Skip to main content
SpringerLink
Log in

Generalized Pressure-Insensitive Criteria

  • Chapter
  • First Online:
Equivalent Stress Concept for Limit State Analysis

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 86))

  • 723 Accesses

Abstract

Bridgman’s observation that the hydrostatic pressure seems to have no effect on the yield behavior of metals (Bridgman in J Appl Phys 18(2):246–258, 1947 [1], Bridgman in Studies in large plastic flow and fracture with special emphasis on the effects of hydrostatic pressure. McGraw-Hill, New York, 1952 [2]) led engineers to develop a plasticity theory that subtracts the mean stress from the principal stresses (Wilson in J Appl Mech 69(1):63–68, 2002 [3]). The criteria are written in the invariants of the stress deviator (1.28) or (1.29) and hence are cylindrical or prismatic surfaces aligned along the hydrostatic axis in the principal stress space. They do not restrict the hydrostatic stresses. The equalities (5.2) and the equation \(\nu _+^\mathrm {in}=\nu _-^\mathrm {in}=\frac{1}{2}\) are valid.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and 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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    This criterion is dedicated to Jurij Antonovič Radcig (1900–1976), who was a professor at the Kazan State University of Technology (KAI), Russia.

References

  1. Bridgman PW (1947) The effect of hydrostatic pressure on the fracture of brittle substances. J Appl Phys 18(2):246–258

    Article  Google Scholar 

  2. Bridgman PW (1952) Studies in large plastic flow and fracture with special emphasis on the effects of hydrostatic pressure. McGraw-Hill, New York

    MATH  Google Scholar 

  3. Wilson CD (2002) A critical reexamination of classical metal plasticity. J Appl Mech 69(1):63–68

    Article  MATH  Google Scholar 

  4. Kolupaev VA (2017) Generalized strength criteria as functions of the stress angle. J Eng Mech (ASCE) 143(9). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001322

  5. Kolupaev VA, Altenbach H (2010) Considerations on the unified strength theory due to Mao-Hong Yu (in German: Einige Überlegungen zur Unified Strength Theory von Mao-Hong Yu). Forsch Ingenieurwes 74(3):135–166

    Google Scholar 

  6. Kolupaev VA, Bolchoun A, Altenbach H (2009) New trends in application of strength hypotheses (in German: Aktuelle Trends beim Einsatz von Festigkeitshypothesen). Konstruktion 61(5):59–66 Springer-VDI-Verlag

    Google Scholar 

  7. Kolupaev VA (2006) 3D-Creep behaviour of parts made of non-reinforced thermoplastics (in German: Dreidimensionales Kriechverhalten von Bauteilen aus unverstärkten Thermoplasten). Dissertation, Martin-Luther-Universität Halle-Wittenberg, Halle-Saale

    Google Scholar 

  8. Kolupaev VA, Moneke M, Becker F (2005) Multiaxial creep of parts made of thermoplastics (in German: Mehraxiales Kriechen von Thermoplast-Formteilen), Düsseldorf, VDI-Verlag, Fortschr.-Ber. VDI Reihe 5, Nr. 703

    Google Scholar 

  9. Altenbach H, Bolchoun A, Kolupaev VA (2014) Phenomenological yield and failure criteria. In: Altenbach H, Öchsner A (eds) Plasticity of pressure-sensitive materials. Engineering Materials. Springer, Berlin, pp 49–152

    Google Scholar 

  10. Bolchoun A, Kolupaev VA, Altenbach H (2011) Convex and non-convex flow surfaces (in German: Konvexe und nichtkonvexe Fließflächen). Forsch Ingenieurwes 75(2):73–92

    Google Scholar 

  11. Podgórski J (1984) Limit state condition and the dissipation function for isotropic materials. Arch Mech 36(3):323–342

    Google Scholar 

  12. Podgórski J (1985) General failure criterion for isotropic media. J Eng Mech 111(2):188–201

    Article  Google Scholar 

  13. Kolupaev VA, Yu MH, Altenbach H (2013) Yield criteria of hexagonal symmetry in the \(\pi \)-plane. Acta Mech 224(7):1527–1540

    Google Scholar 

  14. Roger A (2016) Lines and tangents in polar coordinates. http://orion.math.iastate.edu/alex/166H/polar_lines_tangents.pdf (16 Jan 2016)

  15. Kolupaev VA, Yu MH, Altenbach H, Bolchoun A (2017) Comparison of strength criteria based on the measurements on concrete. J Eng Mech (ASCE). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001419

