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Energetic versus maximally-dissipative local solutions of a quasi-static rate-independent mixed-mode delamination model

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Abstract

A quasi-static rate-independent model of delamination of linearly elastic bodies at small strains, sensitive to mode of delamination, using interfacial damage and interfacial plasticity as two internal parameters, is further developed with the aim to extract representations typically employed in engineering interface-models, i.e. fracture envelope and fracture energy dependence on the mode mixity, which are suitable for the model fitting to experimental data. Moreover, two concepts of solutions are implemented: globally stable energy-conserving solutions or stress-driven maximally-dissipative local solutions, arising by the fully implicit or by a semi-implicit time-stepping procedures, respectively, both yielding numerically stable and convergent time-discretizations. Spatial discretization is performed by the symmetric Galerkin boundary-element method (SGBEM). Alternating quadratic programming is implemented to cope with, respectively, global or local, energy-minimizations in the computation of the time-discretized solutions. Sample 2D numerical examples document applicability of the model as well as efficiency of the SGBEM numerical implementation and facilitate comparison of the two mentioned solution concepts.

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Acknowledgments

The authors are indebted to an anonymous reviewer for many useful suggestions that improved the presentation in particular aspects. A part of the work has been accomplished during the stages of R. V. and T. R. at Universidad de Sevilla whose hospitality is acknowledged. Moreover, the authors acknowledge the support from the Spanish Ministry of Education (Ref. SAB2010-0082) and Spanish Ministry of Economy and Competitiveness (Project MAT2012-37387), from the Junta de Andalucía and European Social Fund through the Project of Excellence P08-TEP-04051, from the Slovak Ministry of Education through the grant 1/0201/11 (VEGA), as well as from the Czech Republic through the grants 201/10/0357, 201/12/0671, and 105/13/18652S (GA ČR), together with the institutional support RVO: 61388998.

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Authors and Affiliations

  1. Civil Engineering Faculty, Technical University of Košice, Vysokoškolská 4, 042 00, Košice, Slovakia

    Roman Vodička

  2. School of Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain

    Vladislav Mantič

  3. Mathematical Institute, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Tomáš Roubíček

  4. Institute of Thermomechanics of the ASCR, Dolejškova 5, 182 00, Praha 8, Czech Republic

    Tomáš Roubíček

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  1. Roman Vodička
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Correspondence to Roman Vodička.

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Vodička, R., Mantič, V. & Roubíček, T. Energetic versus maximally-dissipative local solutions of a quasi-static rate-independent mixed-mode delamination model. Meccanica 49, 2933–2963 (2014). https://doi.org/10.1007/s11012-014-0045-4

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