A critical review of the state of finite plasticity

  • P. M. Naghdi
Review Article


The object of this paper is to provide a critical review of the current state of plasticity in the presence of finite deformation. In view of the controversy regarding a number of fundamental issues between several existing schools of plasticity, the areas of agreement are described separately from those of disagreement. Attention is mainly focussed on the purely mechanical, rate-independent, theory of elastic-plastic materials, although closely related topics such as rate-dependent behavior, thermal effects, experimental and computational aspects, microstructural effects and crystal plasticity are also discussed and potentially fruitful directions are identified.

A substantial portion of this review is devoted to the area of disagreement that covers a detailed presentation of argument(s), bothpro andcon, for all of the basic constitutive ingredients of the rate-independent theory such as the primitive notion or definition of plastic strain, the structure of the constitutive equation for the stress response, the yield function, the loading criteria and the flow and the hardening rules. The majority of current research in finite plasticity theory, as with its infinitesimal counterpart, still utilizes a (classical) stress-based approach which inherently possesses some shortcomings for the characterization of elastic-plastic materials. These and other anomalous behavior of a stress-based formulation are contrasted with the more recent strain-based formulation of finite plasticity. A number of important features and theoretical advantages of the latter formulation, along with its computational potential and experimental interpretation, are discussed separately.


Plastic Strain Critical Review Anomalous Behavior Crystal Plasticity Computational Aspect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Agah-Tehrani, A., Lee, E. H., Mallet, R. L. and Onat, E. T.,The theory of elastic-plastic deformation at finite strain with induced anisotropy modeled as combined isotropic-kinematic hardening. J. Mech. Phys. Solids35, 519–539 (1987).Google Scholar
  2. Anand, L.,Constitutive equations for hot-working of metals. Int. J. Plasticity1, 213–231 (1985).Google Scholar
  3. Anand, L. and Lush, A. M.,A plasticity theory for large deformations at high temperature and its application to hot working of metals. InInterdisciplinary Issues in Materials Processing and Manufacturing, Vol 1, pp. 163–177, Amer. Soc. Mechanical Engineers 1987.Google Scholar
  4. Armstrong, P. E., Hockett, J. E. and Sherby, O. D.,Large strain multi-directional deformation of 1100 aluminum at 300 K. J. Mech. Phys. Solids30, 37–58 (1982).Google Scholar
  5. Asaro, R. J.,Micromechanics of crystals and poly crystals. InAdvances in Applied Mechanics, Vol. 23, pp. 1–115, Academic Press 1983a.Google Scholar
  6. Asaro, R. J.,Crystal plasticity. J. Appl. Mech.50, 921–934 (1983b).Google Scholar
  7. Asaro, R. J. and Rice, J. R.,Strain localization in ductile single crystals. J. Mech. Phys. Solids25, 309–338 (1977).Google Scholar
  8. Atluri, S. N.,On constitutive relations at finite strain: Hypo-elasticity and elasto-plasticity with isotropic or kinematic hardening. Comp. Meth. Appl. Mech. Engng.43, 137–171 (1984).Google Scholar
  9. Backman, M. E.,From the relation between stress and finite elastic and plastic strains under impulsive loading. J. Appl. Phys.35, 2524–2533 (1964).Google Scholar
  10. Bell, J. F.,The experimental foundations of solid mechanics. InS. Flügge's Handbuch des Physik, Vol. VIa/1 (Ed. C. Truesdell), pp. 1–813 (with 481 figures), Springer-Verlag, Berlin, Heidelberg, New York (1973).Google Scholar
  11. Bell, J. F.,Continuum plasticity at finite strain for stress paths of arbitrary composition and direction. InThe Breadth and Depth of Continuum Mechanics—A collection of papers dedicated to J. L. Ericksen (Eds. C. M. Dafermos, D. D. Joseph and F. M. Leslie), pp. 201–232, Springer-Verlag Berlin (1986).Google Scholar
