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On Thermodynamically Consistent Formulations of Dynamic Models of Deformable Media and Their Numerical Implementation

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Book cover Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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Abstract

Mathematical models of the dynamics of elastic-plastic and granular media are formulated as variational inequalities for hyperbolic operators with one-sided constraints describing the transition of a material in plastic state. On this basis a priori integral estimates are constructed in characteristic cones of operators, from which follows the uniqueness and continuous dependence on initial data of solutions of the Cauchy problem and of the boundary-value problems with dissipative boundary conditions. With the help of an integral generalization of variational inequalities the relationships of strong discontinuity in dynamic models of elastic-plastic and granular media are obtained, whose analysis allows us to calculate velocities of shock waves and to construct discontinuous solutions. Original algorithms of solution correction are developed which can be considered as a realization of the splitting method with respect to physical processes.

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Author information

Authors and Affiliations

  1. Institute of Computational Modeling SB RAS, Akademgorodok 50/44, 660036, Krasnoyarsk, Russia

    Vladimir M. Sadovskii

Authors
  1. Vladimir M. Sadovskii
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Sadovskii, V.M. (2013). On Thermodynamically Consistent Formulations of Dynamic Models of Deformable Media and Their Numerical Implementation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_54

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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