Bresler–Pister yield criterion

The Bresler–Pister yield criterion[1] is a function that was originally devised to predict the strength of concrete under multiaxial stress states. This yield criterion is an extension of the Drucker–Prager yield criterion and can be expressed on terms of the stress invariants as

where is the first invariant of the Cauchy stress, is the second invariant of the deviatoric part of the Cauchy stress, and are material constants.

Yield criteria of this form have also been used for polypropylene[2] and polymeric foams.[3]

The parameters have to be chosen with care for reasonably shaped yield surfaces. If is the yield stress in uniaxial compression, is the yield stress in uniaxial tension, and is the yield stress in biaxial compression, the parameters can be expressed as

Figure 1: View of the three-parameter Bresler–Pister yield surface in 3D space of principal stresses for
Figure 2: The three-parameter Bresler–Pister yield surface in the -plane for
Figure 3: Trace of the three-parameter Bresler–Pister yield surface in the -plane for

Alternative forms of the Bresler-Pister yield criterion

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In terms of the equivalent stress ( ) and the mean stress ( ), the Bresler–Pister yield criterion can be written as

 

The Etse-Willam[4] form of the Bresler–Pister yield criterion for concrete can be expressed as

 

where   is the yield stress in uniaxial compression and   is the yield stress in uniaxial tension.

The GAZT yield criterion[5] for plastic collapse of foams also has a form similar to the Bresler–Pister yield criterion and can be expressed as

 

where   is the density of the foam and   is the density of the matrix material.

References

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  1. ^ Bresler, B. and Pister, K.S., (1985), Strength of concrete under combined stresses, ACI Journal, vol. 551, no. 9, pp. 321–345.
  2. ^ Pae, K. D., (1977), The macroscopic yield behavior of polymers in multiaxial stress fields, Journal of Materials Science, vol. 12, no. 6, pp. 1209-1214.
  3. ^ Kim, Y. and Kang, S., (2003), Development of experimental method to characterize pressure-dependent yield criteria for polymeric foams. Polymer Testing, vol. 22, no. 2, pp. 197-202.
  4. ^ Etse, G. and Willam, K., (1994), Fracture energy formulation for inelastic behavior of plain concrete, Journal of Engineering Mechanics, vol. 120, no. 9, pp. 1983-2011.
  5. ^ Gibson, L. J., Ashby, M. F., Zhang, J., and Triantafillou, T. C. (1989). Failure surfaces for cellular materials under multiaxial loads. I. Modelling. International Journal of Mechanical Sciences, vol. 31, no. 9, pp. 635–663.

See also

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