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Variational and Hemivariational Inequalities in Mechanics of Elastoplastic, Granular Media, and Quasibrittle Cracks

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Analysis, Modelling, Optimization, and Numerical Techniques

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 121))

Abstract

This contribution is devoted to the mathematical theory of elastoplastic and granular solids as well as the quasibrittle fracture of nonlinear cracks. Basic variational and hemivariational inequalities describing nonlinear phenomena due to plasticity, internal friction, interfacial interaction, and alike dissipative physics are outlined from the point of view of nonsmooth and nonconvex optimization. Primary results of the nonlinear theory and its application to solid mechanics are surveyed.

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Acknowledgment

B. D. Annin is supported by the Russian Foundation for Basic Research (grant no. 12-01-00507). V. A. Kovtunenko is supported by the Austrian Science Fund (FWF), project P26147-N26. He thanks O. Vasilieva and J. R. Gonzalez for his visit to the Universidad Tecnologica de Pereira and ICAMI 2013 with the support of the Colombian Department for Science (COLCIENCIAS). V. M. Sadovskii is supported by the Complex Fundamental Research Program no. 18 “Algorithms and Software for Computational Systems of Superhigh Productivity” of the Presidium of Russian Academy of Sciences and by the Russian Foundation for Basic Research (grant no. 14–01–00130).

Author information

Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, 630090, Novosibirsk, Russia

    Boris D. Annin

  2. Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrichstr. 36, 8010, Graz, Austria

    Victor A. Kovtunenko

  3. Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, 660036, Krasnoyarsk, Russia

    Vladimir M. Sadovskii

  4. Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Victor A. Kovtunenko

Authors
  1. Boris D. Annin
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  2. Victor A. Kovtunenko
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  3. Vladimir M. Sadovskii
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Corresponding author

Correspondence to Victor A. Kovtunenko .

Editor information

Editors and Affiliations

  1. Department of Electric, Electronic and Computer Science, Universidad Nacional de Colombia, Manizales, Colombia

    Gerard Olivar Tost

  2. Mathematics, Universidad del Valle, Cali, Colombia

    Olga Vasilieva

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Annin, B., Kovtunenko, V., Sadovskii, V. (2015). Variational and Hemivariational Inequalities in Mechanics of Elastoplastic, Granular Media, and Quasibrittle Cracks. In: Tost, G., Vasilieva, O. (eds) Analysis, Modelling, Optimization, and Numerical Techniques. Springer Proceedings in Mathematics & Statistics, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-12583-1_3

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