Acta Mechanica

, Volume 182, Issue 1–2, pp 31–111 | Cite as

Elastoplasticity beyond small deformations

  • H. Xiao
  • O. T. Bruhns
  • A. Meyers


This article is concerned with some essential aspects of representative ideas and viewpoints as well as developments in formulations of rate-independent elastoplasticity beyond the small deformation range. Kinematical and physical foundations underlying the basic variables, and the essential constitutive structures implied by the work postulate are examined and discussed, pro and con, from an integrated viewpoint based on certain coherent threads running through various formulations. Their constitutive and computational implications are elucidated and contrasted by analysing the main structural features based on their basic variables. Emphasis is placed on new issues and new understanding, and on physically pertinent variables and formulations.

In particular, attention is focused on the essential complexity of elastoplastic fields. It is suggested that residual stress fields attendant upon the removal of external loadings or actions should be indispensable prerequisites for ensuring the geometrical compatibility property of an elastoplastic body as material continuum. A further artificial process of destressing an elastoplastic body would inevitably lead to the loss of its geometrical compatibility and thus to the loss of the kinematical grounds for the usual compatible continuous bodies, such as the loss of the notion of line elements, etc. This might suggest that the elastoplastic deformation should be an inherently inseparable physical entity in the usual sense of compatibility.

It is explained that a physically pertinent formulation for the incremental essence of flow-like characteristics of elastoplastic behaviour should be an objective Eulerian formulation based upon the Kirchhoff stress (weighted Cauchy stress) and the natural deformation rate (stretching). According to the latest development, it is possible to establish a straightforward Eulerian rate theory without involving additional ``elastic'' or ``plastic'' deformation-like variables. With so many possibilities in formulating objective Eulerian rate constitutive relations, in particular, for the choices of objective rates among an unlimited number of plausible candidates, it is demonstrated how a unique, self-consistent, general constitutive structure may be derived from two physical consistency criteria by synthesizing and developing a number of essential ideas contributed in previous efforts. With this general self-consistent structure based on Kirchhoff stress and the stretching, it is rigorously found from the work postulate that the normality rule for plastic flow and the convexity property of the yield surface in classical elastoplasticity for the small deformation range may be extended to be general facts even for the case covering the whole deformation range, thus leading to a self-consistent Eulerian rate theory of finite elastoplasticity with the appealingly simple essential structure as in the classical case.


Residual Stress Kirchhoff Stress Residual Stress Field Continuous Body Main Structural Feature 
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-Therani, A., Lee, E. H., Mallett, R. L., Onat, E. T. 1987The theory of elastic-plastic deformation at finite strain with induced anisotropy modeled as combined isotropic-kinematic hardeningJ. Mech. Phys. Solids35519539Google Scholar
  2. Aifantis, E. C. 1987The physics of plastic deformationInt. J. Plasticity3211247CrossRefzbMATHGoogle Scholar
  3. Anand, L. 1979On H. Hencky's approximate strain-energy function for moderate deformationsJ. Appl. Mech.467882zbMATHGoogle Scholar
  4. Anand, L. 1985Constitutive equations for hot-working of metalsInt. J. Plasticity1213231CrossRefzbMATHGoogle Scholar
  5. Anand, L. 1986Moderate deformations in extension-torsion of incompressible isotropic elastic materialsJ. Mech. Phys. Solids34293304Google Scholar
  6. Anthony, K.-H. 1970Die Reduktion von nichteuklidischen geometrischen Objekten in eine euklidische Form und physikalische Deutung der Reduktion durch Eigenspannungszustände in KristallenArch. Rat. Mech. Anal.37161180CrossRefzbMATHMathSciNetGoogle Scholar
  7. Anthony, K.-H. 1970Die Theorie der DisklinationenArch. Rat. Mech. Anal.394388zbMATHGoogle Scholar
  8. Anthony, K.-H. 1971Die Theorie der nichtmetrischen Spannungen in KristallenArch. Rat. Mech. Anal.405078CrossRefzbMATHMathSciNetGoogle Scholar
  9. Asaro, R. J. 1983Crystal plasticityJ. Appl. Mech.50921934zbMATHGoogle Scholar
  10. Asaro, R. J. 1983Micromechanics of crystals and polycrystalsAdv. Appl. Mech.231115Google Scholar
  11. Atluri, S. N. 1984On constitutive relations at finite strain. Hypo-elasticity and elasto-plasticity with isotropic or kinematic hardeningComp. Meth. Appl. Mech. Engng.43137171CrossRefzbMATHGoogle Scholar
  12. Backmann, M. E. 1964Form for the relation between stress and finite elastic and plastic strains under impulsive loadingJ. Appl. Phys.3525242533Google Scholar
  13. Bathe, K. J. 1996Finite element proceduresPrentice-HallEnglewood CliffsGoogle Scholar
  14. Bauschinger, J.: Versuche über die Festigkeit des Bessemer-Stahles von verschiedenem Kohlenstoffgehalt. Mitt. Mech.-Techn. Lab. K. Techn. Hochschule München (1874).Google Scholar
  15. Bažant, Z. P. 1998Easy-to-compute tensors with symmetric inverse approximating Hencky finite strain and its rateJ. Engng Mater. Techn.120131136Google Scholar
  16. Bernstein, B. 1960Hypoelasticity and elasticityArch. Rat. Mech. Anal.690104Google Scholar
  17. Bertram, A.: Axiomatische Einführung in die Kontinuumsmechanik. Mannheim Wien Zürich: B.I. Wissenschaftsverlag 1989.Google Scholar
  18. Bertram, A.: Description of finite inelastic deformations. In: MECAMAT'92 Multiaxial plasticity (Benallal, A., Billardon, R., Marquis, D., eds.), pp. 821–835. Laboratoire de Mécanique et Technologie, Cachan 1993.Google Scholar
  19. Bertram, A. 1999An alternative approach to finite plasticity based on material isomorphismsInt. J. Plasticity15353374CrossRefzbMATHGoogle Scholar
  20. Bertram, A. 2003Finite thermoplasticity based on isomorphismsInt. J. Plasticity1920272050CrossRefzbMATHGoogle Scholar
  21. Bertram, A., Böhlke, T., Kraska, M. 1997Numerical simulation of deformation induced anisotropy of polycrystalsComput. Mat. Sci.9158167Google Scholar
  22. Bertram, A., Böhlke, T., Kraska, M. 1997Numerical simulation of texture development of polycrystals undergoing large plastic deformationsOwen, D. R. J.Onate, E.Hinton, E. eds. Computational plasticity – fundamentals and applicationsCIMNEBarcelona895900Google Scholar
  23. Bertram, A., Kraska, M. 1995Description of finite plastic deformations in single crystals by material isomorphsmsParker, D. F.England, A. H. eds. IUTAM Symp. Anisotropy, Inhomogeneity and Nonlinearity in Solid MechanicsKluwer Academic PublishersDordrecht7790Google Scholar
  24. Bertram, A., Kraska, M. 1995Determination of finite plastic deformations in single crystalsArch. Mech.47203222Google Scholar
  25. Bertram, A., Svendsen, B. 2001On material objectivity and reduced constitutive equationsArch. Mech.53613636MathSciNetGoogle Scholar
  26. Besdo, D. 1981Zur Formulierung von Stoffgesetzen der Plastomechanik im Dehnungsraum nach Ilyushins PostulatIng.-Arch5118CrossRefzbMATHGoogle Scholar
  27. Besseling, J. F. 1968A thermodynamic approach to rheologyParkus, H.Sedov, L. I. eds. IUTAM Symp. Irreversible Aspects of Continuum MechanicsSpringerWien1653Google Scholar
  28. Besseling, J. F., Giessen, E. 1993Mathematical modelling of inelastic deformationChapman & HallLondonGoogle Scholar
  29. Biot, M. A. 1954Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomenaJ. Appl. Phys.2513851391CrossRefzbMATHGoogle Scholar
  30. Böhlke, T.: Crystallographic texture evolution and elastic anisotropy, simulation, modeling, and applications. PhD thesis, Otto-von-Guericke-Universität Magdeburg. Aachen: Shaker Verlag 2001.Google Scholar
  31. Böhlke, T., Bertram, A. 2001The evolution of Hooke's law due to texture development in FCC polycrystalsInt. J. Solids Struct.3894379459Google Scholar
  32. Böhlke, T., Kraska, M., Bertram, A.: Simulation der einfachen Scherung einer polykristallinen Aluminiumlegierung. Technische Mechanik (1997) (Sonderheft).Google Scholar
  33. Bongmba, C. N., Schütte, H. 2002Ein nichtlineares anisotropes Materialmodell auf der Basis der Hencky-Dehnung und der logarithmischen Rate zur Beschreibung duktiler SchädigungTechnische Mechanik22205222Google Scholar
  34. Bongmba, N. C.: Ein finites anisotropes Materialmodell auf der Basis der Hencky-Dehnung und der logarithmischen Rate zur Beschreibung duktiler Schädigung. PhD thesis, Ruhr-Universität Bochum (2001). Mitteil. aus dem Inst. für Mechanik Nr. 127.Google Scholar
  35. Bruhns, O., Lehmann, T. 1979Optimum deformation rate in large inelastic deformationsLippmann, H. eds. Metal forming plasticitySpringerBerlin120138Google Scholar
