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Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue

Centre de Mathématiques Appliquées, École Polytechnique, UMR CNRS 7641, Palaiseau Cedex, 91128, France

Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, Napoli, 80126, Italy

E-mail Address: [email protected]

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and

Gianluca Orlando

Corresponding author

Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, Garching bei München, 85747, Germany

E-mail Address: [email protected]

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https://doi.org/10.1142/S0218202518500379Cited by:13

Abstract

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

Communicated by G. Dal Maso

Keywords:

AMSC: 74C05, 74R99, 35Q74, 74G65, 35A35

References

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Published: 6 April 2018

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Vol. 28, No. 07

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Received 26 May 2017

Revised 20 February 2018

Accepted 26 February 2018

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Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue

Abstract

References

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