Geodesic
A relation between a dynamic fracture model and quasi-static evolution
Versieux, Henrique1
1 Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brasil
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 77-91

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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.

Reçu le :
DOI : 10.1051/m2an/2015032
Classification : 35Q74, 74R10, 74R15
Keywords: Dynamic fracture model, quasi-static fracture model, energy balance, vanishing viscosity

Versieux, Henrique 1

1 Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brasil 
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     title = {A relation between a dynamic fracture model and quasi-static evolution},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {77--91},
     publisher = {EDP-Sciences},
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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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