  36. Bruhns, O. T. 1970Die Berücksichtigung einer isotropen Werkstoffverfestigung bei der elastisch-plastischen Blechbiegung mit endlichen FormänderungenIng.-Arch396372CrossRefGoogle Scholar
  37. Bruhns, O. T. 1993Neue Materialgleichungen der PlastomechanikZAMM73T6T19zbMATHGoogle Scholar
  38. Bruhns, O. T., Bongmba, C. N. 2001On the numerical implementation of a finite strain anisotropic damage model based upon the logarithmic rateEur. J. Finite Elements10385400Google Scholar
  39. Bruhns, O.T., Diehl, H. 1989An internal variable theory of inelastic behaviour at high rates of strainArch. Mech.41427460Google Scholar
  40. Bruhns, O.T., Gupta, N. K., Meyers, A. T. M., Xiao, H. 2003Bending of an elastoplastic strip with isotropic and kinematic hardeningArch. Appl. Mech.72759778Google Scholar
  41. Bruhns, O. T., Meyers, A., Xiao, H. 2004On non-corotational rates of Oldroyd's type and relevant issues in rate constitutive formulationsProc. Roy. Soc. London A460909928MathSciNetGoogle Scholar
  42. Bruhns, O. T., Thermann, K. 1969Elastisch-plastische Biegung eines Plattenstreifens bei endlichen FormänderungenIng.-Arch38141152CrossRefGoogle Scholar
  43. Bruhns, O. T., Xiao, H., Meyers, A. 1999Self-consistent Eulerian rate type elasto-plasticity models based upon the logarithmic stress rateInt. J. Plasticity15479520Google Scholar
  44. Bruhns, O.T., Xiao, H., Meyers, A. 2000The Hencky model of elasticity. A study on Poynting effect and stress response in torsion of tubes and rodsArch. Mech.52489509MathSciNetGoogle Scholar
  45. Bruhns, O. T., Xiao, H., Meyers, A. 2001Constitutive inequalities for an isotropic elastic strain energy function based on Hencky's logarithmic strain tensorProc. Roy. Soc. London A45722072226MathSciNetGoogle Scholar
  46. Bruhns, O. T., Xiao, H., Meyers, A. 2001Large simple shear and torsion problems in kinematic hardening elastoplasticity with logarithmic rateInt. J. Solids Struct.3887018722MathSciNetGoogle Scholar
  47. Bruhns, O. T., Xiao, H., Meyers, A. 2001A self-consistent Eulerian rate type model for finite deformation elastoplasticity with isotropic damageInt. J. Solids Struct.38657683MathSciNetGoogle Scholar
  48. Bruhns, O. T., Xiao, H., Meyers, A. 2002Finite bending of a rectangular block of an elastic Hencky materialJ. Elasticity66237256CrossRefMathSciNetGoogle Scholar
  49. Bruhns, O. T., Xiao, H., Meyers, A. 2003Some basic issues in traditional Eulerian formulations of finite elastoplasticityInt. J. Plasticity1920072026CrossRefGoogle Scholar
  50. Bruhns, O. T., Xiao, H., Meyers, A. 2005A weakened form of Ilyushin's postulate and the structure of self-consistent Eulerian finite elastoplasticityInt. J. Plasticity21199219CrossRefGoogle Scholar
  51. Budianski, B. 1959A reassessment of deformation theories of plasticityJ. Appl. Mech.26259264MathSciNetGoogle Scholar
  52. Budianski, B.: Problems of hydrodynamics and continuum mechanics, chapter Remarks on theories of solid and structural mechanics, pp. 77–83. Philadelphia: SIAM 1969.Google Scholar
  53. Carrol, M. M. 1987A rate-independent constitutive theory for finite inelastic deformationJ. Appl. Mech.541521Google Scholar
  54. Carstensen, C. K., Hackl, K., Mielke, A. 2002Non-convex potentials and microstructures in finite-strain plasticityProc. Roy. Soc. London A458299317MathSciNetGoogle Scholar
  55. Casey, J. 1984A simple proof of a result in finite plasticityQuart. Appl. Math.426171zbMATHMathSciNetGoogle Scholar
  56. Casey, J., Naghdi, P. M. 1980A remark on the use of the decomposition F = F e F p in plasticityJ. Appl. Mech.47672675Google Scholar
  57. Casey, J., Naghdi, P. M. 1981Discussion of Lubarda and Lee (1981), cited belowJ. Appl. Mech.48983984Google Scholar
  58. Casey, J., Naghdi, P. M. 1981On the characterization of strain-hardening in plasticityJ. Appl. Mech.48285296Google Scholar
  59. Casey, J., Naghdi, P. M. 1983On the use of invariance requirements for intermediate configurations associated with the polar decomposition of a deformation gradientQuart. Appl. Math.41339342MathSciNetGoogle Scholar
  60. Casey, J., Naghdi, P. M. 1983A remark on the definition of hardening, softening and perfectly plastic behaviourActa Mech.489194CrossRefMathSciNetGoogle Scholar
  61. Casey, J., Naghdi, P. M. 1984Further constitutive results in finite plasticityQuart. J. Mech. Appl. Math.37231259MathSciNetGoogle Scholar
  62. Casey, J., Tseng, M. 1984A constitutive restriction related to convexity of yield surfaces in plasticityZAMP35478496Google Scholar
  63. Chakrabarty, S. 1988Theory of plasticityMcGraw-HillNew YorkGoogle Scholar
  64. Chen, W. F., Saleeb, A. F. 1994Constitutive equations for engineering materials. Vol. 1, Elasticity and modelingElsevierNew York(rev. edition)Google Scholar
  65. Clayton, J. D., McDowell, D. L. 2003A multiscale multiplicative decomposition for elastoplasticity of polycrystalsInt. J. Plasticity1914011444CrossRefGoogle Scholar
  66. Cleja-Tigoiu, S., Soós, E. 1990Elastoviscoplastic models with relaxed configurations and internal state variablesAppl. Mech. Rev.43131151Google Scholar
  67. Colak, O. U. 2004Modeling of large simple shear using a viscoplastic overstress model and classical plasticity model with different objective stress ratesActa Mech.167171187CrossRefzbMATHGoogle Scholar
  68. Colak, O. U., Krempl, E. 2005Modelling of the monotonic and cyclic Swift effects using an isotropic, finite viscoplasticity theory based on overstress (FVBO)Int. J. Plasticity21573588Google Scholar
  69. Coleman, B., Gurtin, M. E. 1967Thermodynamics with internal state variablesJ. Chem. Phys.47597613CrossRefGoogle Scholar
  70. Cotter, B. A., Rivlin, R. S. 1955Tensors associated with time-dependent stressQuart. Appl. Math.13177182MathSciNetGoogle Scholar
  71. Criscione, J. C. 2003Rivlin's representation formula is ill-conceived for the determination of response functions via biaxial testingJ. Elasticity70129147CrossRefzbMATHMathSciNetGoogle Scholar
  72. Criscione, J. C., Humphrey, J. D., Douglas, A. S., Hunter, W. C. 2000An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticityJ. Mech. Phys. Solids4824452465Google Scholar
  73. Dafalias, Y. F. 1977Il'iushin's postulate and resulting thermodynamic conditions on elasto-plastic couplingInt. J. Solids Struct.13239251zbMATHGoogle Scholar
  74. Dafalias, Y. F. 1983Corotational rates for kinematic hardening at large plastic deformationsJ. Appl. Mech.50561565zbMATHGoogle Scholar
  75. Dafalias, Y. F. 1984The plastic spin concept and a simple illustration of its role in finite plastic transformationsMech. Mater.3223233Google Scholar
  76. Dafalias, Y. F. 1985A missing link in the macroscopic constitutive formulation of large plastic deformationsSawczuk, A. Bianchi, G. eds. Plasticity today, modelling, methods and applicationsElsevierLondon135151Google Scholar
  77. Dafalias, Y. F.: The plastic spin. J. Appl. Mech. 52, 865–871 (1985); Errata, 53, 290 (1986).Google Scholar
  78. Dafalias, Y. F. 1987Issues on the constitutive formulation at large elastoplastic deformations, part 1 KinematicsActa Mech.69119138CrossRefzbMATHGoogle Scholar
  79. Dafalias, Y. F. 1988Issues on the constitutive formulation at large elastoplastic deformations, part 2 KineticsActa Mech.73121146CrossRefGoogle Scholar
  80. Dafalias, Y.F. 1998Plastic spin. Necessity or redundancy? Int. J. Plasticity14909931CrossRefzbMATHGoogle Scholar
  81. Dashner, P. A. 1979A finite strain work-hardening theory for rate independent elasto-plasticityInt. J. Solids Struct.15519528zbMATHGoogle Scholar
  82. Dashner, P. A. 1986Invariance considerations in large strain elasto-plasticityJ. Appl. Mech.535560zbMATHGoogle Scholar
  83. Dashner, P. A. 2001Elastic shadow flow and its theoretical implications for inelastic solidsInt. J. Solids Struct.3834873548zbMATHMathSciNetGoogle Scholar
  84. Desai, C. S., Gallagher, R. H., eds.: Mechanics of engineering materials. Chichester: Wiley 1984.Google Scholar
  85. Desai, C. S.Krempl, E.Kiousis, P. D.Kundu, T. eds. 1987Constitutive laws for engineering materialsElsevierNew YorkGoogle Scholar
  86. Desai, C. S.Krempl, E.Kiousis, P. D.Kundu, T. eds. 1991Constitutive laws for engineering materialsASMENew YorkGoogle Scholar
  87. Dienes, J. K. 1979On the analysis of rotation and stress rate in deforming bodiesActa Mech.32217232CrossRefzbMATHMathSciNetGoogle Scholar
  88. Drucker, D. C.: A more fundamental approach to plastic stress-strain relations. In: Proc. 1st U.S. Natl. Congr. Appl. Mech., pp. 487–491, New York: ASME 1952.Google Scholar
  89. Drucker, D. C. 1959A definition of stable inelastic materialsJ. Appl. Mech.26101106zbMATHMathSciNetGoogle Scholar
  90. Drucker, D. C.: Plasticity. In: Proc. 1st Symp. Naval Structural Mechanics (Goodier, J. N., Hoff, N. J., eds.), pp. 407–455. New York: Pergamon 1960.Google Scholar
  91. Drucker, D. C. 1964On the postulate of stability of material in the mechanics of continuaJ. Mécanique3235249MathSciNetGoogle Scholar
  92. Drucker, D. C. 1988Conventional and unconventional plastic response and representationAppl. Mech. Rev.41151167Google Scholar
