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U.S. Department of Energy
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ASCEND: Asymptotically compatible strong form foundations for nonlocal discretization

Technical Report ·
DOI:https://doi.org/10.2172/1820006· OSTI ID:1820006

Nonlocal models naturally handle a range of physics of interest to SNL, but discretization of their underlying integral operators poses mathematical challenges to realize the accuracy and robustness commonplace in discretization of local counterparts. This project focuses on the concept of asymptotic compatibility, namely preservation of the limit of the discrete nonlocal model to a corresponding well-understood local solution. We address challenges that have traditionally troubled nonlocal mechanics models primarily related to consistency guarantees and boundary conditions. For simple problems such as diffusion and linear elasticity we have developed complete error analysis theory providing consistency guarantees. We then take these foundational tools to develop new state-of-the-art capabilities for: lithiation-induced failure in batteries, ductile failure of problems driven by contact, blast-on-structure induced failure, brittle/ductile failure of thin structures. We also summarize ongoing efforts using these frameworks in data-driven modeling contexts. This report provides a high-level summary of all publications which followed from these efforts.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
DOE Contract Number:
NA0003525
OSTI ID:
1820006
Report Number(s):
SAND2021-11288; 699333
Country of Publication:
United States
Language:
English

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