Simple models of rapid fracture

Marder, Michael

doi:10.1016/0167-2789(93)90230-x

Cited by 17 publications

(14 citation statements)

References 24 publications

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“…However, one should be cautious as this limit predicts that v = 1 also for δ ≤ δ c , which in light of the discussion above, is wrong. This observation was made previously for a related model [10].…”

Section: A the Linear Modelsupporting

confidence: 82%

“…displacement exceeds u 0 . The small dissipation associated with η is essential to ensure the existence of steady states, see [10] and below for details. A sketch of the one-dimensional model is shown in Fig.…”

Section: The Modelsmentioning

confidence: 99%

“…In contradistinction, the tip instabilities observed experimentally [1,2] involve in an essential way the deviation of the crack from the pre-instability straight path. Bearing this limitation of the one-dimensional models in mind and expecting no instability in this framework [10,11], we still want to study the response of the steady state cracks in these simple models to small perturbations. The motivation for that is to gain some insights (or hints) about the kind of near crack tip physics that is overlooked by the common exclusion of elastic nonlinearities, especially as far as perturbations are considered.…”

Section: Response To Perturbations: Linear Stability Analysismentioning

confidence: 99%

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Elastic nonlinearities in a one-dimensional model of fracture

Bouchbinder

2008

Phys. Rev. E

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The dynamics of rapid brittle cracks is commonly studied in the framework of linear elastic fracture mechanics where nonlinearities are neglected. However, recent experimental and theoretical work demonstrated explicitly the importance of elastic nonlinearities in fracture dynamics. We study two simple one-dimensional models of fracture in order to gain insights about the role of elastic nonlinearities and the implications of their exclusion in the common linear elastic approximation. In one model we consider the decohesion of a nonlinear elastic membrane from a substrate. In a second model we follow the philosophy of linear elastic fracture mechanics and study a linearized version of the nonlinear model. By analyzing the steady state solutions, the velocity-load relations and the response to perturbations of the two models we show that the linear approximation fails at finite crack tip velocities. We highlight certain features of the breakdown of the linear theory and discuss possible implications of our results to higher dimensional systems.

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Section: A the Linear Modelsupporting

confidence: 82%

Section: The Modelsmentioning

confidence: 99%

Section: Response To Perturbations: Linear Stability Analysismentioning

confidence: 99%

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Elastic nonlinearities in a one-dimensional model of fracture

Bouchbinder

2008

Phys. Rev. E

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“…6 which induce non-unique value of v. This ambiguousness may be avoided if the definite type of load is considered and its characteristic magnitude is plotted against a crack speed. Such dependences are shown for the cases of constant edge displacements [2,7,13], constant strain or force at one ends of a chain [19] or a moving load [5].…”

Section: Solution Analysismentioning

confidence: 95%

“…Notice that the problem itself is non-linear and superposition principle does not work. Furthermore, numerical simulations showed that there exist regimes that are not compatible with steady-state ones [2,13] and the linear analysis of stability was performed [7]. Apart from that there were numerically observed [10] and theoretically explained later on in [22] so-called clustering quasi steady-state regime, where in average the crack moves regularly but within the period (cluster) it is not seen.…”

Section: Introductionmentioning

confidence: 99%

Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice

Gorbushin

Mishuris

2017

Mech. Solids

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In the present work the authors revisit a classical problem of crack propagation in a lattice. Authors investigate the questions concerning possible admissible steady-state crack propagations in an anisotropic lattice. It was found that for certain values of contrast in elastic and strength properties of a lattice the stationary crack propagation is impossible. Authors also address a question of possible crack propagation at low velocity.

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