Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening
SISSA, Via Bonomea 265, 34136 Trieste, Italy.
Received: 12 February 2015
Revised: 24 September 2015
Accepted: 21 March 2016
In the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.
Mathematics Subject Classification: 49Q10 / 35J20 / 35Q74 / 74R99 / 74G65
Key words: Variational models / free-discontinuity problems / energy release rate / energy derivative / cohesive fracture / crack propagation / quasi-static evolution / local minimizers / Griffith’s criterion / vanishing viscosity
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