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Journal of Engineering Mechanics ASCE, 124 (1998), 842-851.
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ANALYSIS OF ROTATING CRACK MODEL

Milan Jirásek and
Thomas Zimmermann

Swiss Federal Institute of Technology

LSC
-DGC,
EPFL,
1015 Lausanne,
Switzerland

### Abstract

The paper extends the standard rotating crack model to a formulation
with multiple orthogonal cracks. The corresponding stress evaluation
algorithm is described, and a new derivation of the tangent stiffness
matrix is presented. The derivation is extended to the case of equal
principal strains, in which the classical formula for the tangent
shear modulus fails. A condition excluding snapback of the stress-strain
diagram for an arbitrary loading path is derived.
Attention then shifts to stress locking, meaning here spurious stress
transfer across widely opening cracks. The problem is illustrated
by numerical examples. The mechanism of stress transfer is thoroughly analyzed,
and the source of locking is detected.
A remedy and extension of the model to a nonlocal formulation
will be described in a separate paper.
###
Summary and Conclusions

The rotating crack model has been extended to a formulation with multiple
orthogonal cracks. If the stress-cracking strain curve is not too steep,
the response of the model is unique in the sense that, for any
strain increment, only one combination of loading/unloading assumptions
for the cracking directions leads to an admissible solution.
In certain situations, the rotating crack model (even with a single crack)
fails to give a consistently defined response. This happens if two or three
principal strains are equal while the strain histories in the corresponding
principal directions are different. If the strains are equal only at one
isolated time instant, the tangent shear stiffness has a singularity
but the problem can still be handled numerically. However, if the strains
remain equal for a certain period of time,
the generated stress cannot be consistently
derived from the basic assumptions of the model.

Misalignment of the macroscopic crack (cracking band) direction with the sides
of the finite elements leads to spurious stress transfer across a widely
opening crack, which might produce a completely unrealistic structural
response. The source of this type of stress locking is the normal stress
in the lateral principal direction. Due to misalignment of the principal
axes with the overall crack direction, the lateral stress contributes to
internal forces orthogonal to the macroscopic crack.
Spurious cohesive stress transfer across the cracking band induces
secondary cracking, and it might even affect the final failure pattern.

Spurious stress transfer can be alleviated by combining
the rotating crack model with a scalar damage model.

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

EPFL /
24 August 1998 /
Milan.Jirasek@epfl.ch