Constitutive Equations for Concrete in Failure State

For concrete, two simple three‐dimensional failure conditions depending on the first invariant of the stress tensor as well as on the second and third invariant of the stress deviator tensor with two and four material parameters and a nonassociated flow rule are proposed in this paper. First, the basic equations like stress deviator tensor and invariants of the stress tensor and a stress deviator tensor are introduced. Then the proposed failure conditions are presented in a geometrically interpretable form. In the next step, the material parameters are determined by fitting the failure conditions to several test results. Finally, a nonassociated flow rule is introduced. An example illustrates the usefulness of the proposed constitutive equations in the failure state.