We study the relations between a dynamic model proposed by Bourdin, Larsen and Richardson, and quasi-static fracture evolution. We assume the dynamic model has the boundary displacements of the material as input, and consider time-rescaled solutions of this model associated to a sequence of boundary conditions with speed going to zero. Next, we study whether this rescaled sequence converges to a function satisfying quasi-static fracture evolution. Under some hypotheses and assuming the speed of crack propagation slows down following the deceleration of boundary displacements, our main result shows that (up to a subsequence) the rescaled solutions converge to a quasi-static evolution.
DOI : 10.1051/m2an/2015032
Keywords: Dynamic fracture model, quasi-static fracture model, energy balance, vanishing viscosity
Versieux, Henrique 1
@article{M2AN_2016__50_1_77_0,
author = {Versieux, Henrique},
title = {A relation between a dynamic fracture model and quasi-static evolution},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {77--91},
year = {2016},
publisher = {EDP Sciences},
volume = {50},
number = {1},
doi = {10.1051/m2an/2015032},
zbl = {1334.35343},
mrnumber = {3460102},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2015032/}
}
TY - JOUR AU - Versieux, Henrique TI - A relation between a dynamic fracture model and quasi-static evolution JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 77 EP - 91 VL - 50 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2015032/ DO - 10.1051/m2an/2015032 LA - en ID - M2AN_2016__50_1_77_0 ER -
%0 Journal Article %A Versieux, Henrique %T A relation between a dynamic fracture model and quasi-static evolution %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 77-91 %V 50 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2015032/ %R 10.1051/m2an/2015032 %G en %F M2AN_2016__50_1_77_0
Versieux, Henrique. A relation between a dynamic fracture model and quasi-static evolution. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 77-91. doi: 10.1051/m2an/2015032
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