  12. Bell, J. F.,Experiments on the kinematics of large plastic strain in ordered solids. Int. J. Solids Struct.25, 267–278 (1989).Google Scholar
  13. Bertsch, P. K. and Findley, W. H.,An experimental study of subsequent yield surfaces, corners, normality, Bauschinger and allied effects. Proc. 4th U.S. National Congr. Appl. Mech., pp. 893–907, Amer. Soc. Mech. Eng. (1962).Google Scholar
  14. Bodner, S. R. and Partom, Y.,Constitutive equations for elasto-viscoplastic strain hardening materials. J. Appl. Mech.42, 385–389 (1975).Google Scholar
  15. Carroll, M. M.,A rate-independent constitutive theory for finite inelastic deformation. J. Appl. Mech.54, 15–21 (1987).Google Scholar
  16. Casey, J.,A simple proof of a result in finite plasticity. Quart. Appl. Math.42, 61–71 (1984).Google Scholar
  17. Casey, J.,Approximate kinematical relations in plasticity. Int. J. Solids Struct.21, 671–682 (1985).Google Scholar
  18. Casey, J.,On finitely deforming rigid-plastic materials. Int. J. Plasticity2, 247–277 (1986).Google Scholar
  19. Casey, J.,Discussion of Dashner (1986)-cited on this list. J. Appl. Mech.54, 247–248 (1987).Google Scholar
  20. Casey, J. and Jahedmotlagh, H.,The strength-differential effect in plasticity. Int. J. Solids Struct.20, 377–393 (1984).Google Scholar
  21. Casey, J. and Lin, H. H.,Strain-hardening topography of elastic-plastic materials, J. Appl. Mech.50, 795–801 (1983).Google Scholar
  22. Casey, J. and Lin, H. H.,Calculated hardening, softening and perfectly plastic responses of a special class of materials. Acta Mech.51, 49–67 (1984).Google Scholar
  23. Casey, J. and Lin, H. H.,Subcritical, critical and supercritical directions of loading in plasticity J. Méc. Théor. Appl.5, 685–701 (1986).Google Scholar
  24. Casey, J. and Naghdi, P. M.,A remark on the use of the decomposition F=F eFp in plasticity. J. Appl. Mech.47, 672–675 (1980).Google Scholar
  25. Casey, J. and Naghdi, P. M.,On the characterization of strain-hardening in plasticity. J. Appl. Mech.48, 285–296 (1981a).Google Scholar
  26. Casey, J. and Naghdi, P. M.,Discussion of Lubarda and Lee (1981)—cited on this list. J. Appl. Mech.48, 983–984 (1981b).Google Scholar
  27. Casey, J. and Naghdi, P. M.,Discussion of Yoder, P. J. and Iwan, W. D. (1981)—cited on this list. J. Appl. Mech.49, 460–461 (1982).Google Scholar
  28. Casey, J. and Naghdi, P. M.,On the use of invariance requirements for intermediate configurations associated with the polar decomposition of a deformation gradient. Quart. Appl. Math.41, 339–342 (1983a).Google Scholar
  29. Casey, J. and Naghdi, P. M.,A remark on the definition of hardening, softening and perfectly plastic behavior. Acta Mech.48, 91–94 (1983b).Google Scholar
  30. Casey, J. and Naghdi, P. M.,On the nonequivalence of the stress space and strain space formulations of plasticity theory. J. Appl. Mech.50, 350–354 (1983c).Google Scholar
  31. Casey, J. and Naghdi, P. M.,Strain-hardening response of elastic-plastic materials. InMechanics of Engineering Materials (Eds. C. S. Desai and R. H. Gallagher), pp. 61–89, John Wiley & Sons Ltd., England 1984a.Google Scholar
  32. Casey, J. and Naghdi, P. M.,Further constitutive results in finite plasticity. Quart. J. Mech. Appl. Math.37, 231–249 (1984b).Google Scholar
  33. Casey, J. and Naghdi, P. M.,Constitutive results for finitely deforming elastic-plastic materials. InConstitutive Equations: Macro and Computational Aspects (Ed. K. J. Willam), pp. 53–71, Amer. Soc. Mech. Eng. 1984c.Google Scholar
  34. Casey, J. and Naghdi, P. M.,On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity. Arch. Rational Mech. Anal.102, 351–375 (1988).Google Scholar
  35. Casey, J. and Sullivan, T. D.,Pressure dependency, strength-differential effect, and plastic volume expansion in metals. Int. J. Plasticity1, 39–61 (1985).Google Scholar
  36. Casey, J. and Tseng, M.A constitutive restriction related to convexity of yield surfaces in plasticity. ZAMP (J. Appl. Math. Phys),35, 478–496 (1984).Google Scholar
  37. Caulk, D. A. and Naghdi, P. M.,On the hardening response to small deformation of metals. J. Appl. Mech.45, 755–764 (1978).Google Scholar
