 Bresler Pister yield criterion
The BreslerPister yield criterion [Bresler, B. and Pister, K.S., (19858), Strength of concrete under combined stresses, ACI Journal, vol. 551, no. 9, pp. 321345.] 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 DruckerPrager 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. 12091214.] and polymeric foams [Kim, Y. and Kang, S., (2003), Development of experimental method to characterize pressuredependent yield criteria for polymeric foams. Polymer Testing, vol. 22, no. 2, pp. 197202.] .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:$egin\{align\}\; B\; =\; left(cfrac\{sigma\_tsigma\_c\}\{sqrt\{3\}(sigma\_t+sigma\_c)\}\; ight)\; left(cfrac\{4sigma\_b^2\; \; sigma\_b(sigma\_c+sigma\_t)\; +\; sigma\_csigma\_t\}\{4sigma\_b^2\; +\; 2sigma\_b(sigma\_tsigma\_c)\; \; sigma\_csigma\_t\}\; ight)\; \backslash \; C\; =\; left(cfrac\{1\}\{sqrt\{3\}(sigma\_t+sigma\_c)\}\; ight)\; left(cfrac\{sigma\_b(3sigma\_tsigma\_c)\; 2sigma\_csigma\_t\}\{4sigma\_b^2\; +\; 2sigma\_b(sigma\_tsigma\_c)\; \; sigma\_csigma\_t\}\; ight)\; \backslash \; A\; =\; cfrac\{sigma\_c\}\{sqrt\{3\; +\; c\_1sigma\_c\; c\_2sigma\_c^2\; end\{align\}$
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Alternative forms of the BreslerPister yield criterion
In terms of the equivalent stress ($sigma\_e$) and the mean stress ($sigma\_m$), the BreslerPister 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 EtseWillam [Etse, G. and Willam, K., (1994), Fracture energy formulation for inelastic behavior of plain concrete, Journal of Engineering Mechanics, vol. 120, no. 9, pp. 19832011.] form of the BreslerPister yield criterion for concrete can be expressed as:$sqrt\{J\_2\}\; =\; cfrac\{1\}\{sqrt\{3~I\_1\; \; cfrac\{1\}\{2sqrt\{3~left(cfrac\{sigma\_t\}\{sigma\_c^2sigma\_t^2\}\; ight)~I\_1^2$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 BreslerPister yield criterion and can be expressed as:$sqrt\{J\_2\}\; =\; egin\{cases\}\; cfrac\{1\}\{sqrt\{3~sigma\_t\; \; 0.03sqrt\{3\}cfrac\{\; ho\}\{\; ho\_m~sigma\_t\}~I\_1^2\; \backslash \; cfrac\{1\}\{sqrt\{3~sigma\_c\; +\; 0.03sqrt\{3\}cfrac\{\; ho\}\{\; ho\_m~sigma\_c\}~I\_1^2\; end\{cases\}$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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