Multiscale Computations of Microcracking Solids
Final rept. 1 Mar 2005-31 Mar 2009
NORTHWESTERN UNIV EVANSTON IL
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New multiscale methods have been developed for the study of microcracking and dislocations. The multiscale method for microcracking aggregates the effect of an arbitrary number of cracks at the micro level into a single equivalent crack at the macrolevel. The methodology is based on the concept of a perforated unit cell, which excludes all subdomains of the unit cell where the material loses stability in the averaging operations. We have shown that for this approach, the macro bulk material does not lose ellipticity when failure occurs. This is an important development since it avoids the ill-posedness usually associated with multiscale modeling of failure. Comparisons with direct numerical simulations show excellent accuracy. We have also developed new models for dislocations and concurrent methods that couple atomistic models with these new continuum dislocation methods. These enable dislocation dynamics in arbitrary geometries and materials to be modeled in terms of fundamental physics.
- Properties of Metals and Alloys
- Numerical Mathematics