Skip to main content
SpringerLink
Log in

Constitutive Modelling of Dissipative Solids for Localization and Fracture

  • Chapter
Localization and Fracture Phenomena in Inelastic Solids

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 386))

Abstract

The main objective of the lectures is to survey some recent developments in the constitutive modelling of inelastic single and polycrystalline solids which can be used for the description of plastic deformation localization and fracture phenomena. Physical foundations and experimental motivations are given. Particular attention is focused on dynamic fracture (adiabatic shear band localized, spall, ductile and brittle fracture phenomena). The physical and experimental foundations for the microdamage processes are presented. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history dependent, nonlinear process.

The description of the kinematics of finite elasto-viscoplastic deformations is based on notions of the Riemannian space on manifolds and tangent space. A multiplicative decomposition of the deformation gradient is adopted and the Lie derivative is used to define all objective rates for introduced vectors and tensors.

A general constitutive model is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A notion of covariance is understood in the sense of invariance under arbitrary spatial diffeomorphism. The thermodynamic theory of elasto-viscoplasticity of inelastic single crystals and damaged polycrystalline solids is developed. The relaxation time is used as a regularization parameter. By assuming that the relaxation time is equal to zero the thermo-elastic-plastic (rate independent) response for both single crystals and polycrystalline solids is accomplished.

An adiabatic inelastic flow process is analysed and the well-posedness of the Cauchy problem is investigated. The analytical methods for the investigation of plastic deformation localization phenomena are developed. The formation of the adiabatic shear band region is investigated. Criteria for adiabatic shear band localization of plastic deformation are obtained by assuming that some of eigenvalue of the instantaneous adiabatic acoustic tensor for rate independent response is equal to zero.

Numerical solution of the initial-boundary value problem (evolution problem) is discussed. Particular attention is focused on the well-posedness of the evolution problem. Convergence, consistency and stability of the discretised evolution problem are examined. The Lax equivalence theorem is formulated and the conditions of its validity are investigated. Utilizing the finite element method for regularized elasto-viscoplastic model the numerical investigation of localization and fracture phenomena is presented. The results obtained are compared with available experimental observations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abraham, R. and Marsden, J.E.: Foundations of Mechanics, Second Edition, Addison-Wesley, Reading Mass., 1978.

    MATH  Google Scholar 

  2. Abraham, R., Marsden, J.E. and Ratiu, T.: Manifolds, Tensor Analysis and Applications, Springer, Berlin 1988.

    MATH  Google Scholar 

  3. Agah-Tehrani, A., Lee, E.H., Mallett, R.L. and Onat, E.H.: The theory of elastic-plastic deformation at finite strain with induced anisotropy modelled as combined isotropic-kinematic hardening, J. Mech. Phys. Solids, 35 (1987), 519–539.

    MATH  Google Scholar 

  4. Anand, L. and Spitzig, W.A.: Initiation of localized shear band in plane strain, J. Mech. Phys. Solids, 28 (1980), 113–128.

    Google Scholar 

  5. Asaro, R.J.: Crystal plasticity, J. Appl. Mech., 50 (1983), 921–934.

    MATH  Google Scholar 

  6. Asaro, R.J.: Micromechanics of crystals and polycrystals, Adv. Appl. Mech., 23 (1983), 1–115.

    Google Scholar 

  7. Asaro, R.J. and Needleman, A.: Texture development and strain hardening in rate dependent polycrystals, Acta Metall., 33 (1985), 923–953.

    Google Scholar 

  8. Asaro, R.J. and Rice, J.R.: Strain localization in ductile single crystals, J. Mech. Phys. Solids, 25 (1977), 309–338.

    MATH  Google Scholar 

  9. Asay, J.R. and Kerley, G.I.: The response of materials to dynamic loading, Int. J. Impact Engng., 5 (1987), 69–99.

    Google Scholar 

  10. Ashby, M.F. and Frost, H.J.: in: Constitutive Equation in Plasticity, (Ed. A.S. Argon ), MIT Press, Cambridge, Mass., 1975, 117–147.

    Google Scholar 

  11. Ayres, R.A.: Thermal gradients, strain rate and ductility in sheet steel tensile specimen, Metall. Trans., 16A (1985), 37–43.

    Google Scholar 

  12. Balke, H. and Estrin, Y.: Micromechanical modelling of shear banding in single crystals, Int. J. Plast., 10 (1994), 133–147.

    MATH  Google Scholar 

  13. Barbee, T.W., Seaman, L., Crewdson, R. and Curran, D.: Dynamic fracture criteria for ductile and brittle metals, J. Mater., 7 (1972), 393–401.

    Google Scholar 

  14. Basinski, S.J. and Basinski, Z.S.: Plastic deformation and work hardening, in: Dislocations in Solids, Vol.4 Dislocations in Metallurgy, (Ed. F.R.N. Nabarro ), Nort-Holland, Amsterdam 1979, 261–362.

    Google Scholar 

  15. Bassani, J.L.: Plastic flow of crystals, Adv. Appl. Mech., 30 (1994), 191–258.

    Google Scholar 

  16. Batra, R.C.: Effect of material parameters on the initiation and growth of adiabatic shear bands, Int. J. Solids Structures, 23 (1987), 1435–1446.

    Google Scholar 

  17. Batra, R.C. and Ko, K.I.: Analysis of shear bands in dynamic axisymmetric compression of a thermoviscoplastic cylinder, Int. J. Engr. Sci., 31 (1993), 529–547.

    Google Scholar 

  18. Batra, R.C. and Zhang, X.: On the propagation of a shear band in a steel tube, J. Engng. Materials and Technology, 116 (1994), 155–161.

    Google Scholar 

  19. Becker, R., Needleman, A., Richmond, O. and Tvergaard, V.: Void growth and failure in notched bars, J. Mech. Phys. Solids, 36 (1988), 317–351.

    Google Scholar 

  20. Bingham, E.C.: Fluidity and Plasticity, McGraw Hill, New York 1922.

    Google Scholar 

  21. Bluhm, J.I. and Morrissey, R.J.: Fracture in a tension specimen, in: Proc. First Int. Conf. on Fracture, Sendai, (Eds. T. Yokoburi et al.), Japan, Sendai 1965, 1739–1780.

    Google Scholar 

  22. Bridgeman, P.W.: Studies in Large Plastic Flow and Fracture, McGraw Hill, New York 1952.

    Google Scholar 

  23. Campbell, J.D.: Dynamic plasticity macroscopic and microscopic aspects, Material Sci. Engng., 12 (1973), 3–12.

    Google Scholar 

  24. Campbell, J.D. and Ferguson, W.G.: The temperature and strain-rate dependence of the shear strength of mild steel, Phil. Mag., 81 (1970), 63–82.

