The Bresler–Pister yield criterionBresler, B. and Pister, K.S., (1985), Strength of concrete under combined stresses, ACI Journal, vol. 551, no. 9, pp. 321–345. 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 polypropylenePae, K. D., (1977), The macroscopic yield behavior of polymers in multiaxial stress fields, Journal of Materials Science, vol. 12, no. 6, pp. 1209-1214. and polymeric foams.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.
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
{| class="toccolours collapsible collapsed" width="60%" style="text-align:left" !Derivation of expressions for parameters A, B, C |- |The Bresler–Pister yield criterion in terms of the principal stresses is
If is the yield stress in uniaxial tension, then
If is the yield stress in uniaxial compression, then
If is the yield stress in equibiaxial compression, then
Solving these three equations for (using Maple) gives us
Alternative forms of the Bresler-Pister yield criterion In terms of the equivalent stress () and the mean stress (), the Bresler–Pister yield criterion can be written as
The Etse-WillamEtse, 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. 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 criterionGibson, 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. 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
See also Yield surface Yield (engineering) Plasticity (physics)