Journal of the Mathematical Society of Japan

Evolution of a crack with kink and non-penetration

Alexander M. KHLUDNEV, Victor A. KOVTUNENKO, and Atusi TANI

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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.

Article information

Source
J. Math. Soc. Japan, Volume 60, Number 4 (2008), 1219-1253.

Dates
First available in Project Euclid: 5 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1225894039

Digital Object Identifier
doi:10.2969/jmsj/06041219

Mathematical Reviews number (MathSciNet)
MR2467876

Zentralblatt MATH identifier
1153.49040

Subjects
Primary: 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90]
Secondary: 49J40: Variational methods including variational inequalities [See also 47J20] 49K10: Free problems in two or more independent variables 74R10: Brittle fracture

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

Citation

KHLUDNEV, Alexander M.; KOVTUNENKO, Victor A.; TANI, Atusi. Evolution of a crack with kink and non-penetration. J. Math. Soc. Japan 60 (2008), no. 4, 1219--1253. doi:10.2969/jmsj/06041219. https://projecteuclid.org/euclid.jmsj/1225894039


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