International Journal of Solids and Structures, 35 (1998), 4133-4145.
NONLOCAL MODELS FOR DAMAGE AND FRACTURE:
COMPARISON OF APPROACHES
Swiss Federal Institute of Technology
The paper analyzes nonlocal constitutive models
used in simulations of damage and fracture processes in quasibrittle
A number of nonlocal formulations found in the literature
are classified according to the type of variable subjected to nonlocal
averaging. Analytical and numerical solutions of a simple one-dimensional
localization problem are presented. It is shown that
some of the formulations inevitably lead to residual stresses at even
very late stages
of the deformation process and, consequently, they are not capable of
modeling complete separation in a widely open macroscopic crack.
The mechanisms leading to this specific type of stress locking are explained
based on a theoretical analysis of the nonlocal constitutive equations.
It is also pointed out that the nonlocal approach distorts the shape of
the stress-strain diagram, which has to be taken into account when
designing an appropriate local softening law.
It has been shown that certain nonlocal formulations are inherently incapable
of reproducing the entire material degradation process up to
Unless we are interested only in the response at the onset of localization,
models that exhibit the special type of stress locking described in the
paper should be avoided.
Load-displacement diagrams of concrete specimens tested under direct tension
typically exhibit a relatively steep drop immediately after the peak load,
followed by a long tail. The shape of
diagrams obtained with a nonlocal model using a linear local softening law
are not at all realistic. More reasonable response is produced by an
exponential local softening law.
Due to its limited extent, the
present study has dealt exclusively with damage-type models that unload
to the origin. Another sound nonlocal approach can be developed in the
context of plasticity. Comparison of nonlocal damage and plasticity theories
and analysis of the structure and evolution of the process zone shall be
presented in a separate paper.
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13 July 1998 /