  93. Dubey, R. N. 1987Choice of tensor-rates – a methodologySM Archives12233244zbMATHMathSciNetGoogle Scholar
  94. Eckart, C. 1948The thermodynamics of irreversible processes. IV: The theory of elasticity and anelasticityPhys. Rev.73373382zbMATHMathSciNetGoogle Scholar
  95. Eglit, M. E. 1960Tensorial characteristics of finite deformationsPrikl. Mat. Mekh.2414321438Google Scholar
  96. Eringen, A. C., Kafadar, C. B. 1976Polar field theoriesEringen, A. C. eds. Continuum physics, vol. IVAcademic PressNew York173Google Scholar
  97. Eterovic, A. L., Bathe, K. J. 1990A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measuresInt. J. Num. Meth. Engng.3010991115CrossRefGoogle Scholar
  98. Eve, R. A., Gültop, T., Reddy, B. D. 1990An internal variable finite-strain theory of plasticity within the framework of convex analysisQuart. Appl. Math.48625643MathSciNetGoogle Scholar
  99. Fitzjerald, S. 1980A tensorial Hencky measure of strain and strain rate for finite deformationJ. Appl. Phys.5151115115Google Scholar
  100. Fosdick, R., Volkmann, E. 1993Normality and convexity of the yield surface in nonlinear plasticityQuart. Appl. Math.51117127MathSciNetGoogle Scholar
  101. Fox, N. 1968On the continuum theories of dislocations and plasticityQuart. J. Mech. Appl. Math.216775zbMATHGoogle Scholar
  102. Freed, A. D. 1995Natural strainJ. Engng Mater. Techn.117379385Google Scholar
  103. Fressengeas, C., Molinari, A. 1984Représentations du comportement plastique anisotrope aux grandes déformationsArch. Mech.36483000Google Scholar
  104. Freudenthal, A. M., Geiringer, H. 1958The mathematical theories of the inelastic continuumFlügge, S. eds. Handbuch der PhysikSpringerBerlin229433Google Scholar
  105. Freund, L. B. 1970 Constitutive equations for elastic-plastic materials at finite strainInt. J. Solids Struct.611931209zbMATHGoogle Scholar
  106. Geiringer, H.: Fondements mathématiques de la théorie des corps plastiques isotropes. In: Mém. Sci. Math., Vol. 86, pp. 1–89. Paris: Gauthier-Villars 1937.Google Scholar
  107. Germain, P., Nguyen, Q. S., Suquet, P. 1983Continuum thermodynamicsJ. Appl. Mech.5010101020Google Scholar
  108. Giessen, E. 1989Continuum models of large deformation plasticity. Part I : Large deformation plasticity and the concept of a natural reference stateEur. J. Mech. A/Solids81534zbMATHGoogle Scholar
  109. Giessen, E. 1989Continuum models of large deformation plasticity. Part II: A kinematic hardening model and the concept of a plastically induced orientational structureEur. J. Mech. A/Solids889108zbMATHGoogle Scholar
  110. Giessen, E. 1991Micromechanical and thermodynamic aspects of the plastic spinInt. J. Plasticity7365386zbMATHGoogle Scholar
  111. Gilman, J. J. 1960Physical nature of plastic flow and fractureLee, E. H.Symonds, P. S. eds. Plasticity, Proc. 2nd Symp. Naval Structural MechanicsPergamonNew York4399Google Scholar
  112. Gilman, J. J. 1969A unified view of flow mechanics in materialsArgon, A. S. eds. Physics of strength and plasticityThe MIT PressCambridge, MA313Google Scholar
  113. Green, A. E., Adkins, J. E. 1960Large elastic deformationsOxford University PressLondonGoogle Scholar
  114. Green, A. E., Naghdi, P. M.: A general theory of an elastic-plastic continuum. Arch. Rat. Mech. Anal. 18, 251–281 (1965), Corrigenda 19, 408.Google Scholar
  115. Green, A. E., Naghdi, P. M.: A thermodynamic development of elastic-plastic continua. In: Proc. IUTAM Symp. Irreversible aspects of continuum mechanics and transfer of physical characteristics in moving fluids (Parkus, H., Sedov, L. I., eds.), pp. 117–131. Springer 1968.Google Scholar
  116. Green, A. E., Naghdi, P. M. 1971Some remarks on elastic-plastic deformation at finite strainInt. J. Engng. Sci.912191229CrossRefGoogle Scholar
  117. Guo, Z.-H. 1963Time derivatives of tensor fields in non-linear continuum mechanicsArch. Mech.15131163zbMATHGoogle Scholar
  118. Gurtin, M. E., Spear, K. 1983On the relationship between the logarithmic strain rate and the stretching tensorInt. J. Solids Struct.19437444MathSciNetGoogle Scholar
  119. Hackl, K. 1997Generalized standard media and variational principles in classical and finite strain elastoplasticityJ. Mech. Phys. Solids45667688zbMATHMathSciNetGoogle Scholar
  120. Halphen, B., Nguyen, Q. S. 1975Sur les matériaux standards généralisésJ. Mécanique143963Google Scholar
  121. Han, W. M., Reddy, B. D. 1999Plasticity, mathematical theory and numerical analysisSpringerBerlinGoogle Scholar
  122. Hashiguchi, K. 1994On the loading criterionInt. J. Plasticity10871878CrossRefzbMATHGoogle Scholar
  123. Haupt, P. 1977Viskoelastizität und PlastizitätSpringerBerlinGoogle Scholar
  124. Haupt, P. 1984Intermediate configurations and the description of viscoplastic material behavioursNucl. Engng. Des.79289300CrossRefGoogle Scholar
  125. Haupt, P. 1985On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behaviourInt. J. Plasticity1303316CrossRefzbMATHMathSciNetGoogle Scholar
  126. Haupt, P. 2002Continuum mechanics and theory of materials2SpringerBerlinGoogle Scholar
  127. Haupt, P., Tsakmakis, C. 1986On kinematic hardening and large plastic deformationsInt. J. Plasticity2279293CrossRefGoogle Scholar
  128. Haupt, P., Tsakmakis, C. 1989On the application of dual variables in continuum mechanicsContinuum Mech. Thermodyn.1165196CrossRefMathSciNetGoogle Scholar
  129. Haupt, P., Tsakmakis, C. 1996Stress tensors associated with deformation tensors via dualityArch. Mech.48347384MathSciNetGoogle Scholar
  130. Havner, K. S. 1992Finite plastic deformation of crystalline solidsCambridge University PressCambridgeGoogle Scholar
  131. Heiduschke, K. 1995The logarithmic strain space descriptionInt. J. Solids Struct.3210471062zbMATHGoogle Scholar
  132. Hencky, H. 1923Über einige statisch bestimmte Fälle des Gleichgewichts in plastischen KörpernZAMM3241251zbMATHGoogle Scholar
  133. Hencky, H. 1924Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen NachspannungenZAMM4323335Google Scholar
  134. Hencky, H. 1928Über die Form des Elastizitätsgesetzes bei ideal elastischen StoffenZ. Techn. Phys.9215223zbMATHGoogle Scholar
  135. Hencky, H. 1929Das Superpositionsgesetz eines endlich deformierten relaxationsfähigen elastischen Kontinuums und seine Bedeutung für eine exakte Ableitung der Gleichungen für die zähe Flüssigkeit in der Euler'schen FormAnn. Physik.5617630zbMATHGoogle Scholar
  136. Hencky, H. 1929Welche Umstände bedingen die Verfestigung bei der bildsamen Verformung von festen isotropen Körpern?Z. Phys.55145155zbMATHGoogle Scholar
  137. Hencky, H. 1931The law of elasticity for isotropic and quasi-isotropic substances by finite deformationsJ. Rheol.2169176CrossRefGoogle Scholar
  138. Hencky, H. 1932On propagation of elastic waves in materials under high hydrostatic pressurePhilos. Mag.14254258zbMATHGoogle Scholar
  139. Hencky, H. 1932A simple model explaining the hardening effect in polycrystalline metalsJ. Rheol.33036CrossRefGoogle Scholar
  140. Hencky, H. 1933The elastic behaviour of vulcanised rubberRubber Chem. Technol.6217224Google Scholar
  141. Hencky, H. 1935Stresses in rubber tiresMech. Engng.27149153Google Scholar
  142. Hill, R. 1948A theory of the yielding and plastic flow of anisotropic metalsProc. Roy. Soc. A193281297zbMATHGoogle Scholar
  143. Hill, R. 1948A variational principle of maximum plastic work in classical plasticityQuart. J. Mech. Appl. Math.11828zbMATHMathSciNetGoogle Scholar
  144. Hill, R. 1950The mathematical theory of plasticityClarendon PressOxfordGoogle Scholar
  145. Hill, R. 1958A general theory of uniqueness and stability in elastic-plastic solidsJ. Mech. Phys. Solids6236249zbMATHGoogle Scholar
  146. Hill, R. 1959Some basic principles in the mechanics of solids without a natural timeJ. Mech. Phys. Solids7209225zbMATHMathSciNetGoogle Scholar
  147. Hill, R. 1967The essential structure of constitutive laws for metal composites and polycrystalsJ. Mech. Phys. Mech.157995Google Scholar
  148. Hill, R. 1967On the classical constitutive relations for elastic-plastic solidsBromberg, B.Hult, J.Niordson, F eds. Recent progress in applied mechanics. Folke Odqvist VolumeAlmqvist and WiksellStockholm241249Google Scholar
  149. Hill, R.: On constitutive inequalities for simple materials. J. Mech. Phys. Solids 16, 229–242; 315–322 (1968).Google Scholar
  150. Hill, R. 1970Constitutive inequalities for isotropic elastic solids under finite strainProc. Roy. Soc. London A326131147Google Scholar
  151. Hill, R. 1978Aspects of invariance in solid mechanicsAdv. Appl. Mech.18175zbMATHGoogle Scholar
  152. Hill, R., Rice, J. R. 1973Elastic potentials and the structure of inelastic constitutive lawsSIAM J. Appl. Math.25448461CrossRefMathSciNetGoogle Scholar
  153. Hill, R., Rice, J. R. 1987Discussion of Carrol (1987), cited aboveJ. Appl. Mech.54745747Google Scholar
  154. Hodge, P.G., Prager, W. 1948A variational principle for plastic materials with strain-hardeningJ. Math. Phys.27110MathSciNetGoogle Scholar