  16. Kolupaev VA, Yu MH, Altenbach H (2013) Visualisation of the unified strength theory. Arch Appl Mech 83(7):1061–1085

    Google Scholar 

  17. Altenbach H, Kolupaev VA (2009) Fundamental forms of strength hypotheses. In: Krivtsov AM, Indeitcev DA (eds) Proceedings of XXXVI Summer School Advanced Problems in Mechanics, Institute for Problems in Mechanical Engineering RAS, St. Petersburg, pp 32–45

    Google Scholar 

  18. Kolupaev VA, Bolchoun A (2008) Combined yield and fracture criteria (in German: Kombinierte Fließ- und Grenzbedingungen). Forsch Ingenieurwes 72(4):209–232

    Google Scholar 

  19. Hu Q, Li X, Han X, Li H, Chen J (2017) A normalized stress invariant-based yield criterion: Modeling and validation. Int J Plast 99:248–273

    Google Scholar 

  20. Sengoz K (2017) Development of a generalized isotropic yield surface for pressure insensitive metal plasticity considering yield strength differential effect in tension, compression and shear stress states. Dissertation, The School of Engineering and Applied Science, The George Washington University, Washington

    Google Scholar 

  21. de Araújo FC (1962) Elasticidade e plasticidade. Imprensa Portuguesa, Porto

    Google Scholar 

  22. Mendelson A (1968) Plasticity: Theory and application. Krieger, Malabar

    Google Scholar 

  23. Ivlev DD (1958) On the development of a theory of ideal plasticity. J Appl Math Mech 22(6):1221–1230

    Article  MathSciNet  MATH  Google Scholar 

  24. Kolupaev VA, Bolchoun A, Altenbach H (2013) Yield criteria for incompressible materials in the shear stress space. In: Öchnser, A, Altenbach H (eds) Experimental and numerical investigation of advanced materials and structures. Springer, Berlin, pp 107–119

    Google Scholar 

  25. Yu MH (2002) Advances in strength theories for materials under complex stress state in the 20th century. Appl Mech Rev 55(5):169–218

    Article  Google Scholar 

  26. Yu MH (2004) Unified strength theory and its applications. Springer, Berlin

    Book  MATH  Google Scholar 

  27. Pisarenko GS, Lebedev AA (1976) Deformation and strength of materials under complex stress state (in Russ.: Deformirovanie i prochnost’ materialov pri slozhnom naprjazhennom sostojanii). Naukowa Dumka, Kiev

    Google Scholar 

  28. Sokolovsky VV (1950) Theory of plasticity (in Russ.: Teorija plastichnosti). Gos. izd. tekhn.-teor. literatury, Moscow

    Google Scholar 

  29. Billington EW (1986) Introduction to the mechanics and physics of solids. Adam Hilger Ltd., Bristol

    MATH  Google Scholar 

  30. Haythornthwaite RM (1983) Piecewise linear yield criteria in invariant form. J Eng Mech 109(4):1016–1022

    Article  Google Scholar 

  31. Owen DRJ, Hinton E (1986) Finite elements in plasticity, theory and practice. Pineridge Press Limited, Swansea

    MATH  Google Scholar 

  32. Yu MH (1961) General behaviour of isotropic yield function (in Chinese). Scientific and Technological Research Paper of Xi’an Jiaotong University, pp 1–11

    Google Scholar 

  33. Yu MH (1962) Brittle fracture and plastic yield criterion (in Chinese). Scientific and Technological Research Paper of Xi’an Jiaotong University, pp 1–25

    Google Scholar 

  34. Yu MH (1988) Researches on the twin shear stress strength theory (in Chinese). Xi’an Jiaotong University Press, Xi’an

    Google Scholar 

  35. Lagzdin’ A (1997) Smooth convex limit surfaces in the space of symmetric second-rank tensors. Mech Compos Mater 33(2):119–127

    Article  Google Scholar 

  36. Karafillis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41(12):1859–1886

    Article  MATH  Google Scholar 

  37. Ishlinsky AY, Ivlev DD (2003) Mathematical theory of plasticity (in Russ.: Matematicheskaja teorija plastichnosti). Fizmatlit, Moscow

    Google Scholar 

  38. Ivlev DD (1960) On extremum properties of plasticity conditions (in Russ.: Ob ekstremal’nykh svojstvakh uslovij plastichnosti). J Appl Math Mech 24(5):1439–1446

