Volume 50, Number 1, January-February 2016
|Page(s)||77 - 91|
|Published online||16 November 2015|
A relation between a dynamic fracture model and quasi-static evolution
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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