    Google Scholar 

  25. Carroll, M.M. and Holt, A.C.: Static and dynamic pore-collapse relations for ductile solids, J. Appl. Phys., 43 (1972), 1626–1636.

    Google Scholar 

  26. Carroll, M.M., Kim, K.T. and Nesterenko, V.F.: The effect of temperature on viscoplastic pore collapse, J. Appl. Phys., 59 (1986), 1962–1967.

    Google Scholar 

  27. Chakrabarti, A.K. and Spretnak, J.W.: Instability of plastic flow in the direction of pure shear, Metallurgical Transactions, 6A (1975), 733–747.

    Google Scholar 

  28. Chang, Y.W. and Asaro, R.J.: Lattice rotations and shearing in crystals, Arch. Mech., 32 (1980), 369–388.

    Google Scholar 

  29. Chang, Y.W. and Asaro, R.J.: An experimental study of shear localization in aluminum-copper single crystals, Acta Metall., 29 (1981), 241–257.

    Google Scholar 

  30. Chengwei, S., Shiming, Z., Yanping, W. and Cangli, L.: Dynamic fracture in metals at high strain rate, in: High-Pressure Shock Compression of Solids, II. Dynamic Fracture and Fragmentation, (Eds. L. Davison, D.E. Grady and M. Shahinpoor ), Springer-Verlag, New York 1996, 71–89.

    Google Scholar 

  31. Cho, K., Chi, Y.C. and Duffy, J.: Microscopic observations of adiabatic shear bands in three different steels, Brown University Report, 1989.

    Google Scholar 

  32. Coleman, B.D. and Gurtin, M.E.: Thermodynamics with internal state variables, J. Chem. Phys., 47 (1967), 597–613.

    Google Scholar 

  33. Coleman, B.D. and Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13 (1963), 167–178.

    MathSciNet  MATH  Google Scholar 

  34. Conrad, H.: Thermally activated deformation of metals, J. Metals, 16 (1964), 582–588.

    Google Scholar 

  35. Cox, T.B. and Low, J.R.: An investigation of the plastic fracture of AISI 4340 and Nickel-200 grade maraging steels, Met. Trans., 5 (1974), 1457–1470.

    Google Scholar 

  36. Curran, D.R., Seaman, L. and Shockey, D.A.: Dynamic failure in solids, Physics Today, January (1977), 46–55.

    Google Scholar 

  37. Curran, D.R., Seaman, L. and Shockey, D.A.: Linking dynamic fracture to microstructural processes, in: Shock Waves and High-Strain Rate Phenomena in Metals: Concepts and Applications, (Eds. M.A. Meyers and L.E. Murr ), Plenum Press, New York 1981, 129–167.

    Google Scholar 

  38. Curran, D.R., Seaman, L. and Shockey, D.A.: Dynamic failure of solids, Physics Reports, 147 (1987), 253–388.

    Google Scholar 

  39. Dafalias, Y.F.: Corotational rates for kinematic hardening at large plastic deformations, J. Appl. Mech., 50 (1983), 561–565.

    MATH  Google Scholar 

  40. Dafalias, Y.F.: The plastic spin, J. Appl. Mech., 52 (1985), 865–871.

    MathSciNet  MATH  Google Scholar 

  41. Dafalias, Y.F.: Issues on the constitutive formulation at large elastoplastic deformations, Part 1: Kinematics, Acta Mechanica, 69 (1987), 119.

    MATH  Google Scholar 

  42. Dafalias, Y.F.: Issues on the constitutive formulation at large elastoplastic deformations, Part 2: Kinetics, Acta Mechanica, 73 (1988), 121.

    Google Scholar 

  43. Dautray, R. and Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 6. Evolution Problems II, Springer, Berlin 1993.

    Google Scholar 

  44. Day, W.A. and Silhavy, M.: Efficiency and the existence of entropy in classical thermodynamics, Arch. Rational Mech. Anal., 64 (1977), 205–219.

    MATH  Google Scholar 

  45. Dowling, A.R., Harding, J. and Campbell, J.D.: The dynamic punching of metals, J. Inst. of Metals, 98 (1970), 215–224.

    Google Scholar 

  46. Duszek, M.K. and Perzyna, P.: Plasticity of damaged solids and shear band localization, Ing. Arch., 58 (1988a), 330–392.

    Google Scholar 

  47. Duszek, M.K. and Perzyna, P.: Influence of the kinematic hardening on the plastic flow localization in damaged solids, Arch. Mech., 40 (1988b), 595–609.

    MATH  Google Scholar 

  48. Duszek, M.K. and Perzyna, P.: On combined isotropic and kinematic hardening effects in plastic flow processes, Int. J. Plasticity, 7 (1991a), 351–363.

    MATH  Google Scholar 

  49. Duszek, M.K. and Perzyna, P.: The localization of plastic deformation in thermoplastic solids, Int. J. Solids Structures, 27 (1991b), 1419–1443.

    MATH  Google Scholar 

  50. Duszek—Perzyna, M.K., Korbel, K. and Perzyna, P.: Adiabatic shear band localization in single crystals under dynamic loading processes, Arch. Mechanics, 49 (1997), (in print).

    Google Scholar 

  51. Duszek—Perzyna, M.K. and Perzyna, P.: Adiabatic shear band localization in elastic—plastic single crystals, Int. J. Solids Structures, 30 (1993), 61–89.

    Google Scholar 

  52. Duszek—Perzyna, M.K. and Perzyna, P.: Analysis of the influence of different effects on criteria for adiabatic shear band localization in inelastic solids, in: Material Instabilities: Theory and Applications, ASME Congress, Chicago, 9–11 November 1994 (Eds. R.C. Batra and H.M. Zbib), AMD—Vol. 183/MD—Vol. 50, ASME, New York 1994, 59–85.

    Google Scholar 

  53. Duszek—Perzyna, M.K. and Perzyna, P.: Acceleration waves in analysis of adiabatic shear band localization, IUTAM Symposium on Nonlinear Waves in Solids, August 15–20, 1993, Victoria, Canada; (Eds. J.L. Wegner and F.R. Norwood ), ASME 1995, 128–135.

    Google Scholar 

  54. Duszek-Perzyna, M.K. and Perzyna, P.: Adiabatic shear band localization of inelastic single crystals in symmetric double slip process, Archive of Appled Mechanics, 66 (1996), 369–384.

    MATH  Google Scholar 

  55. Duszek-Perzyna, M.K. and Perzyna, P.: Analysis of anisotropy and plastic spin effects on localization phenomena, Arch. Appl. Mechanics, (1997) (in print).

    Google Scholar 

  56. Duszek-Perzyna, M.K., Perzyna, P. and Stein, E.: Adiabatic shear band localization in elastic-plastic damaged solids, Int. J. Plasticity, 8 (1992), 361–384.