    Google Scholar 

  39. Ivlev DD (1966) Theory of ideal plasticity (in Russ.: Teorija idealnoj plastichnosti). Nauka, Moscow

    Google Scholar 

  40. Shesterikov SA (1960) On the theory of ideal plastic solid (in Russ.: K postroeniju teorii ideal’no plastichnogo tela). Prikladnaja Matematika i Mekhanika, Otdelenie Tekhnicheskikh Nauk Akademii Nauk Sojusa SSR, Russian Academy of Science 24(3):412–415

    Google Scholar 

  41. Ivlev DD (2005) Theory of limit state and ideal plasticity (in Russ.: Teorija predel’nogo sostojanija i ideal’noj plastichnosti). Voronezhskij Gosudarstvennyj Universitet, Voronezh

    Google Scholar 

  42. Lequeu PH, Gilormini P, Montheillet F, Bacroix B, Jonas JJ (1987) Yield surfaces for textured polycrystals. Acta Met 35(2):439–451, 1159–1174

    Google Scholar 

  43. Yu MH (1999) Engineering strength theory (in Chinese). Higher Education Press, Beijing

    Google Scholar 

  44. Drucker DC (1957) A definition of stable inelastic material. Technical Report 2, Division of Engineering, Brown University, Providence, Rhode Island

    Google Scholar 

  45. Altenbach J, Altenbach H (1994) Einführung in die Kontinuumsmechanik. Teubner, Stuttgart

    MATH  Google Scholar 

  46. Betten J (2001) Kontinuumsmechanik, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  47. Paul B (1968b) Macroscopic plastic flow and brittle fracture. In: Liebowitz H (ed) Fracture: An advanced treatise, vol II. Academic Press, New York, pp 313–496

    Google Scholar 

  48. Mortara G (2010) A yield criterion for isotropic and cross-anisotropic cohesive-frictional materials. Int J Numer Anal Methods Geomech 34(9):953–977

    MATH  Google Scholar 

  49. Ismar H, Mahrenholz O (1979) Technische Plastomechanik. Vieweg, Braunschweig

    Google Scholar 

  50. Radaev YN (2007) Spatial problem of the mathematical theory of plasticity (in Russ.: Prostranstvennaja zadacha matematicheskoj teorii plastichnosti). Samarskij Universitet, Samara

    Google Scholar 

  51. Skrzypek JJ, Ganczarski AW (2015) Mechanics of anisotropic materials. Engineering Materials. Springer, Heidelberg

    Book  MATH  Google Scholar 

  52. Ziegler H, Nänni J, Wehrli C (1973) Zur Konvexität der Fliessfläche. Zeitschrift für Angewandte Mathematik und Physik ZAMP 24:140–144

    Google Scholar 

  53. Ziegler H (1969) Zum plastischen Potential der Bodenmechanik. Zeitschrift für Angewandte Mathematik und Physik ZAMP 20:659–675

    Google Scholar 

  54. Besdo D, Lehmann T (1993) Grundgleichungen der Plastomechanik. In: Dahl W, Kopp R, Palewski O, Pankert R (eds) Umformtechnik, Plastomechanik und Werkstoffkunde, Verlag Stahleisen mbH and Springer, Düsseldorf, pp 64–86

    Google Scholar 

  55. Brach S, Dormieux L, Kondo D, Vairo G (2016) Nanoporous materials with a general isotropic plastic matrix: exact limit state under isotropic loadings. Int J Plast pp 1–28. http://dx.doi.org/10.1016/j.ijplas.2016.10.007

  56. Carstensen C, Hackl K, Mielke A (2000) Nonconvex potentials and microstructures in finite-strain plasticity. Report, Sonderforschungsbereich Mehrfeldprobleme in der Kontinuumsmechanik, Geschäftsstelle, SFB 404, Stuttgart

    Google Scholar 

  57. Dorn JE (1948) The effect of stress state on the fracture strength of metals. In: Jonassen F, Roop WP, Bayless RT (eds) Fracturing of metals. A seminar on the fracturing of metals held during the twenty-ninth National Metal Congress and Exposition, Chicago, American Society for Metals, Cleveland, Ohio, pp 32–50

    Google Scholar 

  58. Gupta NK, Meyers A (1990) Fitting of experimental yield surfaces. ZAMM 70(3):181–187

    Article  Google Scholar 

  59. Haythornthwaite RM (1960) Mechanics of triaxial tests for soil. Proc ASCE J Soil Mech Found Div 87(SM5):35–62

    Google Scholar 

  60. Hsu TC (1961) Definition of the yield point in plasticity and its effect on the shape of the yield locus. J Strain Anal 1(4):331–338

