Kinematic criteria of dynamic shakedown extended to nonassociative constitutive laws with saturation nonlinear hardening

Alberto Corigliano; Giulio Maier; Slawomir Pycko

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1995)

  • Volume: 6, Issue: 1, page 55-64
  • ISSN: 1120-6330

Abstract

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The class of elastic-plastic material models considered allows for nonassociativity, nonlinear hardening and saturation in the sense that the static internal variables are constrained by a bounding surface described through convex bounding functions. With reference to finite element, generalized variables discretization in space, two dynamic shakedown criteria are established by a kinematic approach in Koiter's sense, based on weak constitutive restrictions and centered on two suitable definitions of admissible yield cycles.

How to cite

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Corigliano, Alberto, Maier, Giulio, and Pycko, Slawomir. "Kinematic criteria of dynamic shakedown extended to nonassociative constitutive laws with saturation nonlinear hardening." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 6.1 (1995): 55-64. <http://eudml.org/doc/244173>.

@article{Corigliano1995,
abstract = {The class of elastic-plastic material models considered allows for nonassociativity, nonlinear hardening and saturation in the sense that the static internal variables are constrained by a bounding surface described through convex bounding functions. With reference to finite element, generalized variables discretization in space, two dynamic shakedown criteria are established by a kinematic approach in Koiter's sense, based on weak constitutive restrictions and centered on two suitable definitions of admissible yield cycles.},
author = {Corigliano, Alberto, Maier, Giulio, Pycko, Slawomir},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Plasticity; Structural dynamics; Shakedown; Inadaptation; structural dynamics; inadaptation; static internal variables; finite element; yield cycles},
language = {eng},
month = {3},
number = {1},
pages = {55-64},
publisher = {Accademia Nazionale dei Lincei},
title = {Kinematic criteria of dynamic shakedown extended to nonassociative constitutive laws with saturation nonlinear hardening},
url = {http://eudml.org/doc/244173},
volume = {6},
year = {1995},
}

TY - JOUR
AU - Corigliano, Alberto
AU - Maier, Giulio
AU - Pycko, Slawomir
TI - Kinematic criteria of dynamic shakedown extended to nonassociative constitutive laws with saturation nonlinear hardening
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1995/3//
PB - Accademia Nazionale dei Lincei
VL - 6
IS - 1
SP - 55
EP - 64
AB - The class of elastic-plastic material models considered allows for nonassociativity, nonlinear hardening and saturation in the sense that the static internal variables are constrained by a bounding surface described through convex bounding functions. With reference to finite element, generalized variables discretization in space, two dynamic shakedown criteria are established by a kinematic approach in Koiter's sense, based on weak constitutive restrictions and centered on two suitable definitions of admissible yield cycles.
LA - eng
KW - Plasticity; Structural dynamics; Shakedown; Inadaptation; structural dynamics; inadaptation; static internal variables; finite element; yield cycles
UR - http://eudml.org/doc/244173
ER -

References

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  4. MAIER, G., A generalization to nonlinear hardening of the first shakedown theorem for discrete elastic-plastic structural models. Atti Acc. Lincei Rend. fis., s. 8, v. 81, 1987, 161-174. Zbl0667.73024MR999429
  5. MAIER, G. - NOVATI, G., Dynamic shakedown and bounding theory for a class of nonlinear hardening discrete structural models. Int. J. Plasticity, 6, 1990, 551-572. Zbl0731.73022
  6. POLIZZOTTO, C. - BORINO, G. - CADDEMI, S. - FUSCHI, P., Shakedown problems for material models with internal variables. Eur. J. Mech., A. Solids, 6, 1991, 621-639. Zbl0745.73010MR1139600
  7. COMI, C. - CORIGLIANO, A., Dynamic shakedown in elastoplastic structures with general internal variable constitutive laws. Int. J. Plasticity, 7, 1991, 679-692. Zbl0755.73042
  8. NAYLORES, B. - WEICHERT, D., La notion de sanctuaire d'élasticité et d'adaptation des structures. C.R. Acad. Sci. Paris, 316, Serie II, 1993, 1493-1498. Zbl0773.73036
  9. CORIGLIANO, A. - MAIER, G. - PYCKO, S., Dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative internal variable constitutive laws. Submitted for publication in Int. J. of Solids and Structures. Zbl0879.73019
  10. PYCKO, S. - MAIER, G., Shakedown theorems for some classes of nonassociated hardening elastic-plastic material models. Submitted for publication in Int. J. Plasticity. Zbl0853.73021
  11. CERADINI, G., Sull'adattamento dei corpi elastoplastici soggetti ad azioni dinamiche. Giornale del Genio Civile, 415, 1969, 239-258. 
  12. MAIER, G., A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes. Meccanica, 5, 1970, 54-66. Zbl0197.23303
  13. KOITER, W. T., General Theorems of Elastic-Plastic Solids. In: S. SNEDDON - R. HILL (eds.), Progress in Solid Mechanics. 1, North Holland, Amsterdam1960, 167-221. Zbl0098.37603MR112405
  14. CORRADI, L. - MAIER, G., Inadaptation theorems in the dynamics of elastic-work hardening structures. Ing. Arch., 43, 1973, 44-57. Zbl0271.73030MR413698
  15. CORRADI, L. - MAIER, G., Dynamic non-shakedown theorem for elastic perfectly plastic continua. J. Mech. Phys. Solids, 22, 1974, 401-413. Zbl0304.73039
  16. CORRADI, L., On compatible finite element models for elastic plastic analysis. Meccanica, 13, 1978, 133-150. Zbl0417.73073
  17. COMI, C. - MAIER, G. - PEREGO, U., Generalized variables and extremum theorems in discretized elasticplastic analysis. Comp. Meth. Appl. Mech. Eng., 96, 1992, 213-237. Zbl0761.73107MR1162380DOI10.1016/0045-7825(92)90133-5
  18. MAIER, G. - HUECKEL, T., Nonassociative and coupled flow rules of elastoplasticity for rock-like materials. Int. J. Rock Mec. Mining Sci., 16, 1979, 77-92. 
  19. DRUCKER, D. C., Conventional and unconventional plastic response and representation. Appl. Mech. Rev., 41, 4, 1988, 151-167. 
  20. MAIER, G., Shakedown theory in perfect elastoplasticity with associated and nonassociated flow laws: a finite element, linear programming approach. Meccanica, 4, 1969, 250-260. Zbl0219.73039
  21. STEIN, E. - ZHANG, G. - KÖNIG, A. J., Shakedown with nonlinear strain hardening including structural computation using finite element method. Int. J. Plasticity, 8, 1992, 1-31. Zbl0766.73026
  22. GAVARINI, C., On elastic recovering of elastic-plastic forced vibration. 1969, Giornale del Genio Civile, 4-5, 251-261 (in Italian). 

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