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Cohesive Fracture in 1D: Quasi-static Evolution and Derivation from Static Phase-Field Models

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Abstract

In this paper we propose a notion of irreversibility for the evolution of cracks in the presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with damage models, and we investigate its applicability to the construction of a quasi-static evolution in a simple one-dimensional model. The cohesive fracture model arises naturally via \(\Gamma \)-convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which may be used as regularization for numerical simulations.

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Acknowledgements

We acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project 211504053 – CRC 1060 The mathematics of emergent effects at the University of Bonn. MB is member of the 2019 INdAM - GNAMPA project Analysis and optimisation of thin structures. FI wishes to thank the warm hospitality of the Institute for Applied Mathematics at the University of Bonn where part of this work has been carried out. FI has been a recipient of scholarships from the Fondation Sciences Mathématiques de Paris, Emergence Sorbonne Université, and the Séphora-Berrebi Foundation, and gratefully acknowledges their support. FI acknowledges support through the PEPS CNRS 2019 Évolution quasi-statique de la rupture cohésive à travers une approche de champ de phase.

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Authors and Affiliations

  1. Department of Mathematics, University of Trento, Via Sommarive 14, 38123, Povo, TN, Italy

    Marco Bonacini

  2. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Sergio Conti

  3. Laboratoire Jacques-Louis Lions (LJLL), Sorbonne-Université, CNRS, Université de Paris, 75005, Paris, France

    Flaviana Iurlano

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  1. Marco Bonacini
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  2. Sergio Conti
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Correspondence to Marco Bonacini.

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Communicated by G. Dal Maso.

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Bonacini, M., Conti, S. & Iurlano, F. Cohesive Fracture in 1D: Quasi-static Evolution and Derivation from Static Phase-Field Models. Arch Rational Mech Anal 239, 1501–1576 (2021). https://doi.org/10.1007/s00205-020-01597-1

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