    Article  Google Scholar 

  61. Hughes TJR (1984) Numerical implementation of constitutive models: rate-independent deviatoric plasticity. In: Nemat-Nasser S (ed) Theoretical foundation for large scale computations of nonlinear material behavior, Mechanics of elastic and inelastic solids, vol 6. Martinus Nijhoff, Dordrecht, pp 29–63

    Chapter  Google Scholar 

  62. Ivey HJ (1961) Plastic stress-strain relations and yield surfaces for aluminium alloys. J Mech Eng Sci 3(1):15–31

    Article  Google Scholar 

  63. Kuczma MS, Stein E (1994) On nonconvex problems in the theory of plasticity. Arch Mech 46(4):505–530

    MathSciNet  MATH  Google Scholar 

  64. Michno MJ, Findley WN (1975) Subsequent yield surfaces for annealed mild steels under servo-controlled strain and load histories: Aging, normality, convexity, corners, Bauschinger and cross effects. Trans ASME J Eng Mater Technol 1:25–32

    Google Scholar 

  65. Paglietti A (2009) Plasticity of cold worked metals - a deductive approach. WIT Press, Boston

    Google Scholar 

  66. Palmer AC, Maier G, Drucker DC (1967) Normality relations and convexity of yield surfaces for unstable materials or structural elements. Trans ASME J Appl Mech 89(6):464–470

    Article  Google Scholar 

  67. Tsutsumi S, Toyosada M, Hashiguchi K (2006) Non-convex mechanical response of pressure dependent yielding materials within associated and non-associated plasticity. J Appl Mech JSCE 9:463–470

    Article  Google Scholar 

  68. Wilkins ML, Streit RD, Reaugh JE (1980) Cumulative-strain-damage model of ductil fracture: simulation and prediction of engineering fracture tests. Report. UCLR-53058, Lawrence Livermore National Laboratory, University of California

    Google Scholar 

  69. Mills LL, Zimmerman RM (1970) Compressive strength of plain concrete under multiaxialloading conditions. American Concrete Institute Journal 67(10):802–807

    Google Scholar 

  70. Kupfer H (1973) Das Verhalten des Betons unter mehrachsiger Kurzzeitbelastung unterbesonderer Berücksichtigung der zweiachsigen Beanspruchung, Deutscher Ausschuss für Stahlbeton, vol 229, Ernst & Sohn, Berlin, 229:1–105

    Google Scholar 

  71. Tasuji ME, Slate FO, Nilson AH (1978) Stress-strain response and fracture of concrete inbiaxial loading. ACI J Proceedings 75(7):306–312

    Google Scholar 

  72. Lade PV, Duncan JM (1973) Cubical triaxial tests on cohesionless soil. J of the Soil Mechanics and Foundations Division 99(10):793–812

    Google Scholar 

  73. Ko HY, Scott RF (1968) Deformation of sand at failure. J of the Soil Mechanics and Foundations Division, American Society of Civil Engineers 94(SM4):883–898

    Google Scholar 

  74. Green GE, Bishop AW (1969) A note on the drained strength of sand under generalized strain conditions, Geotechnique 19(1):144–149

    Google Scholar 

  75. Procter DC, Barden L (1969) Reply to Green, G. E. and Bishop, A.W., A note on the drained strength of sand under generalized strain conditions. Geotechnique 19(3):424–426

    Google Scholar 

  76. Lade PV, Musante HM (1978) Three-dimensional behavior of remolded clay. J of the Geotechnical Engineering Division, ASCE 104(GT2):193–209

    Google Scholar 

  77. Shibata T, Karube D (1965) Influence of the variation of the intermediate principal stress on the mechanical properties of normally consolidated clays. In: Proceeding of the 6th International Conference on Soil Mechanics and Foundation Engineering, Montreal, Division 1(1-2):359–363

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fraunhofer Institute for Structural Durability and System Reliability (LBF), Darmstadt, Germany

    Vladimir A. Kolupaev

Authors
  1. Vladimir A. Kolupaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir A. Kolupaev .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kolupaev, V.A. (2018). Generalized Pressure-Insensitive Criteria. In: Equivalent Stress Concept for Limit State Analysis. Advanced Structured Materials, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-73049-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73049-3_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73048-6

  • Online ISBN: 978-3-319-73049-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation