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Metal-forming problems with combined hardening

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Abstract

A class of quasi-steady metal-forming problems under nonlocal contact and Coulomb’s friction boundary conditions is considered with an incompressible, rigidplastic, strain-rate dependent, isotropic, and kinematic hardening material model. A coupled variational formulation is derived, the convergence of a variable stiffness parameter method with time retardation is proved, and the existence and uniqueness results are obtained.

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References

  1. Hill, R. The Mathematical Theory of Plasticity, Oxford University Press, Oxford (1950)

    MATH  Google Scholar 

  2. Cristescu, N. D. Dynamic Plasticity, World Scientific Publishing Co. Ltd., Singapore (2007)

    Book  MATH  Google Scholar 

  3. Zienkiewicz, O. C. Flow formulation for numerical solution of forming processes. Numerical Analysis of Forming Processes (eds. Pittman, J. F. T., Zienkiewicz, O. C., Wood, R. D., and Alexander, J. M.), John Wiley and Sons, Chichester, 1–44 (1984)

    Google Scholar 

  4. Korneev, V. G. and Langer, U. Approximate Solution of Plastic Flow Theory Problems, B. G. Teubner, Leipzig (1984)

    MATH  Google Scholar 

  5. Han, W. and Reddy, B. D. Plasticity: Mathematical Theory and Numerical Analysis, Springer-Verlag, New York (1999)

    Google Scholar 

  6. Glowinski, R. Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, Berlin (1984)

    MATH  Google Scholar 

  7. Duvaut, G. and Lions, J. L. Inequalities in Mechanics and Physics, Springer-Verlag, Berlin (1976)

    Book  MATH  Google Scholar 

  8. Han, W. and Sofonea, M. Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, American Mathematical Society-International Press, Providence (2002)

    MATH  Google Scholar 

  9. Shillor, M., Sofonea, M., and Telega, J. J. Models and variational analysis of quasistatic contact. Lecture Notes in Physics, Springer, Berlin (2004)

    Google Scholar 

  10. Kikuchi, N. and Oden, J. T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia (1988)

    Google Scholar 

  11. Angelov, T. A. Variational analysis of a rigid-plastic rolling problem. Int. J. Eng. Sci., 42(17–18), 1779–1792 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Angelov, T. A. Existence and uniqueness of the solution of a quasi-steady rolling problem. Int. J. Eng. Sci., 44(11–12), 748–756 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Angelov, T. A. Modelling and analysis of a class of metal-forming problems. Adv. Appl. Math. Mech., 2(6), 722–745 (2010)

    MathSciNet  Google Scholar 

  14. Angelov, T. A. Modelling and numerical approach to a class of metal-forming problems — quasisteady case. Math. Meth. Appl. Sci., 34(11), 1330–1338 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to T. A. Angelov.

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Angelov, T.A. Metal-forming problems with combined hardening. Appl. Math. Mech.-Engl. Ed. 33, 233–242 (2012). https://doi.org/10.1007/s10483-012-1546-8

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  • DOI: https://doi.org/10.1007/s10483-012-1546-8

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