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Time-independent anisotropic plastic behavior by mechanical subelement models

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Abstract

The paper describes a procedure for modelling the anisotropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the viscoplasticity theory.

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References

  1. Duwez, P., On the plasticity of crystals, Physical Review, 47, (1935), 494–501.

    Article  Google Scholar 

  2. Besseling, J. F., A Theory of Plastic-flow for Anisotropic Hardening in Plastic Deformation of an Initially Isotropic Material, Nat. Aero Research Inst. Rept. S410, Amsterdam, (1953).

  3. Leech, J. W., E. A. Witmer and T. H. H. Pian, Numerical calculation technique for large elastic-plastic transient deformations of thin shells, AIAA Journal 6, (1968), 2352–2359.

    Google Scholar 

  4. Zienkiewicz, O. Z., G. C. Nayak and D. R. J. Owen, Composite and Overlay Models in Numerical Analysis of Elastic-Plastic Continua, Foundations of Plasticity, A. Sawszuk ed. Noordhoff, Leyden, (1973), 107–123.

    Google Scholar 

  5. Hunsaker, B., W. E. Haisler and J. A. Stricklin, On the use of two hardening rules of plasticity in incremental and pseudo force analyses, Constitutive equation's in viscoplasticity: Computational and engineering aspect, ASME-VOL. 20, (1973), 139–170.

    Google Scholar 

  6. Pian, T. H. H., Unpublished Lecture Notes on Plasticity, (1966).

  7. Perzyna, P., Fundamental Problems in Viscoplasticity, Advances in Applied Mechanics, Academic Press, New York, Vol. 9, (1966), 243–377.

    Google Scholar 

  8. Pian, T. H. H., Nonlinear creep analysis by assumed stress finite element methods, AIAA Journal, Vol. 12, (1975), 1756–1758.

    Google Scholar 

  9. Pian, T. H. H. and S. W. Lee, Creep and Viscoplastic Analysis by Assumed Stress Hybrid Finite Elements, Finite Elements in Nonlinear Solid and Structural Mechanics, Ed. by P. G. Bergan et al. Tapir Publisher, Trondheim, Norway, (1978), 807–822.

    Google Scholar 

  10. Cormeau, I. C., Numerical stability in quasi-state elasto/viscoplasticity, Int. J. Num. Meth. Engng., 9, (1975), 109–127.

    Google Scholar 

  11. Percy, J. H., W. A. Loden and D. R. Navaratna, A Study of Matrix Analysis Methods for Inelastic Structures, Air Force Dynamics Laboratory Report, RTD-TDA-63-4032, Oct. (1963).

  12. Jensen, W. R., W. E. Falby and N. Prince, Matrix Analysis Methods for Ani ptropic Inelastic Structures, Air Force Flight Dynamics Lab. Report AFFDL-TR-65-220, April, (1966).

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  1. Massachusetts Institute of Technology, Massachusetts, USA

    Theodore H. H. Pian

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  1. Theodore H. H. Pian
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Pian, T.H.H. Time-independent anisotropic plastic behavior by mechanical subelement models. Appl Math Mech 5, 1425–1435 (1984). https://doi.org/10.1007/BF01910433

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  • DOI: https://doi.org/10.1007/BF01910433

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