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Quasi-static evolution in brittle fracture: the case of bounded solutions

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arxiv math/0401198 v1 pith:DJJNZEYW submitted 2004-01-16 math.AP

Gianni Dal Maso , Gilles A. Francfort , Rodica Toader This is my paper · ORCID
classification math.AP
keywords boundedbrittlecaseevolutionquasi-staticassumptioncrackselastic
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abstract

The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\infty$.

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  1. A matrix-valued measure associated to the derivatives of a function of generalised bounded deformation

    math.FA 2025-06 accept novelty 7.0 of 10

    Every GBD function carries a symmetric-matrix-valued measure whose decomposition separates absolutely continuous, Cantor, and jump contributions, and GSBD is exactly the class where the Cantor part vanishes.

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