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Incorporating the Element of Stochasticity in Coarse-Grained Modeling of Materials Mechanics

  • Eric R. Homer
  • Ying Chen
  • Christopher A. Schuh
Living reference work entry

Abstract

Materials are, by their very nature, stochastic. Modeling materials across scales requires models that capture this inherent stochasticity. In this chapter, preceding a section on stochastic, coarse-grained models, we examine the elements of stochasticity and coarse-graining and the different implementations of each. Examples of the methods are also briefly discussed.

Notes

Acknowledgements

ERH was supported by the National Science Foundation under Award no. DMR-1507095. YC was supported by the National Science Foundation under Award no. DMR-1352524.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Eric R. Homer
    • 1
  • Ying Chen
    • 2
  • Christopher A. Schuh
    • 3
  1. 1.Department of Mechanical EngineeringBrigham Young UniversityProvoUSA
  2. 2.Department of Materials Science and EngineeringRensselaer Polytechnic InstituteTroyUSA
  3. 3.Department of Materials Science and EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Section editors and affiliations

  • Ying Chen
    • 1
  • Eric Homer
    • 2
  • Christopher A. Schuh
    • 3
  1. 1.Department of Materials Science and EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Mechanical EngineeringBingham Young UniversityProvoUSA
  3. 3.Department of Materials Science and EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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