Incrementation: Part Three

  • Robert M. Hackett


Expressions relative to incremental polar decomposition are given. The relationships between the deformation gradient and the orthogonal rotation tensor and the right and left stretches are given. From this, the expression for the incremental deformation gradient, in terms of the rotation tensor and the right stretch tensor, and their respective increments, is obtained. Since the obtained expression is approximate, correct to the first order, a correction term, the product of the two incremental terms, is added to the expression. An expression for the exact value is also given. An expression for the incremental Green-Lagrange strain, in terms of the right stretch tensor and the incremental right stretch tensor, correct to the first order, is given. A correction term, expressed as a function of the incremental right stretch tensor, is provided. A numerical example is presented to demonstrate the application of the developed incremental polar decomposition formulation.


Incremental polar decomposition Incremental deformation gradient Incremental right stretch tensor Incremental Green-Lagrange strain Correction term Numerical example 


  1. Ogden RW (1997) Non-linear elastic deformations. Dover, New YorkGoogle Scholar

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© 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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