Generalized Continua Concepts in Coarse-Graining Atomistic Simulations

  • Shuozhi Xu
  • Ji Rigelesaiyin
  • Liming Xiong
  • Youping Chen
  • David L. McDowellEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 90)


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.



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

  • Shuozhi Xu
    • 1
  • Ji Rigelesaiyin
    • 2
  • Liming Xiong
    • 2
  • Youping Chen
    • 3
  • David L. McDowell
    • 4
    • 5
  1. 1.California NanoSystems Institute, University of California, Santa BarbaraSanta BarbaraUSA
  2. 2.Department of Aerospace EngineeringIowa State UniversityAmesUSA
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA
  4. 4.Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  5. 5.School of Materials Science and EngineeringGeorgia Institute of TechnologyAtlantaUSA

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