Similarity measures for identifying material parameters from hysteresis loops using inverse analysis

  • Charles F. JekelEmail author
  • Gerhard Venter
  • Martin P. Venter
  • Nielen Stander
  • Raphael T. Haftka
Original Research


Sum-of-square based error formulations may be difficult to implement on an inverse analysis consisting of multiple tension-compression hysteresis loops. Five alternative measures of similarity between curves are investigated as useful tools to help identify parameters from hysteresis loops with inverse analyses. A new algorithm is presented to calculate the area between curves. Four additional methods are presented from literature, which include the Partial Curve Mapping value, discrete Fréchet distance, Dynamic Time Warping, and Curve Length approach. These similarity measures are compared by solving a non-linear regression problem resembling a single load-unload cycle. The measures are then used to solve more complicated inverse analysis, where material parameters are identified for a kinematic hardening transversely anisotropic material model. The inverse analysis finds material parameters such that a non-linear FE model reproduces the behavior from five experimental hysteresis loops. Each method was shown to find useful parameters for these problems, and should be considered a viable alternative when sum-of-square based methods may be difficult to implement. It is important to consider multiple similarity measures in cases when it is impossible to obtain a perfect match.


Inverse analysis Material parameter identification Hysteresis loops Tension-compression response Similarity measures Goodness of fit 


Funding Information

Charles F. Jekel has received the following funding for his PhD research which has supported this work: University of Florida Graduate Preeminence Award, U.S. Department of Veterans Affairs Educational Assistance, and Stellenbosch University Merritt Bursary. Nielen Stander is a senior scientist at Livermore Software Technology Corporation.

Compliance with Ethical Standards

Conflict of interests

The authors declare that there is no conflict of interest.


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Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  • Charles F. Jekel
    • 1
    Email author
  • Gerhard Venter
    • 2
  • Martin P. Venter
    • 2
  • Nielen Stander
    • 3
  • Raphael T. Haftka
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Mechanical and Mechatronic EngineeringStellenbosch UniversityMatielandSouth Africa
  3. 3.Livermore Software Technology CorporationLivermoreUSA

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