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Generalized Continua Concepts in Coarse-Graining Atomistic Simulations

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Book cover Generalized Models and Non-classical Approaches in Complex Materials 2

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 90))

Abstract

Generalized continuum mechanics (GCM) has attracted increased attention in the context of multiscale materials modeling, an example of which is a bottom-up GCM model, called the atomistic field theory (AFT). Unlike most other GCM models, AFT views a crystalline material as a continuous collection of lattice points; embedded within each point is a unit cell with a group of discrete atoms. As such, AFT concurrently bridges the discrete and continuous descriptions of materials, two fundamentally different viewpoints. In this chapter, we first review the basics of AFT and illustrate how it is realized through coarse-graining atomistic simulations via a concurrent atomistic-continuum (CAC) method. Important aspects of CAC, including its advantages relative to other multiscale methods, code development, and numerical implementations, are discussed. Then, we present recent applications of CAC to a number of metal plasticity problems, including static dislocation properties, fast moving dislocations and phonons, as well as dislocation/grain boundary interactions. We show that, adequately replicating essential aspects of dislocation fields at a fraction of the computational cost of full atomistics, CAC is established as an effective tool for coarse-grained modeling of various nano/micro-scale thermal and mechanical problems in a wide range of monatomic and polyatomic crystalline materials.

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Acknowledgements

These results are in part based upon work supported by the National Science Foundation as a collaborative effort between Georgia Tech (CMMI-1232878) and University of Florida (CMMI-1233113). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors thank Dr. Jinghong Fan, Dr. Qian Deng, Dr. Shengfeng Yang, Dr. Xiang Chen, Mr. Rui Che, and Mr. Weixuan Li for helpful discussions, Mr. Kevin Chu for building the Python scripting interface in PyCAC, and Dr. Aleksandr Blekh for arranging execution of PyCAC via MATIN. The work of SX was supported in part by Georgia Tech Institute for Materials and in part by the Elings Prize Fellowship in Science offered by the California NanoSystems Institute (CNSI) on the UC Santa Barbara campus. SX also acknowledges support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1121053). LX acknowledges the support from the Department of Energy, Office of Basic Energy Sciences under Award Number DE-SC0006539. The work of LX was also supported in part by the National Science Foundation under Award Number CMMI-1536925. DLM is grateful for the additional support of the Carter N. Paden, Jr. Distinguished Chair in Metals Processing. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575.

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Authors and Affiliations

  1. California NanoSystems Institute, University of California, Santa Barbara, Santa Barbara, CA, 93106-6105, USA

    Shuozhi Xu

  2. Department of Aerospace Engineering, Iowa State University, Ames, IA, 50011, USA

    Ji Rigelesaiyin & Liming Xiong

  3. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611-6250, USA

    Youping Chen

  4. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405, USA

    David L. McDowell

  5. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0245, USA

    David L. McDowell

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  1. Shuozhi Xu
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  2. Ji Rigelesaiyin
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  3. Liming Xiong
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  4. Youping Chen
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  5. David L. McDowell
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Correspondence to David L. McDowell .

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Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Joël Pouget

  3. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Martine Rousseau

  4. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Bernard Collet

  5. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Thomas Michelitsch

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Xu, S., Rigelesaiyin, J., Xiong, L., Chen, Y., McDowell, D.L. (2018). Generalized Continua Concepts in Coarse-Graining Atomistic Simulations. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 2. Advanced Structured Materials, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-77504-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-77504-3_12

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