  38. Chaboche, J. L.,Viscoplastic constitutive equations for the description of cyclic and anisotropic behavior of metals. Bull. Acad. Polonaise Sci.25, 33–42 (1977).Google Scholar
  39. Cottrell, A. H.,Dislocations and Plastic Flow in Crystals, Oxford University Press 1953.Google Scholar
  40. Cottrell, A. H.,The nature of metals. Scientific American217 (No. 3, Sept. issue), 90–100 (1967).Google Scholar
  41. Dafalias, Y. F.,Corotational rates for kinematic hardening at large plastic deformations. J. Appl. Mech.50, 561–565 (1983).Google Scholar
  42. Dafalias, Y. F.,Modelling cyclic plasticity: simplicity versus sophistication. InMechanics of Engineering Materials (Eds. C. S. Desai and R. H. Gallagher), pp. 153–178, John Wiley & Sons Ltd., England 1984a.Google Scholar
  43. Dafalias, Y. F.,The plastic spin concept and a simple illustration of its role in finite plastic transformations. Mechanics of Materials3, 223–233 (1984b).Google Scholar
  44. Dafalias, Y. F. and Popov, E. P.,Plastic internal variable formalism of cyclic plasticity. J. Appl. Mech.43, 645–651 (1976).Google Scholar
  45. Dashner, P. A.,Invariance considerations in large strain elaslo-plasticity. J. Appl. Mech.53, 55–60 (1986).Google Scholar
  46. Dienes, J. K.,On the analysis of rotation and stress rate in deforming bodies. Acta Mech.32, 217–232 (1979).Google Scholar
  47. Dienes, J. K.,A discussion of material rotation and stress rate. Acta Mech.65, 1–11 (1986).Google Scholar
  48. Dillon, O. W. Jr.,The response of prestressed aluminum. Int. J. Engng. Sci.2, 327–339 (1964).Google Scholar
  49. Dogui, A. and Sidoroff, F.,Kinematic hardening in large elastoplastic strain. Engng. Fracture Mech.21, 685–695 (1985).Google Scholar
  50. Drucker, D. C.,A reconsideration of deformation theories of plasticity. Trans. ASME71, 587–592 (1949).Google Scholar
  51. Drucker, D. C.,A more fundamental approach to plastic stress-strain relations. Proc. 1st U.S. Natl. Congr. Appl. Mech. (Chicago 1951), pp. 487–491, Amer. Soc. Mech. Eng. 1952.Google Scholar
  52. Drucker, D. C.,A definition of stable inelastic material. J. Appl. Mech.26, 101–106 (1959).Google Scholar
  53. Drucker, D. C.,Plasticity. Proc. 1st Symp. Naval Structural Mechanics (Stanford, CA 1958), pp. 407–455, Pergamon Press 1960.Google Scholar
  54. Drucker, D. C.,On the postulate of stability of material in the mechanics of continuua. J. Mécanique3, 235–249 (1964).Google Scholar
  55. Drucker, D. C.,Plasticity theory, strength-differential (SD) phenomenon, and volume expansion in metals and plastics. Metallurgical Trans.4, 667–673 (1973).Google Scholar
  56. Drucker, D. C.,Conventional and unconventional plastic response and representation. Appl. Mech. Rev.41, 151–167 (1988).Google Scholar
  57. Drucker, D. C. and Palgen, L.,On stress-strain relations suitable for cyclic and other loading. J. Appl. Mech.48, 479–485 (1981).Google Scholar
  58. Eftis, J., Abdel-Kader, M. S. and Jones, D. L.,Comparisons between the modified Chaboche and Bodner-Partom viscoplastic constitutive theories at high temperature. Int. J. Plasticity5, 1–27 (1989).Google Scholar
  59. Eisenberg, M. A.,A generalization of plastic flow theory with application to cyclic hardening and softening phenomena. J. Engng. Mat. Tech.98, 221–228 (1976).Google Scholar
  60. Eisenberg, M. A., Lee, C.-W. and Phillips, A.,Observations on the theoretical and experimental foundations of thermoplasticity. Int. J. Solids Struct.13, 1239–1255 (1977).Google Scholar
  61. Eisenberg, M. A. and Phillips, A. A.,A theory of plasticity with noncoincident yield and loading surfaces. Acta Mech.11, 247–260 (1971).Google Scholar
  62. Eisenberg, M. A. and Yen, C. R.,A theory of multiaxial anisotropic viscoplasticity. J. Appl. Mech.48, 276–284 (1981).Google Scholar
  63. Green, A. E.,A note on “axioms of continuum mechanics.” Bull. IMA18, 7–9; and18, 154 (1982).Google Scholar
  64. Green, A. E. and Naghdi, P. M.,A general theory of an elastic-plastic continuum. Arch. Rational Mech. Anal.18, 251–281 (1965).Google Scholar
