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Nonconvex bundle method with application to a delamination problem

Author

Listed:
  • Minh N. Dao

    (Hanoi National University of Education
    Université de Toulouse)

  • Joachim Gwinner

    (Universität der Bundeswehr München)

  • Dominikus Noll

    (Université de Toulouse)

  • Nina Ovcharova

    (Universität der Bundeswehr München)

Abstract

Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the stress field along the contact boundary. This leads to a hemivariational inequality, which after discretization by finite elements we solve by a nonconvex bundle method, where upper- $$C^1$$ C 1 criteria have to be minimized. As this is in contrast with other classes of mechanical problems with non-monotone friction laws and in other applied fields, where criteria are typically lower- $$C^1$$ C 1 , we propose a bundle method suited for both types of nonsmoothness. We prove its global convergence in the sense of subsequences and test it on a typical delamination problem of material sciences.

Suggested Citation

  • Minh N. Dao & Joachim Gwinner & Dominikus Noll & Nina Ovcharova, 2016. "Nonconvex bundle method with application to a delamination problem," Computational Optimization and Applications, Springer, vol. 65(1), pages 173-203, September.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:1:d:10.1007_s10589-016-9834-0
    DOI: 10.1007/s10589-016-9834-0
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    References listed on IDEAS

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    1. Nina Ovcharova & Joachim Gwinner, 2014. "A Study of Regularization Techniques of Nondifferentiable Optimization in View of Application to Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 754-778, September.
    2. W. Hare & C. Sagastizábal & M. Solodov, 2016. "A proximal bundle method for nonsmooth nonconvex functions with inexact information," Computational Optimization and Applications, Springer, vol. 63(1), pages 1-28, January.
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    Cited by:

    1. Ouayl Chadli & Joachim Gwinner & M. Zuhair Nashed, 2022. "Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 42-65, June.
    2. Wim Ackooij & Welington Oliveira, 2019. "Nonsmooth and Nonconvex Optimization via Approximate Difference-of-Convex Decompositions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 49-80, July.
    3. Najmeh Hoseini Monjezi & S. Nobakhtian, 2019. "A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization," Computational Optimization and Applications, Springer, vol. 74(2), pages 443-480, November.

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