    Google Scholar 

  57. Eftis, J.: Constitutive modelling of spall fracture, in: High-Pressure Shock Compression of Solids, II. Dynamic Fracture and Fragmentation, (Eds. L. Davison, D.E. Grady and M. Shahinpoor ), Springer-Verlag, New York 1996, 399–451.

    Google Scholar 

  58. Eftis, J. and Nemes, J.A.: Constitutive modelling of spall fracture, Arch. Mech., 43 (1991a), 399–435.

    Google Scholar 

  59. Eftis, J. and Nemes, J.A.: Evolution equation for the void volume growth rate in a viscoplastic-damage constitutive model, Int. J. Plasticity, 7 (1991b), 275–293.

    MATH  Google Scholar 

  60. Eftis, J. and Nemes, J.A.: Modelling of impact-induced spall fracture and post spall behaviour of a circular plate, Int. J. Fracture, 53 (1992), 301–324.

    Google Scholar 

  61. Eftis, J., Nemes, J.A. and Randles, P.W.: Viscoplastic analysis of plate-impact spallation, Int. J. Plasticity, 7 (1991), 15–39.

    MATH  Google Scholar 

  62. Eisenberg, M.A. and Yew, C.F.: The anisotropic deformation of yield surfaces, J. Eng. Mat. Tech., 106 (1984), 355–360.

    Google Scholar 

  63. Estrin, Y. and Kubin, L.P.: Load strain hardening and nonuniformity of plastic deformation, Acta Metall., 34 (1986), 2455–2464.

    Google Scholar 

  64. Evans, A.G. and Rawlings, R.D.: The thermally activated deformation of crystalline materials, Phys. Stat. Sol., 34 (1969), 9–31.

    Google Scholar 

  65. Fisher, J.R.: Viod Nucleation in Spheroidized Steels During Tensile Deformation, Ph.D. Dissertation, Brown University 1980.

    Google Scholar 

  66. Flanagan, D.P. and Belytschko, T.: A uniform strain hexahedron and and quadrilateral with orthogonal hourglass control, Int. J. Numerical Methods in Engr., 17 (1981), 679–706.

    MATH  Google Scholar 

  67. Flanagan, D.P. and Taylor, L.M.: An accurate numerical algorithm for stress integration with finite rotations, Computer Methods in Appl. and Engng., 62 (1987), 305–320.

    MATH  Google Scholar 

  68. Follansbee, P.S.: Metallurgical Applications of Shock–Wave and High-StrainRate Phenomena, (Eds. L.E. Murr, K.P. Staudhammer, M.A. Meyeres MA ), Marcel Dekker, New York 1986, 451–480.

    Google Scholar 

  69. Follansbee, P.S. and Kocks, U.F.: A constitutive description of the deformation of copper based on the use of the mechanical treshold stress as an internal state variable, Acta Met., 36 (1988), 81–93.

    Google Scholar 

  70. Fressengeas, C. and Molinari, A.: Inetria and thermal effects on the localization of plastic flow, Acta Metall., 33 (1985), 387–396.

    Google Scholar 

  71. Gilath, I.: Laser-induced spallation and dynamic fracture at ultra high strain rate, in: High-Pressure Shock Compression of Solids, II. Dynamic Fracture and Fragmentation, (Eds. L. Davison, D.E. Grady and M. Shahinpoor ), Springer-Verlag, New York 1996, 90–120.

    Google Scholar 

  72. Gilbert, J.E. and Knops, R.J.: Stability of general systems, Arch. Rat. Mech. Anal., 25 (1967), 271–284.

    MathSciNet  MATH  Google Scholar 

  73. Giovanola, J.H.: Adiabatic shear banding under pure shear loading, Mechanics of Materials, 7 (1988), 59–87.

    Google Scholar 

  74. Glansdorff, P. and Prigogine, I.: Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley-Interscience, London 1977.

    Google Scholar 

  75. Gorman, J.A., Wood, D.S. and Vreeland, T.: Mobility of dislocation in aluminium, J. Appl. Phys., 40 (1969), 833–841.

    Google Scholar 

  76. Grebe, H.A., Pak, H.R. and Meyer, M.A.: Adiabatic shear band localization in titanium and Ti-6PctA1–4PctV alloy, Met. Trans., 16A (1985), 761–775.

    Google Scholar 

  77. Green, A.E. and Naghdi, P.M.: A general theory of an elastic-plastic continuum, Arch. Rat. Mech. Anal., 18 (1965), 251–281.

    MathSciNet  MATH  Google Scholar 

  78. Green, A.E. and Naghdi, P.M.: Some remarks on elastic-plastic deformation at finite strain, Int. J. Engn. Sci., 9 (1971), 1219–1229.

    MATH  Google Scholar 

  79. Green, A.E. and Naghdi, P.M.: On thermodynamics and the nature of the second law, Proc. R. Soc. Lond., A357 (1977), 253–270.

    MathSciNet  Google Scholar 

  80. Green, A.E. and Naghdi, P.M.: On thermodynamics and the nature of the second law for mixtures of interacting continua, Quart. J. Mech. Appl. Maths., 31 (1978), 265–293.

    MathSciNet  Google Scholar 

  81. Gurson, A.L.: Plastic flow and fracture behaviour of ductile materials incorporating void nucleation, growth, and interaction, PhD Thesis, Brown University, 1975.

    Google Scholar 

  82. Gurson, A.L.: Continuum theory of ductile rupture by void nucleation and growth–Part I–Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technology, 99 (1977), 2–15.

    Google Scholar 

  83. Gurtin, M.E.: Thermodynamic and stability, Arch. Rational Mech. Anal., 59 (1975), 63–96.

    MathSciNet  MATH  Google Scholar 

  84. Hadamard, J.: Lecons sur la propagation des ondes et les equations de l’hydrodynamique, Chap. 6, Paris 1903.

    Google Scholar 

  85. Haken, H.: Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems, Reviews of Modern Physics, 47 (1975), 67–121.

    MathSciNet  Google Scholar 

  86. Haken, H.: Advanced Synergetics, Springer, Berlin 1987.

    Google Scholar 

  87. Haken, H.: Information and Self-Organization, Springer, Berlin 1988.

    MATH  Google Scholar 

  88. Hale, K.J.: Dynamic systems and stability, J. Math. Anal. Appl., 26 (1969), 39–59.

    MathSciNet  MATH  Google Scholar 

  89. Hartley, K.A., Duffy, J. and Hawley, R.H.: Measurement of the temperature profile during shear band formulation in steels deforming at high strain rates, J. Mech. Phys. Solids, 35 (1987), 283–301.

