| Issue |
ESAIM: M2AN
Volume 50, Number 1, January-February 2016
|
|
|---|---|---|
| Page(s) | 77 - 91 | |
| DOI | https://doi.org/10.1051/m2an/2015032 | |
| Published online | 16 November 2015 | |
A relation between a dynamic fracture model and quasi-static evolution
Instituto de Matemática, Universidade Federal do Rio de
Janeiro, Brasil
henrique@im.ufrj.br; versieux@gmx.com
Received:
5
May
2014
Revised:
13
January
2015
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.
Mathematics Subject Classification: 35Q74 / 74R10 / 74R15
Key words: Dynamic fracture model / quasi-static fracture model / energy balance / vanishing viscosity
© EDP Sciences, SMAI, 2015
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