Journal of Engineering Mechanics ASCE, 128 (2002), 1119-1149.
NONLOCAL INTEGRAL FORMULATIONS OF PLASTICITY AND DAMAGE: SURVEY OF PROGRESS
Zdenek P. Bazant
Northwestern University, Evanston, IL
Swiss Federal Institute of Technology
LSC - ENAC,
Modeling of the evolution of distributed damage such as microcracking,
void formation and softening frictional slip necessitates strain-softening
constitutive models. The nonlocal continuum concept has emerged as an effective
means for regularizing the boundary value problems with strain softening,
capturing the size effects and avoiding spurious localization that gives
rise to pathological mesh sensitivity in numerical computations.
A great variety of nonlocal models have appeared during the last two decades.
This paper reviews the progress in the nonlocal models of integral type,
and discusses their physical justifications, advantages and numerical applications.
Concluding Thoughts and Future Path
While two decades ago strain-softening damage models were regarded as controversial,
the nonlocal concept has by now rendered them respectable and their use
realistic. Nonlocality is now generally accepted as the proper approach
for regularizing the boundary problems of continuum damage mechanics, for
capturing the size effect, and for avoiding spurious localization giving
rise to pathological mesh sensitivity.
The last two decades of research gave birth to a wide variety of nonlocal
models, with differences that are not quite justified by diversity in the
types of materials and practical application. One may now expect a period
of crystalization in which many artificially complex or oversimplified
models will fade, being recognized as superfluous, and only a few will
gain a permanent pedestal in the pantheon of knowledge.
Speculations though could be made in this regard, they are better left
to future scrutiny. The strength of each model's pedestal will be
judged by physics of the microstucture, and the permanence of that pedestal
will be decided by passage of each model through the sieve of practical
applications. Doubtless much further research lies ahead, and polemics
will enliven the path into the future.
The complete paper can be downloaded in an electronic form: PostScript,
EPFL / 16 October 2002 / firstname.lastname@example.org