Numerical approaches to thermally coupled perfect plasticity

Authors

  • Sören Bartels,

    Corresponding author
    1. Department of Applied Mathematics, University of Freiburg, Hermann-Herder-Str. 10, D-79104 Freiburg im Breisgau, Germany
    • Department of Applied Mathematics, University of Freiburg, Hermann-Herder-Str. 10, D-79104 Freiburg im Breisgau, Germany
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  • Tomáš Roubíček

    1. Mathematical Institute, Charles University, Sokolovská 83, CZ-186 75 Praha 8 and Institute of Thermomechanics of the ASCR, Dolejškova 5, CZ-182 00 Praha 8, Czech Republic
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Abstract

The partial differential equations describing viscoelastic solids in Kelvin–Voigt rheology at small strains exhibiting also stress-driven Prandtl-Reuss perfect plasticity are considered and are coupled with a heat-transfer equation through the dissipative heat produced by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the resulting thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Numerical stability is shown and computational simulations are reported to illustrate the practical performance of the method. In a quasistatic case, convergence is proved by careful successive limit passage. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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