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.
Quasi-static evolution in brittle fracture: the case of bounded solutions
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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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A matrix-valued measure associated to the derivatives of a function of generalised bounded deformation
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.