  155. Hoger, A. 1986The material time derivative of logarithmic strainInt. J. Solids Struct.2210191032zbMATHMathSciNetGoogle Scholar
  156. Hoger, A. 1987The stress conjugate to logarithmic strainInt. J. Solids Struct.2316451656zbMATHMathSciNetGoogle Scholar
  157. Huber, M. T.: The specific deformation work as measure of strength. Czasopismo Techniczne (Lwów-Lemberg) 22, 38–40, 49–50, 61–62, 80–81 (1904) (in Polish).Google Scholar
  158. Hughes, T. J. R. 1984Numerical implementation of constitutive models. Rate-independent deviatoric plasticityNemat-Nasser, S.Asaro, R. J.Hegemier, A. eds. Theoretical foundation for large-scale computations for nonlinear material behaviorMartinus Nijhoff PublishersDordrecht2957Google Scholar
  159. Hutchinson, J. W.: Finite strain analysis of elastic-plastic solids and structures. In: Numerical solutions of nonlinear structural problems (Hartung, R. F., ed.), pp. 17–29. ASME 1973.Google Scholar
  160. Hutter, K. 1977The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamicsActa Mech.27154CrossRefMathSciNetGoogle Scholar
  161. Hutter, K. eds. 1993Continuum mechanics in environmental sciences and geophysics. CISM Courses and Lectures, vol. 337SpringerWien New YorkGoogle Scholar
  162. Hwang, K. C., Huang, Y. G. 1999Constitutive relations of solidsTsinghua University PressBeijing(in Chinese)Google Scholar
  163. Ilyushin, A. A. 1961On a postulate of plasticityPrikl. Math. Mekh.25503507zbMATHGoogle Scholar
  164. Jaumann, G. 1911Geschlossenes System physikalischer und chemischer Differential-Gesetze. SitzberAkad. Wiss. Wien, Abt. IIa120385530zbMATHGoogle Scholar
  165. Johnson, G. C., Bammann, D. J. 1984A discussion of stress rates in finite deformation problemsInt. J. Solids Struct.20725737Google Scholar
  166. Johnson, W., Mellor, P. B. 1972Engineering plasticityVan Nostrand ReinholdLondonGoogle Scholar
  167. Kachanov, L. M. 1971Foundations of the theory of plasticityNorth-HollandAmsterdamGoogle Scholar
  168. Kestin, J., Rice, J. R. 1970Paradoxes in the applications of thermodynamics to strained solidsStuart, E. B.Cal'Or, B.Brainard, A. J. eds. A critical review of thermodynamicsMono Book CorpBaltimore275298Google Scholar
  169. Khan, A. S., Huang, S. J. 1995Continuum theory of plasticityWileyNew YorkGoogle Scholar
  170. Kleiber, M. 1986On errors inherent in commonly accepted rate forms of the elastic constitutive lawArch. Mech.38271279zbMATHGoogle Scholar
  171. Koiter,  W. T. 1956A new general theorem on shakedown of elastic-plastic structuresProc. Kon. Ned. Akad. WetB592434MathSciNetGoogle Scholar
  172. Koiter, W. T. 1960General theorems for elastic-plastic solidsSneddon, I. N.Hill, R. eds. Progress in solid mechanics vol. 1, chap. IVNorth-HollandAmsterdam167121Google Scholar
  173. Kojic, M., Bathe, K. J. 1987Studies of finite element procedures – stress solution of a closed elastic strain path with stretching and shearing using the updated Lagrangean-Jaumann formulationCompt. Struct.26175179Google Scholar
  174. Kollmann, F. G., Sansour, C. 1997Viscoplastic shells: theory and numerical analysisArch. Mech.49477511Google Scholar
  175. Kratochvíl, J. 1971Finite-strain theory of crystalline elastic-inelastic materialsJ. Appl. Phys.4211041108Google Scholar
  176. Kratochvíl, J. 1973On a finite strain theory of elastic-plastic materialsActa Mech.16127242CrossRefzbMATHGoogle Scholar
  177. Kratochvíl, J., Dillon, O. W. 1969Thermodynamics of elastic-plastic materials as a theory with internal state variablesJ. Appl. Phys.4032073218Google Scholar
  178. Kratochvíl, J., Šilhavý, M. 1977A theory of inelastic behaviour of materials, part II: Inelastic materialsArch. Rat. Mech. Anal.65131Google Scholar
  179. Krausz, A. S.Krausz, K. eds. 1996Unified constitutive laws of plastic deformationAcademic PressNew YorkGoogle Scholar
  180. Krawietz, A. 1981Passivität, Konvexität und Normalität bei elastisch-plastischem MaterialIng.-Arch51257274zbMATHGoogle Scholar
  181. Krempl, E. 1975On the interaction of rate and history dependence in structural metalsActa Mech.225390CrossRefzbMATHGoogle Scholar
  182. Krempl, E. 1981Plasticity and variable heredityArch. Mech.33289306zbMATHMathSciNetGoogle Scholar
  183. Kröner, E. 1955Die inneren Spannungen und der Inkompatibilitätstensor in der ElastizitätstheorieZ. Angew. Phys.7249257zbMATHGoogle Scholar
  184. Kröner, E. 1958Kontinuumstheorie der Versetzungen und EigenspannungenSpringerBerlinGoogle Scholar
  185. Kröner, E. 1960Allgemeine Kontinuumstheorie der Versetzungen und EigenspannungenArch. Rat. Mech. Anal.4273334zbMATHGoogle Scholar
  186. Kröner, E. 1963Dislocation: A new concept in the continuum theory of plasticityJ. Math. Phys.422737Google Scholar
  187. Kröner, E. 1966Dislocation field theoryGruber, B. eds. Theory of crystal defectsAcademic PressNew York231256Google Scholar
  188. Kröner, E. 1970Initial studies of a plasticity theory based upon statistical mechanicsKanninen, M. F.Adler, W. F.Rosenfield, A. R.Jaffer, R. I. eds. Inelastic behaviour of solidsMcGraw-HillNew York137147Google Scholar
  189. Kröner, E., Teodosiu, C. 1974Lattice defect approach to plasticity and viscoplasticitySawczuk, A. eds. Problems of plasticityNoordhoffLeyden4588Google Scholar
  190. Kuroda, M. 1996Roles of plastic spin in shear bandingInt. J. Plasticity12671693CrossRefzbMATHGoogle Scholar
  191. Le, K. C., Stumpf, H. 1993Constitutive equations for elastoplastic bodies at finite strain: Thermodynamic implementationActa Mech.100155170CrossRefMathSciNetGoogle Scholar
  192. Lee, E. H. 1969Elastic-plastic deformation at finite strainsJ. Appl. Mech.3616zbMATHGoogle Scholar
  193. Lee, E. H. 1981Some comments on elastic-plastic analysisInt. J. Solids Struct.17859872zbMATHGoogle Scholar
  194. Lee, E. H. 1985Finite deformation effects in plasticity analysisSawczuk, A.Bianchi, G. eds. Plasticity today, modelling, methods and applicationsElsevierLondon6174Google Scholar
  195. Lee, E. H. 1991Some basic aspects of elastic-plastic theory involving finite strainDesai, C. S.Krempl, E.Kiousis, P. D.Kundu, T. eds. Constitutive laws for engineering materialsElsevierNew York141146Google Scholar
  196. Lee, E. H. 1996Some anomalies in the structure of elastic-plastic theory at finite strainCarroll, M. M.Hayes, M. eds. Nonlinear effects in fluids and solidsPlenum PressNew York227249Google Scholar
  197. Lee, E. H., Liu, D. T. 1967Finite strain elastic-plastic theory with application to plane-wave analysisJ. Appl. Phys.381927Google Scholar
  198. Lee, E. H., Liu, D. T. 1968Finite strain elastic-plastic theoryParkus, H.Sedov, L. I. eds. Proc. IUTAM Symp. Irreversible aspects of continuum mechanics and transfer of physical characteristics in moving fluidsSpringerWien New York213221Google Scholar
  199. Lee, E. H.Mallett, R. L. eds. 1982Plasticity of metals at finite strain, theory, computation and experimentStanford University and RPIStanfordGoogle Scholar
  200. Lee, E. H., Mallett, R. L., Wertheimer, T. B. 1983Stress analysis for anisotropic hardening in finite-deformation plasticityJ. Appl. Mech.50554560Google Scholar
  201. Lee, E. H., McMeeking, R. M. 1980Concerning elastic and plastic components of deformationInt. J. Solids Struct.16715721MathSciNetGoogle Scholar
  202. Lehmann, T. 1960Einige Betrachtungen zu den Grundlagen der UmformtechnikIng.-Arch29121zbMATHMathSciNetGoogle Scholar
  203. Lehmann, T. 1962Zur Beschreibung großer plastischer Formänderungen unter Berücksichtigung der WerkstoffverfestigungRheol. Acta2247254CrossRefGoogle Scholar
  204. Lehmann, T. 1964Anisotrope plastische FormänderungenRheol. Acta3281285CrossRefzbMATHGoogle Scholar
  205. Lehmann, T. 1968PlastizitätstheorieKienzle, O. eds. Mechanische UmformtechnikSpringerBerlin Heidelberg1257Google Scholar
  206. Lehmann, T. 1972Anisotrope plastische FormänderungenRomanian J. Techn. Sci. Appl. Mech1710771086Google Scholar
  207. Lehmann, T. 1972Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen für große elasto-plastische FormänderungenIng.-Arch41297310CrossRefzbMATHGoogle Scholar
  208. Lehmann, T. 1972Some thermodynamic considerations of phenomenological theory of non-isothermal elastic-plastic deformationsArch. Mech.24975989zbMATHMathSciNetGoogle Scholar
  209. Lehmann, T. 1973On large elastic-plastic deformationsSawczuk, A. eds. Foundations of plasticityNoordhoffLeyden571585Google Scholar
  210. Lehmann, T. 1974Einige Betrachtungen zur Thermodynamik großer elasto-plastischer FormänderungenActa Mech.20187207CrossRefzbMATHGoogle Scholar
  211. Lehmann, T. 1977On the theory of large, non-isothermic, elastic-plastic and elastic-visco-plastic deformationsArch. Mech.29393409zbMATHGoogle Scholar
  212. Lehmann, T. 1978Some aspects of non-isothermic large inelastic deformationsSM Archives3261317zbMATHMathSciNetGoogle Scholar
  213. Lehmann, T. 1982On the concept of stress-strain relations in plasticityActa Mech42263275CrossRefzbMATHGoogle Scholar
