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{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: egin{align} B = & left(cfrac{sigma_t-sigma_c}{sqrt{3}(sigma_t+sigma_c)} ight) left(cfrac{4sigma_b^2 - sigma_b(sigma_c+sigma_t) + sigma_csigma_t}{4sigma_b^2 + 2sigma_b(sigma_t-sigma_c) - sigma_csigma_t} ight) \ C = & left(cfrac{1}{sqrt{3}(sigma_t+sigma_c)} ight) left(cfrac{sigma_b(3sigma_t-sigma_c) -2sigma_csigma_t}{4sigma_b^2 + 2sigma_b(sigma_t-sigma_c) - sigma_csigma_t} ight) \ A = & cfrac{sigma_c}{sqrt{3 + c_1sigma_c -c_2sigma_c^2 end{align}

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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: sqrt{J_2} = egin{cases} cfrac{1}{sqrt{3~sigma_t - 0.03sqrt{3}cfrac{ ho}{ ho_m~sigma_t}~I_1^2 \ -cfrac{1}{sqrt{3~sigma_c + 0.03sqrt{3}cfrac{ ho}{ ho_m~sigma_c}~I_1^2 end{cases} 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)


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