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Recent Advances in the Numerical Analysis and Simulation of Thermoplasticity at Finite Strains

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Finite Inelastic Deformations — Theory and Applications

Abstract

Novel numerical analysis aspects involved in the algorithmic treatment of a recently proposed formulation of thermoplasticity at finite strains are discussed. Two key aspects in these new developments are: i. The formulation of a new class of return mapping algorithms for multiplicative decomposition which inherit without modification all the features of the standard algorithms restricted to the infinitesimal theory; ii. The development of a new class of staggered coupled algorithms for coupled problems which retain the key property of unconditional stability. The work reported on herein summarizes some of the recent developments at Stanford in the area of inelastic coupled thermomechanical problems at finite strains.

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References

  1. J.H. Argyris & J.St. Doltsinis [ 1981 ], “On the Natural Formulation and Analysis of Large Deformation Coupled Thermomechanical Problems”, Computer Methods in Applied Mechanics and Engineering, 25, 195–253.

    Article  MATH  MathSciNet  Google Scholar 

  2. F. Armero & J.C. Simo, [1991], “A New Unconditionally Stable Fractional Step Method for Nonlinear Coupled Thermomechanical Problems,” SUDAM Report No. 91–5, Stanford University. To appear in International J. Numerical Methods in Engineering.

    Google Scholar 

  3. P. Duhem [ 1911 ] Traite d’Energetique ou de Thermodynamique Generale, Gauthier-Villars, Paris.

    Google Scholar 

  4. J.J. Moreau, [ 1977 ], “Evolution Problem Associated with a Moving Convex Set in a Hilbert Space”, Journal of Differential Equations, Volume 26, pp. 347.

    Article  MATH  MathSciNet  Google Scholar 

  5. J.C. Simo and R.L. Taylor, [1985 ], “Consistent Tangent Operators for Rate-independent Elastoplasticity”, Computer Methods in Applied Mechanics and Engineering 48, 101–118.

    Article  MATH  Google Scholar 

  6. J.C. Simo, [1988a,ó], “A Framework for Finite Strain Elastoplasticity Based on Maximum Plastic Dissipation and Multiplicative Decomposition: Part I. Continuum Formulation; Part II.; Computational Aspects”, Computer Methods in Applied Mechanics and Engineering 66, 199–219 and 68, 1–31.

    Google Scholar 

  7. J.C. Simo, J.G. Kennedy and S.Govindjee, [ 1988 ], “General Return Mapping Algorithms for Multisurface Plasticity and Viscoplasticity,” International Journal of Numerical Methods in Engineering, 26, No. 2, 2161–2185.

    Article  MATH  MathSciNet  Google Scholar 

  8. J.C. Simo and R.L. Taylor, [ 1991 ], “Finite Elasticity in Principal stretches; Formulation and Finite element implementaion,” Computer Methods in Applied Mechanics and Engineering, 85, 273–310.

    Article  MATH  MathSciNet  Google Scholar 

  9. J.C. Simo and C.Miehe [1991], “Coupled Associative Thermoplasticity at finite strains. Formulation, numerical analysis and implementation, Computer Methods in Applied Mechanics and Engineering,(in press)

    Google Scholar 

  10. J.C. Simo, [1991a ], “Nonlinear Stability of the Time Discrete Variational Problem in Nonlinear Heat Conduction and Elastoplasticity,” Computer Methods in Applied Mechanics and Engineering, 88, 111–131.

    Article  MATH  MathSciNet  Google Scholar 

  11. J.C. Simo, [1991b], “Algorithms for Multiplicative Plasticity which Preserve the Structure of the Classical Return Mappings of the Infinitesimal Thery,” SUDAM Report No. 91–4. In press in Computer Methods in Applied Mechanics and Engineering

    Article  MATH  MathSciNet  Google Scholar 

  12. J.C. Simo and F. Armero [1991], “Geometrically Nonlinear Enhanced Strain Methods and the Method of Incompatible Modes,” In press in International J. Numerical Methods in Engineering.

    Google Scholar 

  13. J.C. Simo, N. Tarnow and K.W. Wong [1991], “Exact Energy-Momentum Conserving Algorithms and Symplectic Schemes for Nonlinear Dynamics, Computer Methods in Applied Mechanics and Engineering

    Google Scholar 

  14. N.N. Yanenko, [1971 ] The method of Fractional Steps, Springer-Verlag, Berlin, Heidelberg, New-York.

    Book  MATH  Google Scholar 

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© 1992 Springer-Verlag Berlin Heidelberg

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Simo, J.C., Armero, F. (1992). Recent Advances in the Numerical Analysis and Simulation of Thermoplasticity at Finite Strains. In: Besdo, D., Stein, E. (eds) Finite Inelastic Deformations — Theory and Applications. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84833-9_24

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  • DOI: https://doi.org/10.1007/978-3-642-84833-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84835-3

  • Online ISBN: 978-3-642-84833-9

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