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Khludnev, Alexander M.; Kovtunenko, Victor A.; Tani, Atusi

Evolution of a crack with kink and non-penetration. (English) Zbl 1153.49040

J. Math. Soc. Japan 60, No. 4, 1219-1253 (2008).
Summary: 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 necessary conditions for the optimal crack are derived.

Cited in 14 Documents

MSC:

49Q10 Optimization of shapes other than minimal surfaces
49J40 Variational inequalities
49K10 Optimality conditions for 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
PDFBibTeX XMLCite
\textit{A. M. Khludnev} et al., J. Math. Soc. Japan 60, No. 4, 1219--1253 (2008; Zbl 1153.49040)
Full Text: DOI

References:

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