    Google Scholar 

  90. Hauser, F.E., Simmons, J.A. and Dorn, J.E.: Strain rate effects in plastic wave propagation, in: Response of Metals to High Velocity Deformation, Wiley ( Interscience ), New York 1961, 93–114.

    Google Scholar 

  91. Hill, R.: Acceleration wave in solids, J. Mech. Phys. Solids, 10 (1962), 1–16.

    MathSciNet  MATH  Google Scholar 

  92. Hill, R.: The essential structure of constitutive laws for metal composities and polycrystals, J. Mech. Phys. Solids, 15 (1967), 255–262.

    Google Scholar 

  93. Hill, R.: The Mathematical Theory of Plasticity, last ed., Oxford University Press, Oxford 1983.

    Google Scholar 

  94. Hill, R.: Aspects of invariance in solids mechanics, Adv. Appl. Mech., 18 (1987), 1–75.

    Google Scholar 

  95. Hill, R. and Rice, J.R.: Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20 (1972) 401–413.

    MATH  Google Scholar 

  96. Hill, R. and Rice, J.R.: Elastic potentials and the structure of inelastic constitutive laws, SIAM J. Appl. Math., 25 (1973), 448–461.

    MathSciNet  MATH  Google Scholar 

  97. Hohenemser, K. and Prager, W.: Uber die Ansatze der Mechanik isotroper Kontinua, ZAMM, 12 (1932), 216–226.

    Google Scholar 

  98. Hughes, T.J.R., Kato, T. and Marsden, J.E.: Well-posed quasilinear second order hyperbolic system with application to nonlinear elastodynamics and general relativity, Arch. Rat. Mech. Anal., 63 (1977), 273–294.

    MathSciNet  MATH  Google Scholar 

  99. Hughes, T.J.R. and Winget, J.: Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, Int. J. Numerical Methods in Engng., 15 (1989), 1862–1967.

    MathSciNet  Google Scholar 

  100. Hutchinson, J.W.: Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. Lond., A348 (1976), 101–127.

    MATH  Google Scholar 

  101. Ikegami, K.: Experimental plasticity on the anisotropy of metals, in: Proc. Euromech Colloquium 115, Mechanical Behaviour of Anisotropic Solids, (Ed. J.P. Biehler ), 1982, 201–242.

    Google Scholar 

  102. Ionescu, I.R. and Sofonea, M.: Functional and Numerical Methods in Viscoplasticity, Oxford 1993.

    Google Scholar 

  103. Iwakuma, T. and Nemat-Nasser, S.: Finite elasto-plastic deformation of polyctystalline metals, Proc. R. Soc. Lond., A23 (394) (1984), 87–119.

    Google Scholar 

  104. Jaumann, G.: Geschlossenes System physikalischer und chemischer Differentialgesetze. Sitzgsber. Akad. Wiss. Wien (IIa), 120 (1911), 385–530.

    MATH  Google Scholar 

  105. Johnson, J.N.: Dynamic fracture and spallation in ductile solids, J. Appl. Phys., 52 (1981), 2812–2825.

    Google Scholar 

  106. Johnson, G.C. and Bamman, D.J.: A discussion of stress rates in finite deformation problems, Int. J. Solids & Struct., 20 (1984), 725–737.

    MATH  Google Scholar 

  107. Kawata, K., Hashimoto, S. and Kurokawa, K.: Analyses of high velocity tension of bars of finite length of bcc and fcc metals with their own constitutive equation, in: High Velocity Deformation of Solids, (Eds. H.S. Kawata and J. Shioiri ), Springer Verlag, New York 1978.

    Google Scholar 

  108. Knops, R.J. and Wilkes, E.W.: Theory of elastic stability, in: Handbuch der Physik, VI a/3, Springer, Berlin, Heidelberg, New York 1973.

    Google Scholar 

  109. Kocks, U.F., Argon, A.S. and Ashby, M.F.: Thermodynamics and Kinetics of Slip, Pergamon Press 1975.

    Google Scholar 

  110. Kratochvil, J.: Finite-strain theory of crystalline elastic-inelastic materials, J. Appl. Phys., 42 (1971), 1104.

    Google Scholar 

  111. Kumar, A., Hauser, F.E. and Dorn, J.E.: Viscous drag on dislocations in aluminium at high strain rates, Acta Met., 16 (1968), 1189–1197.

    Google Scholar 

  112. Kumar, A. and Kumble, R.G.: Viscous drag on dislocations at high strain rates in copper, J. Appl. Physics, 40 (1969), 3475–3480.

    Google Scholar 

  113. Le Roy, G., Embury, J.D., Edward, G. and Ashby, M.F.: A model of ductile fracture based on the nucleation and growth of voids, Acta Met., 29 (1981), 1509–1522.

    Google Scholar 

  114. Lee, E.H.: Elastic-plastic deformations at finite strains, J. Appl. Mech., 35 (1969), 1–6.

    Google Scholar 

  115. Lee, E.H. and Liu, D.T.: Finite-strain elastic-plastic theory partucularly for plane wave analysis, J. Appl. Phys., 38 (1967).

    Google Scholar 

  116. Lindholm, U.S.: Some experiments with the split Hopkinson pressure bar, J. Mech. Phys. Solids, 12 (1964), 317–335.

    Google Scholar 

  117. Lindholm, U.S.: in: Mechanical Behaviour of Materials under Dynamic Loads, (Ed. U.S. Lindholm ), Springer Verlag 1968, 77–95.

    Google Scholar 

  118. Lisiecki, L.L., Nelson, D.R. and Asaro, R.J.: Lattice rotations, necking and localized deformation in f.c.c. single crystals, Scripta Met., 16 (1982), 441–449.

    Google Scholar 

  119. Loret, B.: On the effect of plastic rotation in the finite deformation of anisotropic elastoplastic materials, Mech. Mater., 2 (1983), 287–304.

    Google Scholar 

  120. Loret, B.: On the effects of plastic rotation on the localization of anisotropic elastoplastic solids, in: Plastic Instability, (Eds. J. Salencon et al.), Presses Ponts et Chausees, Paris 1985, 89–100.

    Google Scholar 

  121. Loret, B.: Does deviation from deviatoric associativity lead to the onset of flutter instability?, J. Mech. Phys. Solids, 40 (1992), 1363–1375.

    MathSciNet  MATH  Google Scholar 

  122. Loret, B. and Dafalias, Y.F.: The effects of anisotropy and plastic spin on fold formations, J. Mech. Phys. Solids, 40 (1992), 417–439.

    MATH  Google Scholar 

  123. Lodygowski, T.: On avoiding of spurious mesh sensitivity in numerical analysis of plastic strain localization, CAMES, 2 (1995), 231–248.

