ASCEND: Asymptotically compatible strong form foundations for nonlocal discretization

Technical Report · 01 September 2021

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

Trask, Nathaniel ^[1]; D'Elia, Marta ^[1]; Littlewood, David ^[1]; Silling, Stewart ^[1]; Trageser, Jeremy ^[1]; Tupek, Michael ^[1]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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 Laboratories (SNL-NM), Albuquerque, NM (United States); Sandia National Laboratories (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

Related Subjects

97 MATHEMATICS AND COMPUTING