Bresler Pister yield criterion

The Bresler-Pister yield criterion [Bresler, B. and Pister, K.S., (19858), 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:$sqrt\{J\_2\}\; =\; A\; +\; B~I\_1\; +\; C~I\_1^2$where $I\_1$ is the first invariant of the Cauchy stress, $J\_2$ is the second invariant of the deviatoric part of the Cauchy stress, and $A,\; B,\; C$ are material constants.

Yield criteria of this form have also been used for polypropylene [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.] 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 $A,B,C$ have to be chosen with care for reasonably shaped yield surfaces. If $sigma\_c$ is the yield stress in uniaxial compression, $sigma\_t$ is the yield stress in uniaxial tension, and $sigma\_b$ is the yield stress in biaxial compression, the parameters can be expressed as:

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Alternative forms of the Bresler-Pister yield criterion

In terms of the equivalent stress ($sigma\_e$) and the mean stress ($sigma\_m$), the Bresler-Pister yield criterion can be written as:$sigma\_e\; =\; a\; +\; b~sigma\_m\; +\; c~sigma\_m^2\; ~;~~\; sigma\_e\; =\; sqrt\{3J\_2\}\; ~,~~\; sigma\_m\; =\; I\_1/3\; ~.$

The Etse-Willam [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.] form of the Bresler-Pister yield criterion for concrete can be expressed as:$sqrt\{J\_2\}\; =\; cfrac\{1\}\{sqrt\{3~I\_1\; -\; cfrac\{1\}\{2sqrt\{3~left(cfrac\{sigma\_t\}\{sigma\_c^2-sigma\_t^2\}\; ight)~I\_1^2$where $sigma\_c$ is the yield stress in uniaxial compression and $sigma\_t$ is the yield stress in uniaxial tension.

The GAZT yield criterion [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.] for plastic collapse of foams also has a form similar to the Bresler-Pister yield criterion and can be expressed as:where $ho$ is the density of the foam and $ho\_m$ is the density of the matrix material.

References

See also

*Yield surface
*Yield (engineering)
*Plasticity (physics)