Evolution of a crack with kink and non-penetration
Alexander M. KHLUDNEV, Victor A. KOVTUNENKO, and Atusi TANI
Source: J. Math. Soc. Japan Volume 60, Number 4 (2008), 1219-1253.
Abstract
The nonlinear evolution problem for a crack with a kink in elastic body is considered. This nonlinear formulation accounts the condition of mutual non-penetration between the crack faces. The kinking crack is presented with the help of two unknown shape parameters of the kink angle and of the crack length, which minimize an energy due to the Griffith hypothesis. Based on the obtained results of the shape sensitivity analysis, solvability of the evolutionary minimization problem is proved, and the necessary conditions for the optimal crack are derived.
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1225894039
Digital Object Identifier: doi:10.2969/jmsj/06041219
Journal of the Mathematical Society of Japan