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A characterization of Generalized functions of Bounded Deformation

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arxiv 2502.10861 v1 pith:KN2VJZBM submitted 2025-02-15 math.FA cond-mat.mtrl-sci

Antonin Chambolle , Vito Crismale This is my paper · ORCID
classification math.FAcond-mat.mtrl-sci
keywords boundedcharacterizationconditionscrackdefineddeformationdirectionselasticity
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We show that Dal Maso's GBD space, introduced for tackling crack growth in linearized elasticity, can be defined by simple conditions in a finite number of directions of slicing.

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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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