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Application of a modified semismooth Newton method to some elasto-plastic problems

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  • Sysala, Stanislav

Abstract

Some elasto-plasticity models with hardening are discussed and some incremental finite element methods with different time discretisation schemes are considered. The corresponding one-time-step problems lead to variational equations with various non-linear operators. Common properties of the non-linear operators are derived and consequently a general problem is formulated. The problem can be solved by Newton-like methods. First, the semismooth Newton method is analysed. The local superlinear convergence is proved in dependence on the finite element discretisation parameter. Then it is introduced a modified semismooth Newton method which contain suitable “damping” in each Newton iteration in addition. The determination of the damping coefficients uses the fact that the investigated problem can be formulated as a minimisation one. The method is globally convergent, independently on the discretisation parameter. Moreover the local superlinear convergence also holds. The influence of inexact inner solvers is also discussed. The method is illustrated on a numerical example.

Suggested Citation

  • Sysala, Stanislav, 2012. "Application of a modified semismooth Newton method to some elasto-plastic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 2004-2021.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:10:p:2004-2021
    DOI: 10.1016/j.matcom.2012.03.012
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    Citations

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    Cited by:

    1. Čermák, M. & Sysala, S. & Valdman, J., 2019. "Efficient and flexible MATLAB implementation of 2D and 3D elastoplastic problems," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 595-614.
    2. Lyubimov, Ivan L. (Любимов, Иван) & Kazakova, Maria V. (Казакова, Мария), 2017. "The Demand for Production Inputs as the Reflection of the Level of Property Rights Protection [Структура Спроса На Факторы Производства Как Отражение Защищенности Прав Собственности]," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 4, pages 30-59, August.
    3. Markopoulos, Alexandros & Hapla, Vaclav & Cermak, Martin & Fusek, Martin, 2015. "Massively parallel solution of elastoplasticity problems with tens of millions of unknowns using PermonCube and FLLOP packages," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 698-710.

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