  214. Lehmann, T. 1982Some remarks on the decomposition of deformations and mechanical workInt. J. Engng. Sci.20281288CrossRefzbMATHGoogle Scholar
  215. Lehmann, T. eds. 1984The Constitutive law in thermoplasticity. CISM Courses and Lectures, vol. 281SpringerWien New YorkGoogle Scholar
  216. Lehmann, T. 1989On the balance of energy and entropy at inelastic deformations of solid bodiesEur. J. Mech. A/Solids8235251zbMATHMathSciNetGoogle Scholar
  217. Lehmann, T., Guo, Z. H., Liang, H. Y. 1991The conjugacy between Cauchy stress and logarithm of the left stretch tensorEur. J. Mech. A/Solids10395404MathSciNetGoogle Scholar
  218. Lemaitre, J., Chaboche, J.-L. 1990Mechanics of solid materialsCambridge University PressCambridgeGoogle Scholar
  219. Levitas, V. I. 1996Large deformation of materials with complex rheological properties at normal and high pressureNova Science PublishersNew YorkGoogle Scholar
  220. Lévy, M. 1870Mémoire sur les équations générales des mouvements intérieurs des corps solides ductiles au delà des limites où l'élasticité pourrait les ramener à leur premier étatC. R. Acad. Sci. Paris7013231325zbMATHGoogle Scholar
  221. Lin, H. C., Naghdi, P. M. 1989Necessary and sufficient conditions for the validity of a work inequality in finite plasticityQ. J. Mech. Appl. Math.421321MathSciNetGoogle Scholar
  222. Lin, R. C. 2002Numerical study of consistency of rate constitutive equations with elasticity at finite deformationInt. J. Numer. Meth. Engng.5510531077CrossRefzbMATHGoogle Scholar
  223. Lin, R. C.: Viscoelastic and elastic-viscoelastic-elastoplastic constitutive characterizations of polymers at finite strains, theoretical and numerical aspects. PhD thesis, University of the Federal Armed Forces Hamburg 2002.Google Scholar
  224. Lin, R. C. 2003Hypoelasticity-based analytical stress solutions in the simple shearing processZAMM83163171CrossRefzbMATHGoogle Scholar
  225. Lin, R. C., Brocks, W. 2004On a finite viscoplastic theory based on a new internal dissipation inequalityInt. J. Plasticity2012811311CrossRefGoogle Scholar
  226. Lin, R. C., Schomburg, U. 2003A finite elastic-viscoelastic-elastoplastic material law with damage theoretical and numerical aspectsCompt. Meth. Appl. Mech. Engng.19215911627Google Scholar
  227. Lin, R. C., Schomburg, U., Kletschkowski, T. 2003Analytical stress solutions of a closed deformation path with stretching and shearing using the hypoelastic formulationsEur. J. Mech. A/Solids22443461Google Scholar
  228. Lippmann, H. eds. 1977Engineering plasticity, theory of metal forming processes, CISM Courses and Lectures vol. 139SpringerWien New YorkGoogle Scholar
  229. Lippmann, H. 1981Mechanik des plastischen FließensSpringerBerlinGoogle Scholar
  230. Lippmann, H., Mahrenholtz, O. 1967Plastomechanik der Umformung metallischer WerkstoffeSpringerBerlinGoogle Scholar
  231. Liu, C. S. 2004Lie symmetries of finite strain elastic-perfectly plastic models and exactly consistent schemes for numerical integrationsInt. J. Solids Struct.4118231853zbMATHGoogle Scholar
  232. Liu, C. S., Hong, H. K. 1999Non-oscillation criteria for hypoelastic models under simple shear deformationJ. Elasticity57201241CrossRefMathSciNetGoogle Scholar
  233. Liu, C. S., Hong, H. K. 2001Using comparison theorem to compare corotational stress rates in the model of perfect elastoplasticityInt. J. Solids Struct.3829692987MathSciNetGoogle Scholar
  234. Loret, B. 1983On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materialsMech. Mater.2287304CrossRefGoogle Scholar
  235. Lubarda, V. A. 1991Some aspects of elasto-plastic constitutive analysis of elastically anisotropic materialsInt. J. Plasticity7625636CrossRefzbMATHGoogle Scholar
  236. Lubarda, V. A. 2001Elastoplasticity theoryCRC PressNew YorkGoogle Scholar
  237. Lubarda, V. A., Lee, E. H. 1981A correct definition of elastic and plastic deformation and its computational significanceJ. Appl. Mech.483540MathSciNetGoogle Scholar
  238. Lubarda, V. A., Shih, C. F. 1994Plastic spin and related issues in phenomenological plasticityJ. Appl. Mech.61524529Google Scholar
  239. Lubliner, J. 1972On the thermodynamic foundations of nonlinear solid MechInt. J. Non-Linear Mech.7237254zbMATHGoogle Scholar
  240. Lubliner, J. 1973On the structure of the rate equations of materials with internal variablesActa Mech.17109119CrossRefzbMATHMathSciNetGoogle Scholar
  241. Lubliner, J. 1984A maximal-dissipation principle in generalized plasticityActa Mech.52225237CrossRefzbMATHMathSciNetGoogle Scholar
  242. Lubliner, J. 1986Normality rules in large-deformation plasticityMech. Materials52934CrossRefGoogle Scholar
  243. Lubliner, J. 1990Plasticity theoryMacmillanNew YorkGoogle Scholar
  244. Lucchesi, M., Owen, D. R., Podio-Guidugli, P. 1988Materials with elastic range: A theory with a view toward applications. Part IIIArch. Rat. Mech. Anal.1175396MathSciNetGoogle Scholar
  245. Lucchesi, M., Padovani, C., Pagni, A., Podio-Guidugli, P. 1993Materials with elastic range and plastic change of volumeInt. J. Plasticity93549Google Scholar
  246. Lucchesi, M., Podio-Guidugli, P. 1990Materials with elastic range: A theory with a view toward applications. Part IIArch. Rat. Mech. Anal.110942CrossRefMathSciNetGoogle Scholar
  247. Ludwik, P. 1909Elemente der technologischen MechanikSpringerBerlinGoogle Scholar
  248. Macvean, D. B. 1968Die Elementararbeit in einem Kontinuum und die Zuordnung von Spannungs- und VerzerrungstensorenZAMM19157185zbMATHGoogle Scholar
  249. Mahrenholtz, O., Wilmanski, K. 1990Note on simple shear of plastic monocrystalsMech. Res. Commun.17393402CrossRefGoogle Scholar
  250. Mandel, J. P.: Contribution théorique à l'étude de l'écrouissage et des lois de l'écoulement plastique. In: Proc. 11th Int. Congr. Appl. Mech., pp. 502–509 (1964).Google Scholar
  251. Mandel, J. P. 1972Plasticité Classique et Viscoplasticité. CISM Courses and Lectures, vol. 97SpringerWienGoogle Scholar
  252. Mandel, J. P. 1973Equations constitutives et directeurs dans les milieux plastiques et viscoplastiquesInt. J. Solids Struct.9725740zbMATHGoogle Scholar
  253. Mandel, J. P. 1973Relations de comportement des milieux élastiques-viscoplastiques. Notion de répère directeurSawczuk, A. eds. Foundations of plasticityNoordhoffLeyden387399Google Scholar
  254. Mandel, J. P. 1974Director vectors and constitutive equations for plastic and viscoplastic mediaSawczuk, A. eds. Problems of plasticityNoordhoffLeyden135143Google Scholar
  255. Mandel, J. P. 1974Thermodynamics and plasticityDomingos, J. J.Nina, M. N. R.Whitelaw, J. H. eds. Foundations of continuum thermodynamicsMacMillanLondon283304Google Scholar
  256. Mandel, J. P. 1981Sur la définition de la vitesse de déformation élastique et sa relation avec la vitesse de contrainteInt. J. Solids Struct.17873878zbMATHMathSciNetGoogle Scholar
  257. Mandel, J. P. 1982Définition d'un repère privilégié pour l'étude des transformations anélastiques du polycristalJ. Méc. Théor. Appl.1723zbMATHMathSciNetGoogle Scholar
  258. Marsden, E., Hughes, T. J. R. 1983Mathematical foundations of elasticityPrentice-HallEnglewood CliffsGoogle Scholar
  259. Martin, J. B. 1975Plasticity, Fundamentals and general resultsThe MIT PressCambridgeGoogle Scholar
  260. Maugin, G. A. 1992The thermomechanics of plasticity and fractureCambridgeCambridge University PressGoogle Scholar
  261. Maugin, G. A. 2003Geometry thermodynamics of structural rearrangements: Ekkehart Kröner's legacyZAMM837584CrossRefzbMATHMathSciNetGoogle Scholar
  262. Mazur, E. F. 1961On the definition of stress rateQuart. Appl. Math.19160163MathSciNetGoogle Scholar
  263. McMeeking, R. M., Rice, J. R. 1975Finite-element formulations for problems of large elastic-plastic deformationInt. J. Solids Struct.11601616Google Scholar
  264. Meixner, J. 1954Thermodynamische Theorie der elastischen RelaxationZ. Naturforschung9(a)654663Google Scholar
  265. Melan, E. 1938Zur Plastizität des räumlichen KontinuumsIng.-Arch9116126CrossRefzbMATHGoogle Scholar
  266. Meyers, A. 1999On the consistency of some Eulerian strain ratesZ. Angew. Math. Mech.79171177CrossRefzbMATHMathSciNetGoogle Scholar
  267. Meyers, A., Bruhns, O. T., Xiao, H. 2000Large strain response of kinematic hardening elastoplasticity with the logarithmic rate: Swift effect in torsionMeccanica35229247CrossRefGoogle Scholar
  268. Meyers, A., Schieße, P., Bruhns, O. T. 2000Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain ratesActa Mech.13991103CrossRefGoogle Scholar
  269. Meyers, A., Xiao, H., Bruhns, O. T. 2003Applications to an Eulerian finite elastoplasticity modelGupta, N. K. eds. Plasticity and impact mechanics, Proc. 8th Int. Symp. IMPLAST 2003 Phoenix Publishing HouseNew Delhi3541Google Scholar
  270. Meyers, A., Xiao, H., Bruhns, O. T. 2004Comparison of objective stress rates in single parameter strain cyclesTopping, B. H. V.Mota Soares, C. A. eds. Proc. 7th Int. Conf. on Comput. Struct. TechnCivil-Comp. PressStirling, UK147148Google Scholar
  271. Miehe, C. 1994On the representation of Prandtl-Reuss tensors within the framework of multiplicative elastoplasticityInt. J. Plasticity10609621CrossRefzbMATHGoogle Scholar
