Scalar damage model for concrete without explicit evolution law

Based on the fact that for an isotropic material model the elastic predictor and the projected stress tensors have the same eigenvectors, it is shown that the scalar damage can be obtained directly from the projection algorithm. This eliminates the difficulty of a proper definition of equivalent strain which serves as a driving force for evolution of damage in concrete. Moreover, if eigenvectors are known it is not more necessary to use invariants of the stress tensor for the formulation of loading surface. In the present model the loading surface is represented in the polynomial form. This has two advantages: (i) it automatically fulfils C1 continuity and (ii) plane stress formulation is achieved by simply setting the third stress to zero. The performance of the model is illustrated on example of a mixed-mode fracture of concrete. It is shown that for the present example the model prediction strongly depends on the choice of the stress degradation law.