    Google Scholar 

  124. Lodygowski, T., Lengnick, M., Perzyna, P. and Stein E.: Viscoplastic numerical analysis of dynamic plastic strain localization for a ductile material, Archives of Mechanics, 46 (1994), 1–25.

    Google Scholar 

  125. Lodygowski, T. and Perzyna, P.: Localized fracture of inelastic polycrystalline solids under dynamic loading processes, I. J. Damage Mechanics, (1997), (in print).

    Google Scholar 

  126. Lodygowski, T. and Perzyna, P.: Numerical modelling of localized fracture of inelastic solids in dynamic loading processes, Int. J. Num. Meth. Engrg., 40 (1997), (in print).

    Google Scholar 

  127. Mac Kenzie, J.H.: The elastic constants of a solid containing spherical holes, Proc. Phys. Soc., 63B (1950), 2–11.

    Google Scholar 

  128. Malvern, L.E.: The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effects, J. Appl. Mech., 18 (1951), 203–208.

    MathSciNet  Google Scholar 

  129. Mandel, J.: Plasticité Classique et Viscoplasticite, CISM Lecture Notes No. 97, Udine, Springer-Verlag; Vien 1971.

    Google Scholar 

  130. Mandel, J.: Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques, Int. J. Solids Structures, 9 (1973), 725.

    MATH  Google Scholar 

  131. Mandel, J.: Thermodynamics and plasticity, in: Foundations of Continuum Thermodynamics, (Eds. J.J. Delgado et al.), MacMillan, New York 1974.

    Google Scholar 

  132. Mandel, J.: Définition d’un repère privilégé pour l’etude des transformations anélastiques du polycrystal, J. Méc. Théo. Appl., 1 (1982), 7.

    MathSciNet  MATH  Google Scholar 

  133. Marchand, A., Cho, K. and Duffy, J.: The formation of adiabatic shear bands in an AISI 1018 cold-rolled steel, Brown University Report 1988.

    Google Scholar 

  134. Marchand, A. and Duffy, J.: An experimental study of the formation process of adiabatic shear bands in a structural steel, J. Mech. Phys. Solids, 36 (1988),283

    Google Scholar 

  135. Marsden, J.E. and Hughes, T.J.R.: Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, New York 1983.

    Google Scholar 

  136. Mason, W.P.: Phonon viscosity and its effect on acoustic wave attenuation and dislocation motion, J. Acoustical Soc. Amer., 32 (1960), 458–472.

    Google Scholar 

  137. Mason, J.J., Rosakis, A.J. and Ravichandran, R.: On the strain and strain rate dependence of the fraction of plastic work converted to heat: an experimental study using high speed infrared detectors and the Kolsky bar, Mechanics of Materials, 17 (1994), 135–145.

    Google Scholar 

  138. Matic, P., Kirby II, G.C. and Jolies, M.I.: The relation of tenssile specimen size and geometry effects to unique constitutive parameters for ductile materials, Proc. R. Soc. Lond., A417 (1988), 309–333.

    Google Scholar 

  139. Mear, M.E. and Hutchinson, J.E.: Influence of yield surface curvature on flow localization in dilatant plasticity, Mech. Mater., 4 (1985), 395–407.

    Google Scholar 

  140. Mecking, H. and Kocks, U.F.: Kinetics of flow and strain-hardening, Acta Metall., 29 (1981), 1865–1875.

    Google Scholar 

  141. Mehrabadi, M.M. and Nemat-Nasser, S.: Some basic kinematical relations for finite deformations of continua, Mechanics of Materials, 6 (1987), 127–138.

    Google Scholar 

  142. Meyers, M.A. and Aimone, C.T.: Dynamic fracture (spalling) of metals, Prog. Mater. Sci., 28 (1983), 1–96.

    Google Scholar 

  143. Müller, I.: On the entropy inequality, Arch. Rational Mech. Anal., 26 (1967), 118–141.

    MATH  Google Scholar 

  144. Müller, I.: Thermodynamics of mixtures of fluids, J. Mécanique, 14 (1975), 267–303.

    MATH  Google Scholar 

  145. Nabarro, F.R.N.: Theory of Crystal Dislocations, Oxford 1967.

    Google Scholar 

  146. Nadai, A.: Theory of Flow and Fracture of Solids, Vol. 1, McGraw Hill, New York 1950.

    Google Scholar 

  147. Needleman, A. and Rice, J.R.: Limits to ductility set by plastic flow localization, in: Mechanics of Sheet Metal Forming, (Ed. D.P. Koistinen and N.M. Wang ), Plenum, New York 1978, 237–267.

    Google Scholar 

  148. Nemat-Nasser, S.: Phenomenological theories of elastoplasticity and strain localization at high strain rates, Appl. Mech. Rev., 45 (1992), S19 - S45.

    MathSciNet  Google Scholar 

  149. Nemat-Nasser, S.: Decomposition of strain measures and their rates in finite deformation elastoplasticity, Int. J. Solids Structures, 15 (1979), 155–166.

    MATH  Google Scholar 

  150. Nemat-Nasser, S., Chung, T.D. and Taylor, L.M.: Phenomenological modelling of rate-dependent plasticity for high strain rate problems, Mechanics of Materials, 7 (1989), 319–344.

    Google Scholar 

  151. Nemat-Nasser, S. and Obata, M.: Rate-dependent, finite elasto-plastic deformation of polycrystals, Proc. R. Soc. Lond., A407 (1986), 343–375.

    Google Scholar 

  152. Nemes, J.A. and Eftis, J.: Several features of a viscoplastic study of plate-impact spallation with multidimensional strain, Computers and Structures, 38 (1991), 317–328.

    MATH  Google Scholar 

  153. Nemes, J.A. and Eftis, J.: Pressure-shear waves and spall fracture described by a viscoplastic-damage constitutive moddel, Int. J. Plasticity, 8 (1992), 185–207.

    MATH  Google Scholar 

  154. Nemes, J.A. and Eftis, J.: Constitutive modelling on the dynamic fracture of smooth tensile bars, Int. J. Plasticity, 9 (1993), 243–270.

    MATH  Google Scholar 

  155. Nemes, J.A., Eftis, J. and Randles, P.W.: Viscoplastic constitutive modelling of high strain-rate deformation, material damage and spall fracture, J. Appl. Mech., 57 (1990), 282–291.

    Google Scholar 

  156. Nicolis, G. and Prigogine, I.: Self-Organization in Nonequilibrium Systems, Wiley-Interscience, New York 1977.

    MATH  Google Scholar 

  157. Oldroyd, J.: On the formulation of rheological equations of state, Proc. R. Soc. Lond., A200 (1950), 523–541.

    MathSciNet  MATH  Google Scholar 

  158. Peirce, D., Asaro, J.R. and Needleman, A.: An analysis of nonuniform and localized deformation in ductile single crystals, Acta Metall., 30 (1982), 1087–1119.

