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Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, October 26, 2018 - 12:00 to 13:00

Location:

STAG 160

Event Link:

Guest Speaker:

Institution:

Intel and Numerical Solutions, Inc.

Abstract:

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.