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Optimization-Based Coupling of Local and Nonlocal Models: Applications to Peridynamics

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Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Abstract

Nonlocal continuum theories such as peridynamics (Silling and Lehoucq, 2010) and physics-based nonlocal elasticity (Di Paola et al., 2009) can capture strong nonlocal effects due to long-range forces at the mesoscale or microscale. For problems where these effects cannot be neglected, nonlocal models are more accurate than classical partial differential equations (PDEs) that only consider interactions due to contact. However, the improved accuracy of nonlocal models comes at the price of a computational cost that is significantly higher than that of PDEs.

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Acknowledgements

This material is based upon work supported by the US DOE’s Laboratory Directed Research and Development (LDRD) program at Sandia National Laboratories and the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research. Part of this research was carried under the auspices of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4). Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. SAND2017-3003 B.

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Authors and Affiliations

  1. Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA

    Marta D’Elia, Pavel Bochev, David Littlewood & Mauro Perego

Authors
  1. Marta D’Elia
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  2. Pavel Bochev
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  3. David Littlewood
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  4. Mauro Perego
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Correspondence to Marta D’Elia .

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Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, USA

    George Z. Voyiadjis

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D’Elia, M., Bochev, P., Littlewood, D., Perego, M. (2018). Optimization-Based Coupling of Local and Nonlocal Models: Applications to Peridynamics. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-22977-5_31-1

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  • DOI: https://doi.org/10.1007/978-3-319-22977-5_31-1

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  • Print ISBN: 978-3-319-22977-5

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