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- W4287907811 abstract "We analyze a finite-difference approximation of a functional of Ambrosio-Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step $delta$ is smaller than the ellipticity parameter $varepsilon$, we show the $Gamma$-convergence of the model to the Griffith functional, containing only a term enforcing Dirichlet boundary conditions and no $L^p$ fidelity term. Restricting to two dimensions, we also address the case in which a (linearized) constraint of non-interpenetration of matter is added in the limit functional, in the spirit of a recent work by Chambolle, Conti and Francfort." @default.
- W4287907811 created "2022-07-26" @default.
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- W4287907811 date "2020-01-02" @default.
- W4287907811 modified "2023-10-16" @default.
- W4287907811 title "A derivation of Griffith functionals from discrete finite-difference models" @default.
- W4287907811 doi "https://doi.org/10.48550/arxiv.2001.00480" @default.
- W4287907811 hasPublicationYear "2020" @default.
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