  65. Green, A. E. and Naghdi, P. M.,A thermodynamic development of elastic-plastic continua. Proc. IUTAM Symp. on Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids (Eds. H. Parker and L. I. Sedov), pp. 117–131, Springer-Verlag 1966.Google Scholar
  66. Green, A. E. and Naghdi, P. M.,Some remarks on elastic-plastic deformation at finite strain. Int. J. Engng. Sci.9, 1219–1229 (1971).Google Scholar
  67. Green, A. E. and Naghdi, P. M.,Rate-type constitutive equations and elastic-plastic materials. Int. J. Engng. Sci.11, 725–734 (1973).Google Scholar
  68. Green, A. E. and Naghdi, P. M.,On thermodynamics and the nature of the Second Law. Proc. R. Soc. Lond.A357, 253–270 (1977).Google Scholar
  69. Green, A. E. and Naghdi, P. M.,The Second Law of thermodynamics and cyclic processes. J. Appl. Mech.45, 487–492 (1978a).Google Scholar
  70. Green, A. E. and Naghdi, P. M.,On thermodynamic restrictions in the theory of elastic-plastic materials. Acta Mech.30, 157–162 (1978b).Google Scholar
  71. Green, A. E. and Naghdi, P. M.,A note on invariance under superposed rigid body motions. J. Elasticity9, 1–8 (1979).Google Scholar
  72. Green, A. E. and Naghdi, P. M.,Aspects of the Second Law of thermodynamics in the presence of electromagnetic effects. Quart. J. Mech. Appl. Math.37, 179–193 (1984).Google Scholar
  73. Green, G.,On the laws of reflection and refraction of light at the common surface of two non-crystallized media. Trans. Cambridge Phil. Soc.7, (1835–1842) 1−24=Papers, 245–269 (1839).Google Scholar
  74. Havner, K. S.,The theory of finite plastic deformation of crystalline solids. InMechanics of Solids-the Rodney Hill 60th Anniv. Vol. (Eds. H. G. Hopkins and M. J. Sewell), pp. 265–302, Pergamon Press 1982.Google Scholar
  75. Havner, K. S. and Shalaby, A. H.,A simple mathematical theory of finite distortional latent hardening in single crystals. Proc. R. Soc. Lond.A358, 47–70 (1977).Google Scholar
  76. Hecker, S. S.,Experimental investigation of corners in the yield surface. Acta Mech.13, 69–86 (1972).Google Scholar
  77. Hecker, S. S.Experimental studies of yield phenomena in biaxially loaded metals. InConstitutive Equations in Viscoplasticity: Computational and Engineering Aspects (Eds. J. A. Stricklin and K. J. Saczalski), pp. 1–33, Amer. Soc. Mech. Eng. 1976.Google Scholar
  78. Helling, D. E. and Canova, G. R.,Multiaxial yield behavior of 1100 aluminum following various magnitudes of prestrain. Int. J. Plasticity1, 163–174 (1985).Google Scholar
  79. Hertzberg, R. W.,Deformation and Fracture Mechanics of Engineering Materials (2nd ed.), John Wiley & Sons 1983.Google Scholar
  80. Hill, R.,The Mathematical Theory of Plasticity, Oxford University Press 1950.Google Scholar
  81. Hill, R.,Constitutive laws and waves in rigid-plastic solids. J. Mech. Phys. Solids10, 89–98 (1962).Google Scholar
  82. Hill, R.,Generalized constitutive relations for incremental deformation of metal crystals by multislip. J. Mech. Phys. Solids14, 95–102 (1966).Google Scholar
  83. Hill, R. and Havner, K.,Perspectives in the mechanics of elastoplastic crystals. J. Mech. Phys. Solids30, 5–22 (1982).Google Scholar
  84. Hill, R. and Rice, J. R.,Elastic potentials and the structure of inelastic constitutive laws. SIAM J. Appl. Math.25, 448–461 (1973).Google Scholar
  85. Hill, R. and Rice, J. R.,Discussion of Carroll (1987)—cited on this list. J. Appl. Mech.54, 745–747 (1987).Google Scholar
  86. Hirth, J. P. and Lothe, J.,Theory of Dislocations (2nd ed.), John Wiley & Sons 1982.Google Scholar
  87. Hodge, P. G. Jr.,The theory of piece-wise linear isotropic plasticity. Proc. IUTAM Colloquium on Deformation and Flow in Solids (Madrid, 1955), pp. 147–169, Springer-Verlag 1956a.Google Scholar
  88. Hodge, P. G. Jr.,Minimum principles of piecewise linear isotropic plasticity. J. Rational Mech. Anal.5, 917–938 (1956b).Google Scholar
  89. Hudson, J. A., Brown, E. T. and Fairhurst, C.,Shape of the complete stress-strain curve for rock. InStability of Rock Slopes, Proc. 13th Symp. on Rock Mechanics (Ed. E. J. Cording, Urbana, IL), pp. 773–795, Amer. Soc. Civil Eng. 1972.Google Scholar
