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Thermoviscoplasticity at small strains. (English) Zbl 1153.74011

Summary: We investigate a viscoelastic solid in Kelvin-Voigt rheology involving plasticity coupled with a heat transfer equation through a temperature-dependent yield stress. No hardening is studied, but the evolution of plastic strain is considered to be rate-dependent. A numerical scheme which is semi-implicit in time and employs lowest-order finite elements on weakly acute triangulations in space is devised and its convergence is proved by careful subsequent limit passage. Computational studies underline robustness and efficiency of the method and illustrate physical effects such as the softening of material due to dissipated energy that causes a rise in temperature and a local decrease in the yield stress.

MSC:

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74F05 Thermal effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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