    Google Scholar 

  159. Peirce, D., Asaro, J.R. and Needleman, A.: Material rate dependence and localized deformation in crystalline solids, Acta Metall., 31 (1983), 1951–1976.

    Google Scholar 

  160. Perzyna, P.: The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math., 20 (1963), 321–332.

    MathSciNet  MATH  Google Scholar 

  161. Perzyna, P.: Fundamental problems in viscoplasticity, Advances in Applied Mechanics, 9 (1966), 243–377.

    Google Scholar 

  162. Perzyna, P.: Thermodynamic theory of viscoplasticity, Advances in Applied Mechanics, 11 (1971), 313–354.

    Google Scholar 

  163. Perzyna, P.: Thermodynamics of a unique material structure, Arch. Mechanics, 27 (1975), 791–806.

    MathSciNet  MATH  Google Scholar 

  164. Perzyna, P.: Coupling of dissipative mechanisms of viscoplastic flow, Arch. Mechanics, 29 (1977), 607–624.

    MathSciNet  MATH  Google Scholar 

  165. Perzyna, P.: Modified theory of viscoplasticity. Application to advanced flow and instability phenomena, Arch. Mechanics, 32 (1980), 403–420.

    MATH  Google Scholar 

  166. Perzyna, P.: Thermodynamics of dissipative materials, in: Recent Developments in Thermodynamics of Solids, (Eds. G. Lebon and P. Perzyna ), Springer, Wien 1980, 95–220.

    Google Scholar 

  167. Perzyna, P.: Stability phenomena of dissipative solids with internal defects and imperfections, in: Proc. XV-th IUTAM Congress, Toronto, August 1980, Theoretical and Applied Mechanics, (Eds. F.P.J. Rimrott and B. Tabarrok ), North-Holland, Amsterdam 1981, 369–376.

    Google Scholar 

  168. Perzyna, P.: Stability problems for inelastic solids with defects and imperfections, Arch. Mechanics, 33 (1981), 587–602.

    MathSciNet  MATH  Google Scholar 

  169. Perzyna, P.: Application of dynamical system methods to flow processes of dissipative solids, Arch. Mechanics, 34 (1982), 523–539.

    MathSciNet  MATH  Google Scholar 

  170. Perzyna, P.: Stability of flow processes for dissipative solids with internal imperfections, ZAMP, 35 (1984a), 848–867.

    MATH  Google Scholar 

  171. Perzyna, P.: Constitutive modelling of dissipative solids for postcritical behaviour and fracture, ASME J. Eng. Materials and Technology, 106 (1984b), 410–419.

    Google Scholar 

  172. Perzyna, P.: Dependence of fracture phenomena upon the evolution of constitutive structure of solids, Arch. Mechanics, 37 (1985), 485–501.

    Google Scholar 

  173. Perzyna, P.: Constitutive modelling for brittle dynamic fracture in dissipative solids, Arch. Mechanics, 38 (1986), 725–738.

    MathSciNet  MATH  Google Scholar 

  174. Perzyna, P.: Internal state variable description of dynamic fracture of ductile solids, Int. J. Solids Structures, 22 (1986), 797–818.

    Google Scholar 

  175. Perzyna, P.: Temperature and rate dependent theory of plasticity of crystalline solids, Revue Phys. Appl., 23 (1988), 445–459.

    Google Scholar 

  176. Perzyna, P.: Influence of anisotropic effects on micro—damage process in dissipative solids, in: Proc. IUTAM/ICM Symposium on Yielding, Damage and Failure of Anisotropic Solids, Villerd—de—Lance, August 1987, Mech. Eng. Publl. Limited, London 1990, 483–507.

    Google Scholar 

  177. Perzyna, P.: Constitutive equations for thermoplasticity and instability phenomena in thermodynamic flow processes, in: Progress in Computational Analysis of Inelastic Structures, (Ed. E. Stein ), Springer-Verlag, Wien 1993, 1–78.

    Google Scholar 

  178. Perzyna, P.: Adiabatic shear band localization fracture of solids in dynamic loading proceses, Proc. of Int. Conference on Mechanical and Physical Behaviour of Materials under Dynamic Loading, Oxford, September 26–30, 1994; (Ed. J. Harding ), Les Editions de Physique Le Ulis 1994, 441–446.

    Google Scholar 

  179. Perzyna, P.: Instability phenomena and adiabatic shear band localization in thermoplastic flow processes, Acta Meclianica, 106 (1994), 173–205.

    MathSciNet  MATH  Google Scholar 

  180. Perzyna, P.: Interactions of elastic-viscoplastic waves and localization phenomena in solids, IUTAM Symposium on Nonlinear Waves in Solids, August 15–20, 1993, Victoria, Canada; (Eds. J.L. Wegner and F.R. Norwood ), ASME 1995, 114–121.

    Google Scholar 

  181. Perzyna, P.: Thermodynamic theory of inelastic single crystals, Continuum Mechanics and Thermodynamics, (1997), ( Submitted for publication).

    Google Scholar 

  182. Perzyna, P.: Thermodynamics and synergetics of inelastic single crystals, Mathematics and Mechanics of Solids, (1997), ( Submitted for publication).

    Google Scholar 

  183. Perzyna, P. and Drabik, A.: Description of micro-damage process by porosity parameter for nonlinear viscoplasticity, Arch. Mechanics, 41 (1989), 895–908.

    Google Scholar 

  184. Perzyna, P. and Drabik, A.: Micro-damage mechanism in adiabatic processes, Int. J. Plasticity, (1997) (in print).

    Google Scholar 

  185. Perzyna, P. and Duszek-Perzyna, M.K.: Phenomenological modelling of adiabatic shear band localization fracture of solids in dynamic loading processes, in: Localized Damage III; Computer–Aided Assessment and Control, (Eds. M.H. Aliabadi, A. Carpinteri, S. Kalisky, D.J. Cartwright ), Computational Mechanics Publications., Southampton 1994, 579–588.

    Google Scholar 

  186. Perzyna, P. and Duszek-Perzyna, M.K.: Constitutive modelling of inelastic single crystals for localization phenomena, in: Constitutive Laws: Experiments and Numerical Implementation, (Eds. A.M. Rajendran, R.C. Batra ), CIMME, Barcelona 1995, 70–83.

    Google Scholar 

  187. Perzyna, P. and Korbel, K.: Analysis of the influence of substructure of crystal on the localization phenomena of plastic deformation, Mechanics of Materials, 24 (1996), 141–158.

