Abstract :
A model is presented herein for predicting the
evolution of numerous cracks on multiple length scales, the
objective of such a model being to develop the capability to
predict failure of structural components to perform their
intended tasks. Such a capability would then be useful as a
predictive tool for designing structural components so as
not to fail, but rather to succeed in performing their
intended tasks. The model developed herein is somewhat
involved, being based in continuum mechanics and thermodynamics,
but is nevertheless expected to be cost
effective (wherever sufficient accuracy permits) when
compared to more costly experimental means of determining
component life. An essential ingredient within the
context of the model is that cracks must develop on widely
differing length scales. Where this is observed to occur in
nature, which is surprisingly often, there are potential
simplifications over more generally described but practically
untenable approaches, that can lead to (at least partly)
computational multiscale algorithms capable of assimilating
failure due to multiple cracking with a high degree of
accuracy. The model presented herein will be briefly described
within a mathematical framework, and an example
problem will be presented that is representative of certain
currently relevant technologies.
