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October, 2008 Evolution of a crack with kink and non-penetration
Alexander M. KHLUDNEV, Victor A. KOVTUNENKO, Atusi TANI
J. Math. Soc. Japan 60(4): 1219-1253 (October, 2008). DOI: 10.2969/jmsj/06041219


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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Alexander M. KHLUDNEV. Victor A. KOVTUNENKO. Atusi TANI. "Evolution of a crack with kink and non-penetration." J. Math. Soc. Japan 60 (4) 1219 - 1253, October, 2008.


Published: October, 2008
First available in Project Euclid: 5 November 2008

zbMATH: 1153.49040
MathSciNet: MR2467876
Digital Object Identifier: 10.2969/jmsj/06041219

Primary: 49Q10
Secondary: 49J40 , 49K10 , 74R10

Keywords: crack with non-penetration , Griffith fracture , kink of crack , shape sensitivity analysis and optimization

Rights: Copyright © 2008 Mathematical Society of Japan


Vol.60 • No. 4 • October, 2008
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