Bresler–Pister yield criterion

The Bresler–Pister yield criterion[1] 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

is the second invariant of the deviatoric part of the Cauchy stress, and

Yield criteria of this form have also been used for polypropylene[2] and polymeric foams.

have to be chosen with care for reasonably shaped yield surfaces.

is the yield stress in uniaxial compression,

is the yield stress in uniaxial tension, and

is the yield stress in biaxial compression, the parameters can be expressed as 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

(using Maple) gives us In terms of the equivalent stress (

), the Bresler–Pister yield criterion can be written as The Etse-Willam[4] form of the Bresler–Pister yield criterion for concrete can be expressed as where

is the yield stress in uniaxial compression and

is the yield stress in uniaxial tension.

The GAZT yield criterion[5] for plastic collapse of foams also has a form similar to the Bresler–Pister yield criterion and can be expressed as where

is the density of the matrix material.

Figure 1: View of the three-parameter Bresler–Pister yield surface in 3D space of principal stresses for
Figure 2: The three-parameter Bresler–Pister yield surface in the -plane for
Figure 3: Trace of the three-parameter Bresler–Pister yield surface in the -plane for