Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2018, Article ID 1895208, 11 pages
https://doi.org/10.1155/2018/1895208
Research Article

Identifying Elastic and Viscoelastic Material Parameters by Means of a Tikhonov Regularization

1Saarland University, 66041 Saarbrücken, Germany
2Department of Mathematics, Saarland University, 66041 Saarbrücken, Germany
3Mathematical Image Analysis Group, Saarland University, 66041 Saarbrücken, Germany

Correspondence should be addressed to Thomas Schuster; ed.bs-inu.mun@retsuhcs.samoht

Received 20 July 2017; Revised 8 December 2017; Accepted 10 January 2018; Published 18 February 2018

Academic Editor: Mohsen Asle Zaeem

Copyright © 2018 Stefan Diebels et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Baaser, C. Hopmann, and A. Schobel, “Reformulation of strain invariants at incompressibility,” Archive of Applied Mechanics, vol. 83, no. 2, pp. 273–280, 2013. View at Publisher · View at Google Scholar · View at Scopus
  2. H. Baaser and R. Noll, Simulation von Elastomerbauteilen: Materialmodelle und Versuche zur Parameterbestimmung, dVM-Tag Elastomere, 2009.
  3. H. Baaser, A. Schobel, W. Michaeli, and U. Masberg, “Vergleich von äquibiaxialen Prüfständen zur Kalibrierung von Werkstoffmodellen,” KGK. Kautschuk, Gummi, Kunststoffe, vol. 64, no. 5, pp. 20–24, 2011. View at Google Scholar
  4. M. Johlitz and S. Diebels, “Characterisation of a polymer using biaxial tension tests. Part I: hyperelasticity,” Archive of Applied Mechanics, vol. 81, no. 10, pp. 1333–1349, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Seibert, T. Scheffer, and S. Diebels, “Biaxial testing of elastomers—experimental setup, measurement and experimental optimisation of specimen's shape,” Technische Mechanik, vol. 34, no. 2, pp. 72–89, 2014. View at Google Scholar
  6. S. Cooreman, D. Lecompte, H. Sol, J. Vantomme, and D. Debruyne, “Identification of mechanical material behavior through inverse modeling and DIC,” Experimental Mechanics, vol. 48, no. 4, pp. 421–433, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. N. Trabelsi, Z. Yosibash, C. Wutte, P. Augat, and S. Eberle, “Patient-specific finite element analysis of the human femura double-blinded biomechanical validation,” Journal of Biomechanics, vol. 44, no. 9, pp. 1666–1672, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Klinge, “Inverse analysis for multiphase nonlinear composites with random microstructure,” International Journal for Multiscale Computational Engineering, vol. 10, no. 4, pp. 361–373, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Klinge, “Parameter identification for two-phase nonlinear composites,” Computers & Structures, vol. 108, pp. 118–124, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Klinge and P. Steinmann, “Inverse analysis for heterogeneous materials and its application to viscoelastic curing polymers,” Computational Mechanics, vol. 55, no. 3, pp. 603–615, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. D. Miedzińska, T. Niezgoda, and R. Gieleta, “Numerical and experimental aluminum foam microstructure testing with the use of computed tomography,” Computational Materials Science, vol. 64, pp. 90–95, 2012. View at Publisher · View at Google Scholar · View at Scopus
  12. N. Koprowski-Theiß, Kompressible, viskoelastische Werkstoffe: Experimente, Modellierung und FE-Umsetzung, Dissertation, Universität des Saarlandes, 2011.
  13. I. Rechenberg, Evolutionsstrategie ’94, Werkstatt Bionik und Evolutionstechnik, Frommann-Holzboog, 1994.
  14. R. M. Lewis and V. Torczon, “Pattern search algorithms for bound constrained minimization,” SIAM Journal on Optimization, vol. 9, no. 4, pp. 1082–1099, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. V. Torczon, “On the convergence of pattern search algorithms,” SIAM Journal on Optimization, vol. 7, no. 1, pp. 1–25, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. A. Nelder and R. Mead, “A simplex method for function minimization,” The Computer Journal, vol. 7, no. 4, pp. 308–313, 1965. View at Publisher · View at Google Scholar
  17. A. K. Louis, Inverse und schlecht gestellte Probleme, Teubner, Stuttgart, Germany, 1989.
  18. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  19. A. Rieder, Keine Probleme mit Inversen Problemen, Vieweg, Wiesbaden, Germany, 2003. View at MathSciNet
  20. T. Schuster, B. Kaltenbacher, B. Hofmann, and K. S. Kazimierski, Regularization Methods in Banach Spaces, De Gruyter, 2012. View at MathSciNet
  21. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems, John Wiley & Sons, New York, NY, USA, 1977. View at MathSciNet
  22. T. Scheffer, Charakterisierung des nichtlinear-viskoelatischen Materialverhaltens gefüllter Elastomere, Universität des Saarlandes, 2016.
  23. T. Scheffer, H. Seibert, and S. Diebels, “Optimisation of a pretreatment method to reach the basic elasticity of filled rubber materials,” Archive of Applied Mechanics, vol. 83, no. 11, pp. 1659–1678, 2013. View at Publisher · View at Google Scholar · View at Scopus
  24. O. H. Yeoh, “Characterization of elastic properties of carbon-black-filled rubber vulcanizates,” Rubber Chemistry and Technology, vol. 63, no. 5, pp. 792–805, 1990. View at Publisher · View at Google Scholar
  25. P. Haupt, Continuum mechanics and theory of materials, Springer, Berlin, Germany, 2000. View at MathSciNet
  26. B. D. Coleman and W. Noll, “The thermodynamics of elastic materials with heat conduction and viscosity,” Archive for Rational Mechanics and Analysis, vol. 13, pp. 167–178, 1963. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. N. Koprowski-Theiss, M. Johlitz, and S. Diebels, “Characterizing the time dependence of filled EPDM,” Rubber Chemistry and Technology, vol. 84, no. 2, pp. 147–165, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 67, no. 2, pp. 301–320, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. B. Jin, D. A. Lorenz, and S. Schiffler, “Elastic-net regularization: Error estimates and active set methods,” Inverse Problems, vol. 25, no. 11, Article ID 115022, 2009. View at Publisher · View at Google Scholar · View at Scopus