pages range : | 1019-1057 |
Volume number: | 202 |
Start page: | 1019 |
End page: | 1057 |
ISSN: | 0003-9527 |
eISSN: | 1432-0673 |
DOI-Link der Erstveröffentlichung: |
Abstract
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.
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.