  272. Miehe, C. 1995A theory of large-strain isotropic thermoplasticity based on metric transformation tensorsArch. Appl. Mech.664564zbMATHGoogle Scholar
  273. Miehe, C. 1998A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metricInt. J. Solids Struct.3538593897zbMATHGoogle Scholar
  274. Miehe, C. 1998A formulation of finite elastoplasticity based on dual co- and contra-variant eigenvector triads normalized with respect to a plastic metricCompt. Meth. Appl. Mech. Engng.159223260zbMATHMathSciNetGoogle Scholar
  275. Miehe, C., Apel, N., Lambrecht, M. 2002Anisotropic additive plasticity in the logarithmic strain space. Modular kinematic formulation and implementation based on incremental minimization principles for standard materialsComput. Meth. Appl. Mech. Engng.19153835425MathSciNetGoogle Scholar
  276. Miehe, C., Schröder, J. 2001A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticityInt. J. Numer. Meth. Engng.50273298Google Scholar
  277. Miehe, C., Stein, E., Wagner, W.: Associative multiplicative elasto-plasticity: Formulation and aspects of the numerical implementation including stability analysis. Computer 978 (1994).Google Scholar
  278. von Mises, R.: Mechanik der festen Körper im plastisch deformablen Zustand. In: Nachr. Königl. Ges. Wiss., Math. Phys. Kl., pp. 582–592. Göttingen 1913.Google Scholar
  279. Mises, R. 1928Mechanik der plastischen Formänderung von KristallenZAMM8161185zbMATHGoogle Scholar
  280. Moran, B., Ortiz, M., Shih, C. F. 1990Formulation of implicit finite element methods for multiplicative finite deformation plasticityInt. J. Numer. Meth. Engng.29483514CrossRefMathSciNetGoogle Scholar
  281. Moreau, J. J. 1970Sur les lois de frottement, de plasticité et de viscositéC. R. Acad. Sci. Paris, sér. A271608611Google Scholar
  282. Moreau, J. J. 1976Application of convex analysis to the treatment of elastoplastic systemsGermain, P.Nayroles, B. eds. Applications of methods of functional analysis to problems in mechanicsSpringerBerlin5689Google Scholar
  283. Moss, W. C. 1984On instabilities in large deformation simple shear loadingComp. Meth. Appl. Mech. Engng.46329338CrossRefzbMATHGoogle Scholar
  284. Müller, C.: Thermodynamic modeling of polycrystalline shape memory alloys at finite strain. PhD thesis, Ruhr-Universität Bochum 2003.Google Scholar
  285. Müller, I. 1985ThermodynamicsPitmanLondonGoogle Scholar
  286. Müller, I., Ruggeri, T. 1998Rational extended thermodynamics2SpringerBerlinGoogle Scholar
  287. Naghdi, P. M. 1960Stress-strain relations in plasticity and thermoplasticityLee, E. H.Symonds,  P. S. eds. Plasticity, Proc. 2nd Symp. Naval Structural MechanicsPergamon PressNew York121169Google Scholar
  288. Naghdi, P. M. 1990A critical review of the state of finite plasticityZAMP41315394CrossRefzbMATHMathSciNetGoogle Scholar
  289. Naghdi, P. M., Casey, J. 1992A prescription for the identification of finite plastic strainInt. J. Engng. Sci.3012571278MathSciNetGoogle Scholar
  290. Naghdi, P. M., Trapp, J. A. 1975On the nature of normality of plastic strain rate and convexity of yield surfaces in plasticityJ. Appl. Mech.426166Google Scholar
  291. Naghdi, P. M., Trapp, J. A. 1975Restrictions on constitutive equations of finitely deformed elastic-plastic materialsQuart. J. Mech. Appl. Math.282546MathSciNetGoogle Scholar
  292. Naghdi, P. M., Trapp, J. A. 1975The significance of formulating plasticity theory with reference to loading surfaces in strain spaceInt. J. Engng. Sci.13785797CrossRefGoogle Scholar
  293. Naghdi, P. M., Wainwright, W. L. 1961On the time derivative of tensors in mechanics of continuaQuart. Appl. Math.1995109MathSciNetGoogle Scholar
  294. Nagtegaal, J. C., de Jong, J. E. 1982Some aspects of non-isotropic workhardening in finite strain plasticityLee, E. H.Mallett, R. L. eds. Plasticity of metals at finite strain, theory, computation and experimentStanford UniversityStanford65106Google Scholar
  295. Neale, K. W. 1981Phenomenological constitutive laws in finite plasticitySM Archives679128zbMATHGoogle Scholar
  296. Needleman, A. 1982Finite elements for finite strain plasticity problemsLee, E. H.Mallett, R. L. eds. Plasticity of metals at finite strain, theory, computation and experiment Stanford UniversityStanford387436Google Scholar
  297. Needleman, A., Rice, J. R. 1978Limits to ductility set by plastic flow localizationKoistinen, D. P.Wang, N.-M. eds. Mechanics of sheet metal formingPlenum PressLondon237267Google Scholar
  298. Needleman, A., Tvergaard, V. 1977Necking of biaxially stretched elastic-plastic circular platesJ. Mech. Phys. Solids25159183Google Scholar
  299. Nemat-Nasser, S. 1975On non-equilibrium thermodynamics of continuaNemat-Nasser, S. eds. Mechanics today, vol. 2Pergamon PressNew York94158Google Scholar
  300. Nemat-Nasser, S. 1979Decomposition of strain measures and their rates in finite deformation elastoplasticityInt. J. Solids Struct.15155166zbMATHGoogle Scholar
  301. Nemat-Nasser, S. 1982On finite deformation elasto-plasticityInt. J. Solids Struct.18857872zbMATHGoogle Scholar
  302. Nemat-Nasser, S. 1983On finite plastic flow of crystalline solids and geomaterialsJ. Appl. Mech.5011141126zbMATHGoogle Scholar
  303. Nemat-Nasser, S. 1990Certain basic issues in finite-deformation continuum plasticityMeccanica25223229CrossRefzbMATHMathSciNetGoogle Scholar
  304. Nemat-Nasser, S. 1992Phenomenological theories of elastoplasticity and strain localization at high strain ratesJ. Appl. Mech. Rev.45S19S45MathSciNetGoogle Scholar
  305. Nemat-Nasser, S.Asaro, R. J.Hegemier, A. eds. 1984Theoretical foundation for large-scale computations for nonlinear material behaviourMartinus NijhoffDordrechtGoogle Scholar
  306. Nemat-Nasser, S., Hori, M. 1999Micromechanics, overall properties of heterogeneous solidsElsevierNew YorkGoogle Scholar
  307. Nguyen, Q. S. 1973Matériaux elasto-visco-plastiques et élastoplastiques à potentiel généraliséC. R. Acad. Sci. Paris, sér. A277319322Google Scholar
  308. Noll, W. 1955On the continuity of the solid and fluid stateJ. Rat. Mech. Anal.4381zbMATHMathSciNetGoogle Scholar
  309. Noll, W. 1972A new mathematical theory of simple materialsArch. Rat. Mech. Anal.48150CrossRefzbMATHMathSciNetGoogle Scholar
  310. Obata, M., Goto, Y., Matsuura, S. 1990Micromechanical consideration on the theory of elasto-plasticity at finite deformationsInt. J. Engng. Sci.28241252CrossRefGoogle Scholar
  311. Odqvist, F. K. G. 1933Die Verfestigung von flußeisen-ähnlichen KörpernZAMM13360363zbMATHGoogle Scholar
  312. Ogden, R. W. 1984Nonlinear elastic deformationsEllis HarwoodChichesterGoogle Scholar
  313. Oldroyd, J. G. 1950On the formulation of rheological equations of stateProc. Roy. Soc. Lond A200523541MathSciNetGoogle Scholar
  314. Onat, E. T. 1968The notion of state and its implications in thermodynamics of inelastic solidsParkus, H.Sedov, L. I. eds. IUTAM Symp. Irreversible aspects of continuum mechanics and transfer of physical characteristics in moving fluidsSpringerWien New York292314Google Scholar
  315. Onat, E. T. 1970Representation of inelastic mechanical behaviour by means of state variablesBoley, B. A. eds. IUTAM Symp. ThermoinelasticitySpringerBerlin213224Google Scholar
  316. Onat, E. T. 1991Representation of elastic-plastic behaviour in the presence of finite deformations and anisotropyYoung, W. H. eds. Topics in plasticity–anniversary volume in honor of Professor E. H. LeeA. M. PressAnn Arbor4561Google Scholar
  317. Owen, D. R. 1968Thermodynamics of materials with elastic rangeArch. Rat. Mech. Anal.3191112zbMATHGoogle Scholar
  318. Owen, D. R. 1970A mechanical theory of materials with elastic rangeArch. Rat. Mech. Anal.3785110CrossRefzbMATHMathSciNetGoogle Scholar
  319. Owen, D. R. J., Hinton, E. 1980Finite elements in plasticity, theory and practicePineridge PressSwanseaGoogle Scholar
  320. Palgen, L., Drucker, D. C. 1983The structure of stress-strain relations in finite elasto-plasticityInt. J. Solids Struct.19519531Google Scholar
  321. Paulun, J. E., Pecherski, R.B. 1985Study of corotational rates for kinematic hardening in finite deformation plasticityArch. Mech.37661678Google Scholar
  322. Paulun, J. E., Pecherski, R. B. 1987On the application of the plastic spin concept for the description of anisotropic hardening in finite deformation plasticityInt. J. Plasticity3303314CrossRefGoogle Scholar
  323. Perić, D., Owen, D. R. J., Honnor, M. E. 1992A model for finite strain elastoplasticity based on logarithmic strains, computational issuesCompt. Meth. Appl. Mech. Engng.943561Google Scholar
  324. Perzyna, P. 1971Thermodynamic theory of viscoplasticityAdv. Appl. Mech.11313354Google Scholar
  325. del Piero, G. 1975On the elastic-plastic material elementArch. Rat. Mech. Anal.59111129zbMATHMathSciNetGoogle Scholar
  326. Pipkin, A. C., Rivlin, R. S. 1965Mechanics of rate-independent materialsZAMP16313326MathSciNetGoogle Scholar
