Internal report 97/01, LSC-DGC, EPFL, January 1997

ROTATING CRACK MODEL
WITH TRANSITION TO SCALAR DAMAGE:
I. Local Formulation, II. Nonlocal Formulation and Adaptivity

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 (appearance of spurious kinematic modes). The first part of the present study analyzes the sources of stress locking and 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 second part of the report extends the model to a nonlocal formulation, which not only acts as a powerful localization limiter but also alleviates mesh-induced directional bias. A special type of material instability arising due to negative shear stiffness terms in the rotating crack model is analyzed and a remedy based on transition to the scalar damage model is suggested. Then, a simple mesh-adaptive technique suitable for problems with localized cracking is proposed. The technique combines the Zienkiewicz-Zhu error estimator with a criterion based on crack opening. The performance of the present approach is demonstrated on three examples ranging from the simple three-point bending test to analysis of a cracking gravity dam.

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 rotating crack model with transition to scalar damage 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.

Furthermore, a simple adaptive strategy combining the Zienkiewicz-Zhu error estimator with a criterion based on the crack opening has been proposed and integrated into an environment for automated mesh design. Such an approach can greatly facilitate analysis of practical problems, as has been demonstrated by several examples.


Please send me an email if you wish to receive the complete report.


EPFL / 29 November 1996 / Milan.Jirasek@epfl.ch