Journal of Engineering Mechanics ASCE, 124 (1998), 277-284.

## ROTATING CRACK MODEL WITH TRANSITION TO SCALAR DAMAGE

Milan Jirásek and Thomas Zimmermann
Swiss Federal Institute of Technology
LSC -DGC, EPFL, 1015 Lausanne, Switzerland

### Abstract

Traditional smeared-crack models for concrete fracture are known to suffer by stress locking (meaning here spurious stress transfer across widely opening cracks), mesh-induced directional bias, and possible instability at late stages of the loading process. The present paper develops a new model based on a combination of the standard rotating crack model with the scalar damage concept. The combined model keeps the anisotropic character of the rotating crack but it does not transfer spurious stresses across widely open cracks. This is documented by several examples. The model is then extended to a nonlocal formulation, which not only acts as an efficient localization limiter but also alleviates mesh-induced directional bias. Transition to damage can prevent a special type of material instability arising due to negative shear stiffness terms in the rotating crack model.

### Summary and Conclusions

A model combining the advantages of the standard rotating crack model and the isotropic damage model has been developed. The new rotating crack model with transition to scalar damage (RC-SD) keeps the anisotropic character of the RCM but it does not transfer spurious stresses across widely open cracks. The model has been tested on several examples, and it seems to provide reasonable results if the transition from rotating crack to damage takes place at the point where the bilinear stress-separation curve changes its slope.

The RC-SD model has been extended to a nonlocal formulation. Transition to damage not only removes spurious stress transfer across widely opening cracks but also prevents the model from losing material stability due to negative shear stiffness terms that may arise in the standard RCM formulation. The nonlocal formulation substantially alleviates mesh-induced directional bias.

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EPFL / 13 December 1996 / Milan.Jirasek@epfl.ch