  327. Prager, W. 1955The theory of plasticity: A survey of recent achievements (James Clayton lecture)Proc. Inst. Mech. Eng. Lond.1694157MathSciNetGoogle Scholar
  328. Prager, W. 1956A new method of analyzing stresses and strains in work-hardening plastic solidsJ. Appl. Mech.23493496zbMATHMathSciNetGoogle Scholar
  329. Prager, W. 1960An elementary discussion of definitions of stress rateQuart. Appl. Math.18403407MathSciNetGoogle Scholar
  330. Prager, W. 1961Introduction to mechanics of continuaGinnBostonGoogle Scholar
  331. Prager, W. 1962On higher rates of stress and deformationJ. Mech. Phys. Solids10133138zbMATHMathSciNetGoogle Scholar
  332. Prager, W., Hodge, P. G. 1951Theory of perfectly plastic solidsWileyNew YorkGoogle Scholar
  333. Prandtl, L.: Spannungsverteilung in plastischen Körpern. In: Proc. 1st Intern. Congr. Appl. Mech. (Biezeno, C. B., Burgers, J. M., eds.), pp. 43–54. Delft: J. Waltmann Jr. 1925.Google Scholar
  334. Rajagopal, K. R., Srinivasa, A. R.: Mechanics of the inelastic behaviour of materials, parts I and II. Int. J. Plasticity 14, 945–967, 969–995 (1998).Google Scholar
  335. Raniecki, B., Bruhns, O. T. 1981Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strainJ. Mech. Phys. Solids29153172MathSciNetGoogle Scholar
  336. Raniecki, B., Nguyen, H. V. 1984Isotropic elasto-plastic solids at finite strain and arbitrary pressureArch. Mech.36687704Google Scholar
  337. Reckling, K.-A. 1967Plastizitästheorie und ihre Anwendung auf FestigkeitsproblemeSpringerBerlinGoogle Scholar
  338. Reed, K. W., Atluri, S. 1985Constitutive modeling and computational implementation for finite strain plasticityInt. J. Plasticity16387CrossRefGoogle Scholar
  339. Reinhardt, W. D., Dubey, R. N. 1995Eulerian strain-rate as a rate of logarithmic strainMech. Res. Commun.22165170CrossRefGoogle Scholar
  340. Reinhardt, W. D., Dubey, R. N. 1996Coordinate-independent representation of spin tensors in continuum mechanicsJ. Elasticity42133144MathSciNetGoogle Scholar
  341. Reuss, A. 1930Berücksichtigung der elastischen Formänderung in der PlastizitätstheorieZAMM10266274zbMATHGoogle Scholar
  342. Rice, J. R. 1970On the structure of stress-strain relations for time-dependent plastic deformation in metalsJ. Appl. Mech.37728737Google Scholar
  343. Rice, J. R. 1971Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticityJ. Mech. Phys. Solids19433455zbMATHGoogle Scholar
  344. Rice, J. R. 1975Continuum mechanics and thermodynamics of plasticity in relation to micro-scale deformation mechanismArgon, A. S. eds. Constitutive equations in plasticityMIT Press Cambridge2179Google Scholar
  345. Richter, H. 1949Verzerrungstensor, Verzerrungsdeviator und Spannungstensor bei endlichen FormänderungenZAMM296575zbMATHGoogle Scholar
  346. Rougée, P. 1991A new Lagrangian intrinsic approach to large deformations in continuous mediaEur. J. Mech. A/Solids101539zbMATHGoogle Scholar
  347. Roy, S., Fossum, A. F., Dexter, R. J. 1992On the use of polar decomposition in the integration of hypoelastic constitutive lawsInt. J. Engng. Sci.30119133MathSciNetGoogle Scholar
  348. Rubin, M. B. 1994Plasticity theory formulated in terms of physically based microstructural variables – Part ITheory. Int. J. Solids Struct.3126152634zbMATHGoogle Scholar
  349. Rubin, M. B. 1994Plasticity theory formulated in terms of physically based microstructural variables – Part II: ExamplesInt. J. Solids Struct.3126352652zbMATHGoogle Scholar
  350. Rubin, M. B. 1996On the treatment of elastic deformation in finite elastic-viscoplastic theoryInt. J. Plasticity12951965CrossRefzbMATHGoogle Scholar
  351. Rubin, M. B. 2001Physical reasons for abandoning plastic deformation measures in plasticity and viscoplasticity theoryArch. Mech.53519539zbMATHGoogle Scholar
  352. Rudnicki, J. W., Rice, J. R. 1975Conditions for the localization of deformation in pressure-sensitive dilatant materialsJ. Mech. Phys. Solids23371394Google Scholar
  353. Saint-Venant, M. 1870Sur l'établissement des équations des mouvements intérieurs opérés dans les corps solides au delà des limites où l'élasticité pourrait les ramener à leur premier étatC. R. Acad. Sci. Paris70473480Google Scholar
  354. Sansour, C. 2001On the dual variable of the logarithmic strain tensor, the dual variable of the Cauchy stress tensor, and related issuesInt. J. Solids Struct.3892219232zbMATHMathSciNetGoogle Scholar
  355. Sansour, C., Bednarczyk, H. 1993A study on rate-type constitutive equations and the existence of a free energy functionActa Mech.100205221CrossRefMathSciNetGoogle Scholar
  356. Sawczuk, A. eds. 1973Foundations of plasticityNoordhoffLeydenGoogle Scholar
  357. Sawczuk, A. eds. 1974Problems of plasticityNoordhoffLeydenGoogle Scholar
  358. Sawczuk, A.Bianchi, G. eds. 1985Plasticity today, modelling, methods and applicationsElsevierLondonGoogle Scholar
  359. Schieck, B., Stumpf, H. 1995The appropriate corotational rate, exact formula for the plastic spin and constitutive model for finite elastoplasticityInt. J. Solids Struct.3236433667MathSciNetGoogle Scholar
  360. Schmidt, R. 1932Über den Zusammenhang von Spannungen und Formänderungen im VerfestigungsgebietIng.-Arch3215235CrossRefzbMATHGoogle Scholar
  361. von Schmid, E.: Neuere Untersuchungen an Metallkristallen. In: Proc. 1st. Intern. Congr. Appl. Mech. (Biezeno, C. B., Burgers, J. M., eds.), pp. 342–353. Delft: J. Waltmann Jr. 1925.Google Scholar
  362. Schütte, H., Bruhns, O. T. 2002On a geometrically nonlinear damage model based on a multiplicative decomposition of the deformation gradient and the propagation of microcracksJ. Mech. Phys. Solids50827853MathSciNetGoogle Scholar
  363. Sedov, L. I. 1960Different definitions of the rates of change of tensorsPrikl. Mat. Mekh.14579586MathSciNetGoogle Scholar
  364. Sedov, L. I. 1966Foundations of the nonlinear mechanics of continuaPergamon PressOxfordGoogle Scholar
  365. Sidoroff, F. 1973The geometrical concept of intermediate configuration and elastic-plastic finite strainArch. Mech.25299308zbMATHMathSciNetGoogle Scholar
  366. Sidoroff, F., Dogui, A. 2001Some issues about anisotropic elastic-plastic models at finite strainInt. J. Solids Struct.3895699578Google Scholar
  367. Šilhavý, M. 1977On transformation laws for plastic deformations of materials with elastic rangeArch. Rat. Mech. Anal.63169182Google Scholar
  368. Šilhavý, M. 1997Mechanics and thermodynamics of continuous mediaSpringerBerlinGoogle Scholar
  369. Šilhavý, M., Kratochvíl, J. 1977A theory of inelastic behaviour of materials. Part I. Ideal inelastic materialsArch. Rat. Mech. Anal.6597Google Scholar
  370. Simó, J. C. 1988A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition, Part I. Continuum formulationComput. Meth. Appl. Mech. Engng.66199219zbMATHGoogle Scholar
  371. Simó, J. C., Hughes, T. J. R. 1998Computational inelasticitySpringerNew YorkGoogle Scholar
  372. Simó, J. C., Meschke, G. 1993A new class of algorithms for classical plasticity extended to finite strain. Application to geomaterialsComput. Mech.11253278MathSciNetGoogle Scholar
  373. Simó, J. C., Miehe, C. 1992Associative coupled thermoplasticity at finite strains formulation, numerical analysis and implementationComput. Meth. Appl. Mech. Engng.9841104Google Scholar
  374. Simó, J. C., Ortiz, M. 1985A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equationsComput. Meth. Appl. Mech. Engng.49221245Google Scholar
  375. Simó, J. C., Pister, K. S. 1984Remarks on rate constitutive equations for finite deformation problems Computational implicationsComput. Meth. Appl. Mech. Engng.46201215Google Scholar
  376. Sowerby, R., Chu, E. 1984Rotations, stress rates and strain measures in homogeneous deformation processesInt. J. Solids Struct.2010371048Google Scholar
  377. Srinivasa, A. R. 1997On the nature of the response functions in rate-independent plasticityInt. J. Non-Linear Mech.32103119zbMATHMathSciNetGoogle Scholar
  378. Steinmann, P., Miehe, C., Stein, E. 1994Comparison of different finite deformation inelastic damage models within multiplicative elastoplasticity for ductile materialsComput. Mech.13458474CrossRefGoogle Scholar
  379. Stumpf, H., Badur, J. 1990On missing links of rate-independent elasto-plasticity at finite strainsMech. Res. Commun.17353364CrossRefGoogle Scholar
  380. Stumpf, H., Hoppe, U. 1997The application of tensor algebra on manifolds to nonlinear continuum mechanicsZAMM77327339MathSciNetGoogle Scholar
  381. Stumpf, H., Schieck, B. 1994Theory and analysis of shells undergoing finite elastic-plastic strains and rotationsActa Mech.106121CrossRefMathSciNetGoogle Scholar
  382. Svendsen, B. 1998A thermodynamic formulation of finite-deformation elastoplasticity with hardening based on the concept of material isomorphismInt. J. Plasticity14473488CrossRefzbMATHGoogle Scholar
  383. Svendsen, B. 2001On the modelling of anisotropic elastic and inelastic material behaviour at large deformationInt. J. Solids Struct.3895799599zbMATHGoogle Scholar
