Phenomenological Yield and Failure Criteria

  • Holm AltenbachEmail author
  • Alexandre Bolchoun
  • Vladimir A. Kolupaev
Part of the Engineering Materials book series (ENG.MAT.)


Models for isotropic materials based on the equivalent stress concept are discussed. At first, so-called classical models which are useful in the case of absolutely brittle or ideal ductile materials are presented. Tests for basic stress states are suggested. At second, standard models describing the intermediate range between the absolutely brittle and ideal-ductile behavior are introduced. Any criterion is expressed by various mathematical equations formulated, for example, in terms of invariants. At the same time the criteria can be visualized which simplifies the application. At third, in the main part pressure-insensitive, pressure-sensitive and combined models are separated. Fitting methods based on mathematical, physical and geometrical criteria are necessary. Finally, three examples (gray cast iron, poly(oxymethylene) (POM) and poly(vinyl chloride) (PVC) hard foam) demonstrates the application of different approaches in modeling certain limit behavior. Two appendices are necessary for a better understanding of this chapter: in Chap. 2 applied invariants are briefly introduced and a table of discussed in this chapter criteria with references is given.


Strength criteria Yield criteria Equivalent stress Pressure-insensitive criteria Pressure-sensitive criteria Limit surfaces 


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Authors and Affiliations

  • Holm Altenbach
    • 1
    Email author
  • Alexandre Bolchoun
    • 2
  • Vladimir A. Kolupaev
    • 3
  1. 1.Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für MaschinenbauOtto-von-Guericke-Universtät MagdeburgMagdeburgGermany
  2. 2.Abteilung Werkstoffe und BauteileFraunhofer-Institut für Betriebsfestigkeit und Systemzuverlässigkeit LBFDarmstadtGermany
  3. 3.Deutsches Kunststoff-Institut (DKI)DarmstadtGermany

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