Incrementation: Part Two

  • Robert M. Hackett


While rate equations are exact, the matching (linearized) incremental equations are approximations. It is very important that approximations do not lead to results that differ very much from exact solutions. Incremental formulations for both Green-Lagrange and Almansi strain are given, based upon their corresponding rate equations. Incremental Green-Lagrange and Almansi deviatoric strain expressions are determined, also based upon their corresponding rate equations. The respective error expressions, for incremental Green-Lagrange and Almansi strains and for incremental Green-Lagrange and Almansi deviatoric strains, based upon comparisons with exact expressions are given. A numerical example demonstrating errors associated with incremental strain formulations is presented.


Incremental strain Incremental deviatoric strain Rate equations Error expressions Numerical example 


  1. Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New YorkGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Robert M. Hackett
    • 1
  1. 1.Department of Civil EngineeringThe University of MississippiUniversityUSA

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