Quasistatic evolution of a brittle thin film

Details Quasistatic evolution of a brittle thin film Quasistatic evolution of a brittle thin film

2006-04-26

arxiv.org/abs/math/0604557v1

Calc. Var. Part. Diff. Eq. 26 (2006), no. 1, 69-118

Mathematics

Analysis of PDEs

43 pages

Scientific paper

This paper deals with the quasistatic crack growth of a homogeneous elastic brittle thin film. It is shown that the quasistatic evolution of a three-dimensional cylinder converges, as its thickness tends to zero, to a two-dimensional quasistatic evolution associated with the relaxed model. Firstly, a $\Gamma$-convergence analysis is performed with a surface energy density which does not provide weak compactness in the space of Special Functions of Bounded Variation. Then, the asymptotic analysis of the quasistatic crack evolution is presented in the case of bounded solutions that is with the simplifying assumption that every minimizing sequence is uniformly bounded in $L^\infty$.

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