  384. Svendsen, B., Bertram, A. 1999On frame-indifference and form-invariance in constitutive theoryActa Mech.132195207CrossRefMathSciNetGoogle Scholar
  385. Szabó, L., Balla, M. 1989Comparison of some stress ratesInt. J. Solids Struct.25279297Google Scholar
  386. Tanner, R. I., Tanner, E. 2003Heinrich Hencky, a rheological pioneerRheol. Acta4293101CrossRefGoogle Scholar
  387. Taylor, G. I., Quinney, H. 1931The plastic distortion of metalsPhil. Trans. Roy. Soc. A230323362Google Scholar
  388. Thermann, K. 1984Foundations of large deformationsLehmann, T. eds. The constitutive law in thermoplasticity CISM Courses and Lectures, vol. 281SpringerWien323351Google Scholar
  389. Tokuoka, T. 1971Yield conditions and flow rules derived from hypo-elasticityArch. Rat. Mech. Anal.42239252CrossRefzbMATHMathSciNetGoogle Scholar
  390. Tresca, H. E. 1864Mémoire sur l'écoulement des corps solides soumis à de fortes pressionsC. R. Acad. Sci. Paris59754758Google Scholar
  391. Tresca, H. E.: On the flow of solids, with practical applications in forgings. In: Proc. Inst. Mech. Eng. Lond, pp. 114–150 (1867).Google Scholar
  392. Tresca, H. E.: On further applications of flow of solids. In: Proc. Inst. Mech. Eng. Lond, pp. 301–345 (1878).Google Scholar
  393. Truesdell, C. 1952The mechanical foundations of elasticity and fluid dynamicsJ. Rat. Mech. Anal.1125300zbMATHMathSciNetGoogle Scholar
  394. Truesdell, C. 1955Hypo-elasticityJ. Rat. Mech. Anal.483133zbMATHMathSciNetGoogle Scholar
  395. Truesdell, C. 1955The simplest rate theory of pure elasticityComm. Pure Appl. Math.8123132zbMATHMathSciNetGoogle Scholar
  396. Truesdell, C. 1956Hypo-elastic shearJ. Appl. Phys.27441447CrossRefMathSciNetGoogle Scholar
  397. Truesdell, C., Noll, W. 1965The nonlinear field theories of mechanics.Flügge, S. eds. Handbuch der Physik, vol. III/3SpringerBerlinGoogle Scholar
  398. Truesdell, C., Toupin, R. A. 1960The classical field theoriesFlügge, S. eds. Handbuch der Physik vol. III/1SpringerBerlin226793Google Scholar
  399. Truesdell, C. A. eds. 1984Rational thermodynamics2SpringerNew YorkGoogle Scholar
  400. Tsakmakis, C. 1997Remarks on Il'iushin's postulateArch. Mech.49677695zbMATHMathSciNetGoogle Scholar
  401. Tsakmakis, C. 2004Description of plastic anisotropy effects at large deformations-part I: Restrictions imposed by the second law and the postulate of Il'iushinInt. J. Plasticity20167198CrossRefzbMATHGoogle Scholar
  402. Tvergaard, V. 1978Effect of kinematic hardening on localized necking in biaxially stretched sheetsInt. J. Mech. Sci20651658zbMATHGoogle Scholar
  403. Unksov, E. P. 1961An engineering theory of plasticityButterworthsLondonGoogle Scholar
  404. Valanis, K. C. 1966Thermodynamics of large viscoelastic deformationsJ. Math. Phys.45197212zbMATHGoogle Scholar
  405. Valanis, K. C.: A theory of viscoplasticity without a yield surface, parts I and II. Arch. Mech. 23, 517–533, 535–551 (1971).Google Scholar
  406. Valanis, K. C. 1975On the foundations of the endochronic theory of viscoplasticityArch. Mech.27857868zbMATHMathSciNetGoogle Scholar
  407. Valanis, K. C. 1980Fundamental consequences of a new intrinsic time measure. Plasticity as a limit of the endochronic theoryArch. Mech.32171191zbMATHMathSciNetGoogle Scholar
  408. Valanis, K. C. 1984Continuum foundations of endochronic plasticityJ. Engng. Mater. Techn.106367Google Scholar
  409. Watanabe, O., Atluri, S. N. 1986Internal time, general internal variable, and multi-yield-surface theories of plasticity and creep: a unification of conceptsInt. J. Plasticity23757Google Scholar
  410. Weber, G., Anand, L. 1990Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solidsComput. Meth. Appl. Mech. Engng.79173202CrossRefGoogle Scholar
  411. Willis, J. R. 1969Some constitutive equations applicable to problems of large dynamic plastic deformationJ. Mech. Phys. Solids17359369zbMATHGoogle Scholar
  412. Wriggers, P. 2001Nichtlineare Finite-Element-MethodenSpringerBerlinGoogle Scholar
  413. Xia, Z., Ellyin, F. 1993A stress rate measure for finite elastic plastic deformationActa Mech.98114CrossRefGoogle Scholar
  414. Xiao, H. 1995Unified explicit basis-free expressions for time rate and conjugate stress of an arbitrary Hill's strainInt. J. Solids Struct.3233273340zbMATHGoogle Scholar
  415. Xiao, H. 1996On anisotropic scalar functions of a single symmetric tensorProc. Roy. Soc. Lond A45215451561zbMATHGoogle Scholar
  416. Xiao, H. 1998On anisotropic invariants of a symmetric tensor: Crystal classes, quasi-crystal classes and othersProc. Roy. Soc. Lond A45412171240zbMATHGoogle Scholar
  417. Xiao, H., Bruhns, O. T., Meyers, A. 1997Hypo-elasticity model based upon the logarithmic stress rateJ. Elasticity475168CrossRefMathSciNetGoogle Scholar
  418. Xiao, H., Bruhns, O. T., Meyers, A. 1997Logarithmic strain, logarithmic spin and logarithmic rateActa Mech.12489105CrossRefMathSciNetGoogle Scholar
  419. Xiao, H., Bruhns, O. T., Meyers, A. 1997A new aspect in the kinematics of large deformationsGupta, N. K. eds. Plasticity and impact mechanics New Age International Ltd New Delhi100109Google Scholar
  420. Xiao, H., Bruhns, O. T., Meyers, A. 1998On objective corotational rates and their defining spin tensorsInt. J. Solids Struct.3540014014MathSciNetGoogle Scholar
  421. Xiao, H., Bruhns, O. T., Meyers, A. 1998Strain rates and material spinsJ. Elasticity52141CrossRefMathSciNetGoogle Scholar
  422. Xiao, H., Bruhns, O. T., Meyers, A. 1999Existence and uniqueness of the integrable-exactly hypoelastic equation τ°* =λ (tr D )I +2μ D and its significance to finite inelasticityActa Mech.1383150CrossRefGoogle Scholar
  423. Xiao, H., Bruhns, O. T., Meyers, A. 1999A natural generalization of hypoelasticity and Eulerian rate type formulation of hyperelasticityJ. Elasticity565993CrossRefMathSciNetGoogle Scholar
  424. Xiao, H., Bruhns, O. T., Meyers, A. 2000 The choice of objective rates in finite elastoplasticity General results on the uniqueness of the logarithmic rateProc. Roy. Soc. Lond A45618651882MathSciNetGoogle Scholar
  425. Xiao, H., Bruhns, O. T., Meyers, A. 2000A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradientInt. J. Plasticity16143177CrossRefGoogle Scholar
  426. Xiao, H., Bruhns, O. T., Meyers, A. 2001Large strain responses of elastic-perfect plasticity and kinematic hardening plasticity with the logarithmic rate: Swift effect in torsionInt. J. Plasticity17211235CrossRefGoogle Scholar
  427. Xiao, H., Bruhns, O.T., Meyers, A. 2002Basic issues concerning finite strain measures and isotropic stress-deformation relationsJ. Elasticity67123CrossRefMathSciNetGoogle Scholar
  428. Xiao, H., Bruhns, O. T., Meyers, A. 2003A closed-form solution to finite bending of a compressible elastic-perfectly plastic rectangular blockDefence Sci. J.532539Google Scholar
  429. Xiao, H., Bruhns, O. T., Meyers, A. 2003On postulates of plasticity in classical elastoplasticityActa Mech.1662742CrossRefGoogle Scholar
  430. Xiao, H., Bruhns, O. T., Meyers, A. 2004Explicit dual stress-strain and strain-stress relations of incompressible isotropic hyperelastic solids via deviatoric Hencky strain and Cauchy stressActa Mech.1682133CrossRefGoogle Scholar
  431. Xiao, H., Chen, L. S. 2002Hencky's elasticity model and linear stress-strain relations in isotropic finite hyperelasticityActa Mech.1575160CrossRefGoogle Scholar
  432. Xiao, H., Chen, L. S. 2003Hencky's logarithmic strain and dual stress-strain and strain-stress relations in isotropic finite hyperelasticityInt. J. Solids Struct.4014551463Google Scholar
  433. Yang, W., Cheng, L., Hwang, K. C. 1992Objective corotational rates and shear oscillationInt. J. Plasticity8643656CrossRefGoogle Scholar
  434. Zaremba, S.: Sur une forme perfectionée de la théorie de la relaxation. Bull. Int. Acad. Sci. Cracovie, pp. 594–614 (1903).Google Scholar
  435. Zbib, H. M., Aifantis, E. C.: On the concept of relative and plastic spins and its implications to large deformation theories I-II. Acta Mech. 75, 15–33, 35–56 (1988).Google Scholar
  436. Ziegler, H. 1958An attempt to generalize Onsager's principle, and its significance for rheological problemsZAMP9748763MathSciNetGoogle Scholar
  437. Ziegler, H. 1959A modification of Prager's hardening ruleQuart. Appl. Math.175565zbMATHMathSciNetGoogle Scholar
  438. Ziegler, H.: Some extremum principles in irreversible thermodynamics with application to continuum mechanics. In: Progress in solid mechanics, vol. 4 (Sneddon, I. N., Hill, R., eds.). Amsterdam: North-Holland 1963.Google Scholar
  439. Ziegler, H.: An introduction to thermomechanics. Amsterdam: North-Holland 1977.Google Scholar
  440. Ziegler, H., Wehrli, C. 1987The derivation of constitutive equations from the free energy and the dissipation functionAdv. Appl. Mech.25183238MathSciNetGoogle Scholar
  441. Zyczkowski, M. 1981Combined loadings in the theory of pasticityPWN-Polish Scientific PublWarsawGoogle Scholar

Copyright information

© Springer-Verlag Wien 2006

Authors and Affiliations

  1. 1.Ruhr-Universität BochumBochumGermany

Personalised recommendations