Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations

Reference work entry


In this chapter, we review two crystal plasticity methodologies based on Green’s functions for the prediction of microstructure-property relations in polycrystalline aggregates. The first, known as the viscoplastic self-consistent (VPSC) formulation, is a mean-field theory. The second, known as the viscoplastic fast Fourier transform-based (VPFFT) formulation, is a full-field method. The assumptions and main equations of these Green’s function-based crystal plasticity formulations are presented using a unified notation, pointing out their similarities and differences and cross-validating their predictions.



This chapter contains results of the author’s collaboration with C.N. Tomé, P. Ponte Castañeda, R. Brenner, O. Castelnau, P. Gilormini, M. Zecevic, M. Knezevic, and R.J. McCabe. Parts of this work were supported by Los Alamos National Laboratory’s Laboratory-Directed Research and Development (LDRD) program, project 20180441ER.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Fluid Dynamics and Solid Mechanics, T-3 Group, Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

Section editors and affiliations

  • Wei Cai
    • 1
  • Somnath Ghosh
    • 2
  1. 1.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.Dept. of Mechanical EngineeringJohns Hopkins UniveristyBaltimoreUSA

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