  90. Hughes, T. J. R.,Numerical implementation of constitutive models: rate-independent deviatoric plasticity. Workshop on the Theoretical Foundation for Large Scale Computations of Nonlinear Material Behavior (Northwestern Univ.) pp. 24–26, 1983.Google Scholar
  91. Il'iushin, A. A.,On a postulate of plasticity. J. Appl. Math. Mech. [Transl. of PMM]25, 746–750 (1961).Google Scholar
  92. Ivey, H. J.,Plastic stress-strain relations and yield surfaces for aluminum alloys. J. Mech. Engng. Sci.3, 15–31 (1961).Google Scholar
  93. Iwakuma, T. and Nemat-Nasser, S.,Finite elastic-plastic deformation of polycrystalline metals. Proc. R. Soc. Lond.A394, 87–119 (1984).Google Scholar
  94. Kadashevich, In. I. and Novozhilov, V. V.,The theory of plasticity which takes into account residual microstresses. J. Appl. Math. Mech. [Transl. of PMM]22, 104–118 (1958).Google Scholar
  95. Koiter, W. T.,On partially plastic thick-walled tubes. InC. B. Biezeno Anniv. Vol. on Applied Mechanics, pp. 233–251, Haarlem 1953a.Google Scholar
  96. Koiter, W. T.Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface. Quart. Appl. Math.11, 350–354 (1953b).Google Scholar
  97. Krieg, R. D.,A practical two surface plasticity theory. J. Appl. Mech.42, 641–646 (1975).Google Scholar
  98. Kröner, E.,Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rational Mech. Anal.4, 273–334 (1960).Google Scholar
  99. Lamba, H. S. and Sidebottom, O. M.,Cyclic plasticity for nonproportional paths: part 1-cyclic hardening, erasure of memory, and subsequent strain-hardening experiments. J. Engng. Mat. Tech.100, 96–103 (1978a).Google Scholar
  100. Lamba, H. S. and Sidebottom, O. M.,Cyclic plasticity for nonproportional paths: part 2-comparison with predictions of three incremental plasticity models. J. Engng. Mat. Tech.100, 104–111 (1978b).Google Scholar
  101. Lee, D. and Zaverl, F. Jr.,A generalized strain rate dependent constitutive equation for anisotropic materials. Acta Metallurgica26, 1771–1780 (1978).Google Scholar
  102. Lee, D. and Zaverl, F. Jr.,A description of history dependent plastic flow behavior of anisotropic metals. J. Engng. Materials and Technology, Trans. ASME101, 59–67 (1979).Google Scholar
  103. Lee, E. H.,Elastic-plastic deformation at finite strains. J. Appl. Mech.36, 1–6 (1969).Google Scholar
  104. Lee, E. H.,Some comments on elastic-plastic analysis. Int. J. Solids Structures17, 859–872 (1981).Google Scholar
  105. Lee, E. H.,Finite deformation effects in elastic-plastic analysis. InMechanics of Material Behavior (D. C. Drucker Anniv. Vol., Eds. J. G. Dvorak and R. T. Shield), pp. 231–238, Elsevier 1984.Google Scholar
  106. Lee, E. H.,Mathematical modeling of elastic-plastic behavior at finite strain and application to the analysis of forming processes. InInterdisciplinary Issues in Materials Processing and Manufacturing, Vol. 1, pp. 269–277, Amer. Soc. Mech. Eng. 1987.Google Scholar
  107. Lee, E. H. and Liu, D. T.,Finite strain elastic-plastic theory with application to plane-wave analysis. J. Appl. Phys.38, 19–27 (1967).Google Scholar
  108. Lee, E. H., Mallett, R. L., and Wertheimer, T. B.,Stress anlaysis for anisotropic hardening in finite-deformation plasticity. J. Appl. Mech.50, 554–560 (1983).Google Scholar
  109. Levy, M.,Mémoire sur les équations générales des mouvements intérieurs des corps solides ductiles au delà des limites où l'élasticité pourrait les ramener à leur premier état. C. R. Acad. Sci. Paris70, 1323–1325 (1870).Google Scholar
  110. Lin, H. C. and Naghdi, P. M.,Necessary and sufficient conditions for the validity of a work inequality in finite plasticity. Quart. J. Mech. Appl. Math.42, 13–21 (1989).Google Scholar
  111. Liu, M. C. and Krempl, E.A uniaxial viscoplastic model based on total strain and overstress. J. Mech. Phys. Solids27, 377–391 (1979).Google Scholar
  112. Loret, B.,On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials. Mechanics of Materials2, 287–304 (1983).Google Scholar
  113. Lubarda, V. A. and Lee, E. H.,A correct definition of elastic and plastic deformation and its computational significance. J. Appl. Mech.48, 35–40 (1981).Google Scholar
