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The Willam–Warnke yield criterion is a function that is used to predict when failure will occur in concrete and other cohesive-frictional materials such as rock, soil, and ceramics. This yield criterion has the functional form
where I 1 {\displaystyle I_{1}} is the first invariant of the Cauchy stress tensor, and J 2 , J 3 {\displaystyle J_{2},J_{3}} are the second and third invariants of the deviatoric part of the Cauchy stress tensor. There are three material parameters that have to be determined before the Willam-Warnke yield criterion may be applied to predict failure.
In terms of I 1 , J 2 , J 3 {\displaystyle I_{1},J_{2},J_{3}} , the Willam-Warnke yield criterion can be expressed as
where λ {\displaystyle \lambda } is a function that depends on J 2 , J 3 {\displaystyle J_{2},J_{3}} and the three material parameters and B {\displaystyle B} depends only on the material parameters. The function λ {\displaystyle \lambda } can be interpreted as the friction angle which depends on the Lode angle. The quantity B {\displaystyle B} is interpreted as a cohesion pressure. The Willam-Warnke yield criterion may therefore be viewed as a combination of the Mohr–Coulomb and the Drucker–Prager yield criteria.