    Google Scholar 

  188. Perzyna, P. and Korbel, K.: Analysis of the influence of variuos effects on criteria for adiabatic shear band localization in single crystals, Acta Mechanica, (1997) (in print).

    Google Scholar 

  189. Philips, A. and Lu, W.Y.: An experimental investigation of yield surface and loading surface of pure aluminium with stress-controlled and strain-controlled paths of loading, ASME J. Eng. Mater. Technol., 106 (1984), 349–354.

    Google Scholar 

  190. Prager, W.: The theory of plasticity: a survey of recent achievements, (J. Clayton Lecture), Proc. Inst. Mech. Eng., 169 (1955), 41.

    MathSciNet  Google Scholar 

  191. Prager, W.: Introduction to Mechanics of Continua, Gin and Co., New York 1961.

    MATH  Google Scholar 

  192. Qin, Q. and Bassani, J.L.: Non-Schmid yield behavior in single crystals, J. Mech. Phys. Solids, 40 (1992), 813–833.

    MathSciNet  Google Scholar 

  193. Qin, Q. and Bassani, J.L.: Non-associated plastic flow in single crystals, J. Mech. Phys. Solids, 40 (1992), 835–862.

    MathSciNet  MATH  Google Scholar 

  194. Rajendren, A.M. and Bless, S.J.: High strain rate material behaviour, in: AFWALTR-85–4009, Materials Laboratory, Air Force Wright Aeronautical Laboratories, Wright-Patterson Air Force Base, Ohio, 45433, 1985.

    Google Scholar 

  195. Rashid, M.M., Gray, G.T. and Nemat-Nasser, S.: Heterogeneous deformations in copper single crystals at high and low strain rates, Philosophical Magazine A, 65 (1992), 707–735.

    Google Scholar 

  196. Regazzoni, G., Johnson, J.N. and Follansbee, P.S.: Theoretical study of the dynamic tensile test, ASME J. Appl. Mech., 53 (1986), 519–528.

    Google Scholar 

  197. Regazzoni, G. and Montheillet, F.: Influence of strain rate on the flow stress and ductility of copper and tantalum at room temperature, in: Third Int’l. Conf. on the Mechanical Properties of Materials at High Rates, (Ed. J. Harding), The Institute of Physics, 70, pp. 63–70, 1984.

    Google Scholar 

  198. Rice, J.R.: On the structure of stress-strain relations for time-dependent plastic deformation in metals, J. Appl. Mech., 37 (1970), 728–737.

    Google Scholar 

  199. Rice, J.R.: Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19 (1971), 433–455.

    MATH  Google Scholar 

  200. Rice, J.R.: Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms, in: Constitutive Equations in Plasticity, (Ed. A.S. Argon ), The MIT Press, Cambridge 1975, 23–75.

    Google Scholar 

  201. Rice, J.R.: The localization of plastic deformation, in: Theoretical and Applied Mechanics, (Ed. W.T. Koiter ), North-Holand 1976, 207–220.

    Google Scholar 

  202. Rice, J.R. and Rudnicki, J.W.: A note on some features of the theory of localization of deformation, Int. J. Solids Structures, 16 (1980), 597–605.

    MathSciNet  MATH  Google Scholar 

  203. Rice, J.R. and Thomson, R.: Ductile versus brittle behaviour of crystals, Phil. Mag., 29 (1974), 73–97.

    Google Scholar 

  204. Richtmyer, R.D.: Principles of Advance Mathematical Physics, Vol. I, Springer, New York 1978.

    Google Scholar 

  205. Richtmyer, R.D. and Morton, K.W.: Difference Methods for Initial-Value Problems, John Wiley, New York 1967.

    MATH  Google Scholar 

  206. Ritchie, R.O., Knott, J.F. and Rice, J.R.: On thee relationship between critical tansile stress and fracture toughness in mild steel, J. Mech. Phys. Solids, 21 (1973), 395–410.

    Google Scholar 

  207. Rogers, H.C. and Shastry, C.V.: Material factors in adiabatic shearing in steels, in: Shock Waves and High-Strain-Rate Phenomena in Metals, (Eds. M.A. Meyers and L.E. Murr ), Plenum, New York 1981, 285–298.

    Google Scholar 

  208. Rudnicki, J.W. and Rice, J.R.: Conditions for the localization of deformation in pressure—sensitive dilatant materials, J. Mech. Phys. Solids, 23 (1975), 371–394.

    Google Scholar 

  209. Saje, M., Pan, J. and Needleman, A.: Void nucleation effects on shear localization in porous plastic solids, Int. J. Fracture, 19 (1982), 163–182.

    Google Scholar 

  210. Seaman, L., Curran, D.R. and Shockey, D.A.: Stanford Res. Inst. Tech. Rep., No. AFWL-TR-71–156, Dec. 1971.

    Google Scholar 

  211. Seaman, L., Curran, D.R. and Murri, W.J.: A continuum model for dynamic tensile microfracture and fragmentation, J. Appl. Mech., 52 (1985), 593–600.

    Google Scholar 

  212. Seeger, A.: The generation of lattice defects by moving dislocations and its application to the temperature dependence of the flow—stress of f.c.c. crystals, Phil. Mag., 46 (1955), 1194–1217.

    Google Scholar 

  213. Seeger, A.: Kristalplastizitat, in: Handbuch der Physik VII/2, (Ed. S. Flugge ), Springer—Verlag 1958, 1–208.

    Google Scholar 

  214. Serrin, J.: Conceptual analysis of the classical second laws of thermodynamics, Arch. Rational Mech. Anal., 70 (1979), 355–371.

    MathSciNet  Google Scholar 

  215. Shawki, T.G. and Clifton, R.J.: Shear band formation in thermal viscoplastic materials, Mechanics of Materials, 8 (1989), 13–43.

    Google Scholar 

  216. Shield, R.T. and Ziegler, H.: On Prager’s hardening rule, ZAMP, 9a (1958), 260–276.

    MathSciNet  Google Scholar 

  217. Shima, S. and Oyane, M.: Plasticity for porous solids, Int. J. Mech. Sci, 18 (1976), 285–291.

    Google Scholar 

  218. Shockey, D.A., Seaman, L. and Curran, D.R.: in: Metallurgical Effects at High Strain Rates, (Eds. R.W. Rohde, B.M. Butcher, J.R. Holland, and C.H. Karbes ), Plenum Press, New York 1973, 473.

    Google Scholar 

  219. Shockey, D.A., Seaman, L. and Curran, D.R.: The microstatistical fracture mechanics approach to dynamic fracture problem, Int. J. Fracture, 27 (1985), 145–157.

    Google Scholar 

  220. Shockey, D.A., Seaman, L. Dao, K.C. and Curran, D.R.: Kinetics of void development in fracturing A533B tensile bars, Trans. ASME J. Pressure Vessel. Tech., 102 (1980), 14–21.