  114. Mair, W. M. and Pugh, H. L. D.,Effect of prestrain on yield surfaces in copper. J. Mech. Engng. Sci.6, 150–163 (1964).Google Scholar
  115. Mandel, J.,Thermodynamics and plasticity. InFoundations of Continuum Thermodynamics (Eds. J. J. D. Domingos, M. N. R. Nina and J. H. Whitelaw), pp. 283–304, MacMillan, London 1973.Google Scholar
  116. Mandel, J.,Sur la définition de la vitesse de déformation élastique et sa relation avec la vitesse de contrainte. Int. J. Solids Struct.17, 873–878 (1981).Google Scholar
  117. Mandel, J.,Définition d'un repère privilégié pour l'étude des transformation anélastiques du polycristal [Definition of a frame suitable to the study of anelastic transformations of the polycrystals]. J. Méc. théor. appl.1, 7–23 (1982).Google Scholar
  118. Mises, R., von.,Mechanik der Festen Körper in Plastisch-Deformablen Zustand. Nachr. Konigl. Ges. Wissen Göttingen, Mathem-Physik. Klasse, 582–592, 1913.Google Scholar
  119. Mroz, M.,On the description of anisotropic workhardening. J. Mech. Phys. Solids15, 163–175 (1967).Google Scholar
  120. Nabarro, F. R. N.,Theory of Crystal Dislocation, Dover-slightly corrected version of the book first published in 1967 by Oxford University Press 1987.Google Scholar
  121. Naghdi, P. M.,Stress-strain relations in plasticity and thermoplasticity. Proc. 2nd Symp. Naval Structural Mechanics (Providence, RI 1959), pp. 121–167, Pergamon Press 1960.Google Scholar
  122. Naghdi, P. M.,The theory of shells and plates. InS. Flügge's Handbuch der Physik, Vol. VIa/2, (Ed. C. Truesdell), pp. 425–640, Springer-Verlag, Berlin 1972.Google Scholar
  123. Naghdi, P. M.,Recent developments in finite deformation plasticity. InPlasticity Today: Modelling, Methods and Applications (Eds. A. Sawczuk and G. Bianchi), pp. 75–83, Elsevier Applied Science Publishers Ltd., Essex, England 1984a.Google Scholar
  124. Naghdi, P. M.,Constitutive restrictions for idealized elastic-viscoplastic materials. J. Appl. Mech.51, 93–101 (1984b).Google Scholar
  125. Naghdi, P. M.,Some remarks on rate-dependent plasticity. InMechanics of Material Behavior (D. C. Drucker Anniv. Vol., Eds. G. J. Dvorak and R. T. Shield), pp. 289–309, Elsevier Sci. Publ. 1984c.Google Scholar
  126. Naghdi, P. M., Essenburg, F. and Koff, W.,An experimental study of initial yield and subsequent yield surfaces in plasticity. J. Appl. Mech.25, 201–209 (1958).Google Scholar
  127. Naghdi, P. M. and Nikkel, D. J. Jr.,Calculations for uniaxial stress and strain cycling in plasticity. J. Appl. Mech.51, 487–493 (1984).Google Scholar
  128. Naghdi, P. M. and Nikkel, D. J. Jr.,Two-dimensional strain cycling in plasticity. J. Appl. Mech.53, 821–830 (1986).Google Scholar
  129. Naghdi, P. M., Rowley, J. C. and Beadle, C. W.,Experiments concerning the yield surface and the assumption of linearity in the plastic stress-strain relations. J. Appl. Mech.22, 416–420 (1955).Google Scholar
  130. Naghdi, P. M. and Trapp, J. A.,On finite elastic-plastic deformation of metals. J. Appl. Mech.41, 254–260 (1974).Google Scholar
  131. Naghdi, P. M. and Trapp, J. A.,The significance of formulating plasticity theory with reference to loading surfaces in strain space. Int. J. Engng. Sci.13, 785–797 (1975a).Google Scholar
  132. Naghdi, P. M. and Trapp, J. A.,Restrictions on constitutive equations of finitely deformed elastic-plastic materials. Quart. J. Mech. Appl. Math.28, 25–46 (1975b).Google Scholar
  133. Nagtegaal, J. C. and DeJong, J. E.,Some aspects of non-isotropic work-hardening in finite strain plasticity. Proc. of the Workshop onPlasticity of metals at finite strain: Theory, experiments and computation (Eds. E. H. Lee and R. L. Mallett), Div. Appl. Mech., Stanford U. and Dept. Mech. Eng., R.P.I., pp. 65–102, 1982.Google Scholar
  134. Nemat-Nasser, S.,Discussion of Naghdi and Trapp (1974)—cited on this list. J. Appl. Mech.41, 1146 (1974).Google Scholar
  135. Nemat-Nasser, S.,Decomposition of strain measures and their rates in finite deformation elastoplasticity. Int. J. Solids Struct.15, 155–166 (1979).Google Scholar
