Failure detection of smeared crack formulations

The smeared-crack approach of strain-softening is a popular engineering concept for the numerical simulation of tensile failure processes in concrete and rock. Despite numerous publications on the equivalent constitutive formulation of cracked solids, very little is known about the failure prediction of the smeared crack approach, for proportional and non-proportional loading histories. Two failure indicators are examined at the constitutive level in order to investigate the differences between the fixed and rotating crack concepts. The directional stiffness parameter is used to detect singularities of the tangent stiffness of the smeared crack formulation. This instability indicator signals continuous failure due to material branching. In contrast, the localization indicator is used to signal the formation of weak discontinuities associated with singularities of the localization tensor, and thus provides further insight into the incipient faliure process. This faliure diagnostics indicated the advent of kinematic degradation from a continuum into a discontinuum. In the present paper both failure indicators will be investigated for two loading scenarios involving pure shear and combined tension with shear.