The modeling of fracture problems within geometrically linear elasticity is often based on the space of generalized functions of bounded deformation GSBD$$(Ω), p ∈ (1, ∞), their treatment is however hindered by the very low regularity of those functions and by the lack of appropriate density results. We construct here an approximation of GSBD$$ functions, for p ∈ (1, ∞), with functions which are Lipschitz continuous away from a jump set which is a finite union of closed subsets of C1 hypersurfaces. The strains of the approximating functions converge strongly in L$$ to the strain of the target, and the area of their jump sets converge to the area of the target. The key idea is to use piecewise affine functions on a suitable grid, which is obtained via the Freudenthal partition of a cubic grid.
Accepté le :
DOI : 10.1051/cocv/2018021
Keywords: Generalized functions of bounded deformation, p-growth, piecewise finite elements, brittle fracture
Conti, Sergio 1 ; Focardi, Matteo 1 ; Iurlano, Flaviana 1
@article{COCV_2019__25__A34_0,
author = {Conti, Sergio and Focardi, Matteo and Iurlano, Flaviana},
title = {Approximation of fracture energies with p-growth via piecewise affine finite elements},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2019},
publisher = {EDP Sciences},
volume = {25},
doi = {10.1051/cocv/2018021},
zbl = {1437.65182},
mrnumber = {4003465},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2018021/}
}
TY - JOUR AU - Conti, Sergio AU - Focardi, Matteo AU - Iurlano, Flaviana TI - Approximation of fracture energies with p-growth via piecewise affine finite elements JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2018021/ DO - 10.1051/cocv/2018021 LA - en ID - COCV_2019__25__A34_0 ER -
%0 Journal Article %A Conti, Sergio %A Focardi, Matteo %A Iurlano, Flaviana %T Approximation of fracture energies with p-growth via piecewise affine finite elements %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2018021/ %R 10.1051/cocv/2018021 %G en %F COCV_2019__25__A34_0
Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana. Approximation of fracture energies with p-growth via piecewise affine finite elements. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 34. doi: 10.1051/cocv/2018021
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