  136. Nemat-Nasser, S.,On finite deformation elasto-plasticity. Int. J. Solids Struct.18, 857–872 (1982).Google Scholar
  137. Nemat-Nasser, S.,On finite plastic flow of crystalline solids and geomaterials. J. Appl. Mech.50, 1114–1126 (1983).Google Scholar
  138. Onat, E. T.,Shear flow of kinematically hardening rigid-plastic materials. InMechanics of Materials Behavior (D. C. Drucker Anniv. Vol., Eds. J. Dvorak and R. T. Shield), pp. 311–323, Elsevier 1984.Google Scholar
  139. Orowan, E., von,Zur Kristallplastizität III. Über den Mechanismus des Gleitvorganges. Z. Phys.89, 634–659 (1934).Google Scholar
  140. Owen, D. R.,A mechanical theory of materials with elastic range. Arch. Rational Mech. Anal.37, 85–110 (1970).Google Scholar
  141. Palgen, L. and Drucker, D. C.,The structure of stress-strain relations in finite elasto-plasticity. Int. J. Solids Struct.19, 519–531 (1983).Google Scholar
  142. Palmer, A. C., Maier, G. and Drucker, D. C.,Normality relations and convexity of yield surfaces for unstable materials or structural elements. J. Appl. Mech.34, 464–470 (1967).Google Scholar
  143. Perzyna, P.,The constitutive equations for rate sensitive plastic materials. Quart. Appl. Math.20, 321–332 (1963).Google Scholar
  144. Perzyna, P.,Fundamental problems in viscoplasticity. InAdvances in Applied Mechanics, Vol. 9, pp. 243–377, Academic Press 1966.Google Scholar
  145. Phillips, A.,Pointed vertices in plasticity. Proc. 2nd Symp. Naval Structural Mechanics (Providence, RI 1959), pp. 202–214, Pergamon Press 1960.Google Scholar
  146. Phillips, A.,Experimental plasticity. Some thoughts on its present status and possible future trends. InInternational Symposium on Foundations of Plasticity, Vol. II, Problems of Plasticity (Ed. A. Sawczuk, Warsaw 1972), pp. 193–233, Noordhoff 1974.Google Scholar
  147. Phillips, A. and Gray, G. A.,Experimental investigation of corners in the yield surface. J. Basic Engineering, Trans. ASME83, 275–287 (1961).Google Scholar
  148. Phillips, A. and Kasper, R.,On the foundations of thermoplasticity-an experimental investigation, J. Appl. Mech.40, 891–896 (1973).Google Scholar
  149. Phillips, A., Liu, K. and Justusson, W. J.,An experimental investigation of yield surfaces at elevated temperatures. Acta. Mech.14, 119–146 (1972).Google Scholar
  150. Phillips, A. and Sierakowski, R. L.,On the concept of the yield surface. Acta Mech.1, 29–35 (1965).Google Scholar
  151. Phillips, A. and Wu, H. C.,A theory of viscoplasticity. Int. J. Solids Struct.9, 15–30 (1973).Google Scholar
  152. Polanyi, M., von,Über eine Art Gitterstörung, die einen Kristall plastisch machen könnte. Z. Phys.89, 660–664 (1934).Google Scholar
  153. Prager, W.,On the use of singular yield conditions and associated flow rules. J. Appl. Mech.20, 317–320 (1953).Google Scholar
  154. Prager, W.,The theory of plasticity: A survey of recent achievements (James Clayton Lecture). Proc. Instn. Mech. Engrs.169, 41–57 (1955).Google Scholar
  155. Prager, W.,A new method of analyzing stress and strains in work-hardening plastic solids. J. Appl. Mech.23, 493–496 (1956).Google Scholar
  156. Prager, W. and Hodge, P. G. Jr.,Theory of perfectly plastic solids. John Wiley 1951.Google Scholar
  157. Read, H. E. and Hegemier, G. A.,Strain softening of rock, soil and concrete-a review article. Mechanics of Materials3, 271–294 (1984).Google Scholar
  158. Rivlin, R. S.,Some comments on the endochronic theory of plasticity. Int. J. Solids Struct.17, 231–248 (1981a).Google Scholar
  159. Rivlin, R. S.,Comments on “on the substance of Rivlin's remarks on the endochronic theory” by K. C. Valanis. Int. J. Solids Struct.17, 267–268 (1981b).Google Scholar
  160. Rubin, M. B.,An elastic-viscoplastic model for large deformation. Int. J. Engng. Sci.24, 1083–1095 (1986).Google Scholar
  161. Rubin, M. B.,An elastic-viscoplastic model for metals subjected to high compression. J. Appl. Mech.54, 532–538 (1987a).Google Scholar
  162. Rubin, M. B.,An elastic-viscoplastic model exhibiting continuity of solid and fluid stales. Int. J. Engng. Sci.25, 1175–1191 (1987b).Google Scholar
