# Bresler Pister yield criterion

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:$sqrt\left\{J_2\right\} = A + B~I_1 + C~I_1^2$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:$sigma_e = a + b~sigma_m + c~sigma_m^2 ~;~~ sigma_e = sqrt\left\{3J_2\right\} ~,~~ sigma_m = I_1/3 ~.$

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:$sqrt\left\{J_2\right\} = cfrac\left\{1\right\}\left\{sqrt\left\{3~I_1 - cfrac\left\{1\right\}\left\{2sqrt\left\{3~left\left(cfrac\left\{sigma_t\right\}\left\{sigma_c^2-sigma_t^2\right\} ight\right)~I_1^2$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

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

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