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

Тип публикации: статья из журнала

Год издания: 2013

Идентификатор DOI: 10.1007/978-3-642-41515-9_54

Ключевые слова: dynamics, granular medium, elasticity, plastic shock wave, discontinuous solution, variational inequality, Computational algorithm

Аннотация: 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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Издание

Журнал: Lecture Notes in Computer Science

Выпуск журнала: Т.8236, №

Номера страниц: 479-486

ISSN журнала: 03029743

Издатель: Springer-Verlag GmbH

Авторы

  • Sadovskii Vladimir M. (Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences)

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