The Bresler–Pister yield criterion 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 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 and polymeric foams. 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 !Derivation of expressions for parameters A, B, C 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 A,B,C (using Maple) gives us

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 The Etse-Willam form of the Bresler–Pister yield criterion for concrete can be expressed as where \sigma_c is the yield stress in uniaxial compression and \sigma_t is the yield stress in uniaxial tension. The GAZT yield criterion for plastic collapse of foams also has a form similar to the Bresler–Pister yield criterion and can be expressed as where \rho is the density of the foam and \rho_m is the density of the matrix material.