    Google Scholar 

  221. Simo, J.C.: A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation, Comput. Meths. Appl. Mech. Engrg., 66 (1988), 199–219.

    MathSciNet  MATH  Google Scholar 

  222. Simo, J.C.: A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part II. Comput.tional aspects, Comput. Meths. Appl. Mech. Engrg., 66 (1988), 1–31.

    Google Scholar 

  223. Simo, J.C. and Taylor, R.L.: Consistent tangent operators for rate—dependent plasticity, Comput. Meths. Appl. Mech. Engrg., 48 (1985), 101–118.

    MATH  Google Scholar 

  224. Sluys, L.J., Bolck, J. and de Borst, R.: Wave propagation and localization in viscoplastic media, Proc. Third Inter. Conference on Computational Plasticity, Fundamentals and Applications, Barcelona, April 6–10, 1992, (Eds. D.R.J. Owen, E. Onate and E. Hinton), Pineridge Press, Swansea 1992, 539–550.

    Google Scholar 

  225. Sokolnikoff, I.S.: The Mathematical Theory of Elasticity, (2d. ed.), Mc GrawHill, New York 1956.

    Google Scholar 

  226. Spitzig, W.A.: Deformation behaviour of nitrogenated Fe-Ti-Mn and Fe-Ti single crystals, Acta Metall., 29 (1981), 1359–1377.

    Google Scholar 

  227. Strang, G. and Fix, G.J.: An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs 1973.

    MATH  Google Scholar 

  228. Taylor, G.I.: Analysis of plastic strain in a crystal, in: Stephen Timoshenko 60th Anniversary Volume, (Ed. J.M. Lessels ), Macmillan, New York 1938.

    Google Scholar 

  229. Taylor, G.I. and Quinney, H.: The latent energy remaining in a metal after cold working, Proc. R. Soc. Lond., A143 (1934), 307–326.

    Google Scholar 

  230. Teodosiu, C. and Sidoroff, F.: A theory of finite elastoplasticity of single crystals, Int. J. Engng. Sci., 14 (1976), 165–176.

    MATH  Google Scholar 

  231. Thomas, T.Y.: Theoretical effect of large hydrostatic pressures on the tensile strength of materials, Proc. Nat. Acad. Sci., 57 (1967a), 1195–1197.

    Google Scholar 

  232. Thomas, T.Y.: Effect of pressure on the ductility od solids, Proc. Nat. Acad. Sci., 58 (1967b), 1274–1278.

    Google Scholar 

  233. Thomas, T.Y.: Theory of the physical characteristics of tensile fracture under pressure, Proc. Nat. Acad. Sci., 59 (1968), 700–704.

    Google Scholar 

  234. Truesdell, C.: Rational Thermodynamics, Mc Graw-Hill, New York 1969.

    Google Scholar 

  235. Truesdell, C. and Noll, W.: The Non-Linear Field Theories of Mechanics, in: Handbuch der Physik III/3, (Ed. S. Flügge ), Springer-Verlag, Berlin 1965.

    Google Scholar 

  236. Tvergaard, V.: Effects of yield surface curvature and void nucleation on plastic flow localization, J. Mech. Phys. Solids, 35 (1987), 43–60.

    Google Scholar 

  237. Tvergaard, V. and Needleman, A.: Analysis of the cup-cone fracture in a round tensile bar, Acta Metall., 32 (1984), 157–169.

    Google Scholar 

  238. Tvergaard, V. and Needleman, A.: Effect of material rate sensitivity on failure modes in the Charpy V-notch test, J. Mech. Phys. Solids, 34 (1986), 213–241.

    Google Scholar 

  239. Tvergaard, V. and Needleman, A.: Ductile failure modes in dynamically loaded notched bars, in: Damaga Mechanics in Engineering Materials, (Eds. J.W. Ju, et al.), ASME, New York 1990, 117–128.

    Google Scholar 

  240. Tvergaard, V. and Van der Giessen, E.: Effects of plastic spin on localization predictions for a porous ductile material, J. Mech. Phys. Solids, 39 (1991), 763–781.

    MATH  Google Scholar 

  241. Van der Giessen, E.: Continuum models of large deformation plasticity, Part I: Large deformation plasticity and the concept of a natural reference state, Eur. J. Mech., A/Solids, 8 (1989), 15.

    MATH  Google Scholar 

  242. Van der Giessen, E.: Continuum models of large deformation plasticity, Part II: A kinematic hardening model and the concept of a plastically induced orienta-tional structure, Eur. J. Mech., A/Solids, 8 (1989), 89.

    MATH  Google Scholar 

  243. Van der Giessen, E.: Micromechanical and thermodynamic aspects of the plastic spin, Int. J. Plasticity, 7 (1991), 365–386.

    MATH  Google Scholar 

  244. Willems, J.C.: Dissipative dynamical systems, Arch. Rat. Mech. Anal., 45 (1972), 321–393.

    MathSciNet  MATH  Google Scholar 

  245. Wray, P.J.: Strain-rate dependence of the tensile failure of polycrystalline material at elevated temperatures, J. Appl. Phys., 46 (1969), 4018–4029.

    Google Scholar 

  246. Yokobori, A.T., Yokobori, T.Jr., Sato, K. and Syo, K.: Fatigue crack growth under mixed modes I and II, Fatigue Fract. Engng. Mater. Struct., 8 (1985), 315–325.

    Google Scholar 

  247. Zaremba, S.: Sur une forme perfectionnée de la théorie de la relaxation, Bull. Int. Acad. Sci. Cracovie, (1903), 594–614.

    Google Scholar 

  248. Zaremba, S.: Le principe des mouvements relatifs et les équations de la mécanique physique, Bull. Int. Acad. Sci. Cracovie, (1903), 614–621.

    Google Scholar 

  249. Zbib, H.M. and Jurban J.S.: Dynamic shear banding: A three-dimensional analysis, Int. J. Plasticity, 8 (1992), 619–641.

    Google Scholar 

  250. Ziegler, H.: A modification of Prager’s hardening rule, Quart. Appl. Math., 17 (1959), 55–65.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Polish Academy of Sciences, Warsaw, Poland

    P. Perzyna

Authors
  1. P. Perzyna
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Polish Academy of Sciences, Poland

    Piotr Perzyna

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Wien

About this chapter

Cite this chapter

Perzyna, P. (1998). Constitutive Modelling of Dissipative Solids for Localization and Fracture. In: Perzyna, P. (eds) Localization and Fracture Phenomena in Inelastic Solids. International Centre for Mechanical Sciences, vol 386. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2528-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2528-1_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82918-9

  • Online ISBN: 978-3-7091-2528-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation