In many applications the resolution of mesoscale heterogeneities
remain a significant hurdle to robust and reliable predictive simulations.
In particular, while material variability at the grain scale plays a fundamental
role in material failure, capturing mechanisms at this scale is often computationally
intractable due to the resolution required. Multiscale methods aim to overcome these
difficulties through judicious choice of subscale problem and a robust manner of passing
information between scales. The perdiynamic theory of continuum mechanics presents
an advantage in this endeavor by providing a single model valid at a wide range of scales,
as well as natural modeling of material failure.
The multiscale finite element method seeks to enrich engineering scale
simulations with lower scale heterogeneity by solving lower scale
problems on coarse elements to produce enriched multiscale basis functions.
In this work we present the first work towards application of the multiscale
finite element method to the nonlocal peridynamic theory of solid mechanics.
Additionally, we present a framework for analysis of multiscale finite element
methods for models, local or nonlocal, satisfying minimal assumptions. Finally, we
present preliminary results on a mixed-locality finite element method
coupling local and nonlocal models across scales.