Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 60, Number 4 (2008), 1219-1253.
Evolution of a crack with kink and non-penetration
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.
J. Math. Soc. Japan, Volume 60, Number 4 (2008), 1219-1253.
First available in Project Euclid: 5 November 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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