  163. Saint-Venant, A. J. C. B. de,Sur l'établissaient des équations des mouvements intérieures opérés dans les corps solides ductiles au delà des limites où l'élasticité pourrait les ramener à leur premier état. C. R. Acad. Sci.70, 473–480 (1870).Google Scholar
  164. Schmid, E., von,Neuere Untersuchungen an Metallkristallen. Proc. First Int. Congr. Appl. Mech. (Eds. C. B. Biezeno and J. M. Burgers, Delft), pp. 342–353, Technische Boekhandel en Drukkerij J. Waltman Jr. 1924.Google Scholar
  165. Sidoroff, F.,Quelques réflexions sur le principe d'indifférence matérielle pour un milieu ayant un état relâché. C. R. Acad. Sci. Paris, A271, 1026–1029 (1970).Google Scholar
  166. Simo, J. C. and Ortiz, M.,A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Comp. Meth. Appl. Mech. Engng.49, 221–245 (1985).Google Scholar
  167. Spitzig, W. A., Sober, R. J. and Richmond, O.,Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Metallurgica23, 885–893 (1975).Google Scholar
  168. Stouffer, D. C. and Bodner, S. R.,A constitutive model for the deformation induced anisotropic plastic flow of metals. Int. J. Engng. Sci.17, 757–764 (1979).Google Scholar
  169. Stout, M. G., Martin, P. L., Helling, D. E. and Canova, G. R.,Multiaxial yield behavior of 1100 aluminum following various magnitudes of prestrain. Int. J. Plasticity1, 163–174 (1985).Google Scholar
  170. Taylor, G. I.The mechanism of plastic deformation of crystals. Part I.-theoretical. Proc. R. Soc. Lond.A145, 362–387 (1934).Google Scholar
  171. Taylor, G. I. and Elam, C. F.,The distortion of an aluminum crystal during a tensile test. Proc. R. Soc. Lond.A102, 643–667 (1923).Google Scholar
  172. Taylor, G. I. and Elam, C. F.,The plastic extension and fracture of aluminum crystals. Proc. R. Soc. Lond.A108, 28–51 (1925).Google Scholar
  173. Taylor, G. I. and Quinney, H.,The plastic distortion of metals. Trans. Royal Soc. Lond.A230, 323–362 (1931).Google Scholar
  174. Tokuoka, T.,Yield conditions and flow rules derived from hypoelasticity. Arch. Rational Mech. Anal.42, 239–252 (1971).Google Scholar
  175. Tresca, H. E.,On the flow of solids, with practical applications in forgings. Proc. Instn. Mech. Engnrs., Lond., 114–150 (1867).Google Scholar
  176. Tresca, H. E.,On further applications of flow of solids. Proc. Instn. Mech. Engrs., Lond., 301–345 (1878).Google Scholar
  177. Truesdell. C. and Noll, W.,The non-linear field theories of mechanics. InS. Flügge's Handbuch der Physik, Vol. III/3, pp. 1–602, Springer-Verlag 1965.Google Scholar
  178. Truesdell, C. and Toupin, R.,The classical field theories. InS. Flügge's Handbuch der Physik, Vol. III/1, pp. 226–793, Springer-Verlag 1960.Google Scholar
  179. Valanis, K. C.,A theory of viscoplasticity without a yield surface. Part I.-general theory. Archs. Mech.23, 517–533 (1971).Google Scholar
  180. Valanis, K. C.,On the foundations of the endochronic theory of viscoplasticity. Archs. Mech.27, 857–868 (1975).Google Scholar
  181. Valanis, K. C.,On the substance of Rivlin's remarks on the endochronic theory. Int. J. Solids Struct.17, 249–265 (1981).Google Scholar
  182. Wawersik, W. R. and Fairhurst, C.,A study of brittle rock fracture in laboratory compression experiment. Int. J. Rock Mech. Min. Sci.7, 561–575 (1970).Google Scholar
  183. Weng, G. J.,The yield surface of single crystals at arbitrary strain. Acta Mech.37, 231–245 (1980).Google Scholar
  184. Williams, J. F. and Svensson, N. L.,Effect of tensile prestrain on the yield locus of I100-F aluminum. J. Strain Analysis5, 128–139 (1970).Google Scholar
  185. Woods, L. C.,Frame-indifferent kinetic theory. J. Fluid Mech.136, 423–433 (1983).Google Scholar
  186. Yoder, P. J. and Iwan, W. D.,On the formulation of strain space plasticity with multiple loading surfaces. J. Appl. Mech.48, 773–778 (1981).Google Scholar
  187. Ziegler, H.,A modification of Prager's hardening rule. Quart. Appl. Math.17, 55–65 (1959).Google Scholar

Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • P. M. Naghdi
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

Personalised recommendations