Internal report 97/01, LSC-DGC, EPFL, January 1997
ROTATING CRACK MODEL
Milan Jirásek and
WITH TRANSITION TO SCALAR DAMAGE:
I. Local Formulation, II. Nonlocal Formulation and Adaptivity
Swiss Federal Institute of Technology
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
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
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.
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29 November 1996 /