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Simultaneous estimation of boundary conditions and material model parameters

  • Gerhardus J. Jansen van Rensburg
  • Schalk Kok
  • Daniel N. Wilke
RESEARCH PAPER
  • 76 Downloads

Abstract

Room temperature experimental compression test data is available for different hardmetals. This data indicates the presence of some spatial inhomogeneity due to a compression instability, eccentric loading or time varying equivalent bending moment. To account for this, an inverse analysis is employed that determines not only the constitutive material model parameter values but also the displacement boundary conditions that best replicate the experimental data. The unknown boundary displacement history is approached using a systematically refined piecewise linear approximation, determined alongside material parameter values. The systematic simultaneous estimation of material parameter values and boundary approximations is also investigated using a virtual problem for which the exact solution is known. This investigation confirms that known material parameter values and boundary conditions can be recovered without using any prior knowledge of the exact displacement boundary conditions.

Keywords

Inverse problem Finite element analysis Parameter identification Material model calibration Hardmetal compression 

References

  1. Ageno M, Bolzon G, Maier G (2009) An inverse analysis procedure for the material parameter identification of elastic-plastic free-standing foils. Struct Multidiscip Optim 38:229–243CrossRefMATHGoogle Scholar
  2. Ȧkerström P, Wikman B, Oldenburg M (2005) Material parameter estimation for boron steel from simultaneous cooling and compression experiments. Model Simul Mater Sci Eng 13:1291–1308CrossRefGoogle Scholar
  3. ASTM C1424-04 (2004) Standard test method for monotonic compressive strength of advanced ceramics at ambient temperature. Standard ASTM, PhiladelphiaGoogle Scholar
  4. ASTM E209-00 (2010) Standard practice for compression tests of metallic materials at elevated temperatures with conventional or rapid heating rates and strain rates. Standard ASTM, PhiladelphiaGoogle Scholar
  5. ASTM E9-09 (1989) Standard test methods of compression testing of metallic materials at room temperature. Standard ASTM, PhiladelphiaGoogle Scholar
  6. AZO Materials (2002) Properties: Tungsten Carbide - An Overview. http://www.azom.com/properties.aspx? ArticleID=1203
  7. Bruhns OT, Anding DK (1999) On the simultaneous estimation of model parameters used in constitutive laws for inelastic material behaviour. Int J Plast 15:1311–1340CrossRefMATHGoogle Scholar
  8. Chen X, Ashcroft IA, Wildman RD, Tuck CJ (2017) A combined inverse finite element - elastoplastic modelling method to simulate the size-effect in nanoindentation and characterise materials from the nano to micro-scale. Int J Solids Struct 104–105:25–34CrossRefGoogle Scholar
  9. Dhondt G, Wittig K (1998) CalculiX:a free software Three-Dimensional structural finite element program. http://www.dhondt.de/
  10. Dunlay WA, Tracy CA, Perrone PJ (1989) A Proposed Uniaxial Compression Test for High Strength Ceramics. US Army Materials Technology Lab. Report MTL-TR-89-89Google Scholar
  11. Gamonpilas C, Busso EP (2007) Characterization of elastoplastic properties based on inverse analysis and finite element modeling of two separate indenters. J Eng Mater Technol 129:603–608CrossRefGoogle Scholar
  12. Garbowski T, Maier G, Novati G (2012) On calibration of orthotropic elastic-plastic constitutive models for paper foils by biaxial tests and inverse analyses. Struct Multidiscip Optim 46:111–128CrossRefGoogle Scholar
  13. Ghouati O, Gelin JC (1998) Identification of material parameters directly from metal forming processes. J Mater Process Technol 80–81:560–564CrossRefGoogle Scholar
  14. ISO 4506 (1979) Hardmetals - compression test. Standard International Organization for Standardization, GenevaGoogle Scholar
  15. Jansen van Rensburg GJ, Kok S, Wilke DN (2012) Simultaneous estimation of experimental and material parameters. In: Engopt 2012 - 3rd international conference on engineering optimization, Rio de Janeiro, BrazilGoogle Scholar
  16. Jansen van Rensburg GJ, Kok S, Wilke DN (2014) Simultaneous boundary value and material parameter estimation using imperfect compression data. In: Engopt 2014 - 4th international conference on engineering optimization, Lisbon, PortugalGoogle Scholar
  17. Jansen van Rensburg GJ (2016) Development and implementation of state variable based user materials in computational plasticity. Ph.D. thesis The University of Pretoria, PretoriaGoogle Scholar
  18. Jansen van Rensburg GJ, Kok S, Wilke DN (2017) Steel alloy hot roll simulations and Through-Thickness variation using dislocation Density-Based modeling. Metall and Mater Trans B 48(5):2631–2648CrossRefGoogle Scholar
  19. Jekel CF, Venter G, Venter MP (2016) Obtaining a hyperelastic non-linear orthotropic material model via inverse bubble inflation analysis. Struct Multidiscip Optim 54:927–935CrossRefGoogle Scholar
  20. Jones E, Oliphant E, Peterson P (2001) SciPy: Open Source Scientific Tools for Python. http://www.scipy.org/
  21. Kocks U, Tomé C, Wenk H (1998) Texture and anisotropy. Cambridge University Press, CambridgeMATHGoogle Scholar
  22. Mahnken R, Stein E (1996) A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput Methods Appl Mech Eng 136:225–258CrossRefMATHGoogle Scholar
  23. Mourad H, Bronkhorst C, Addessio F, Cady C, Brown D, Chen S, Gray G (2013) Incrementally objective implicit integration of hypoelastic-viscoplastic constitutive equations based on the mechanical threshold strength model. Comput Mech 53:941–955MathSciNetCrossRefMATHGoogle Scholar
  24. Nelder J, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313MathSciNetCrossRefMATHGoogle Scholar
  25. Schmaltz S, Willner K (2014) Comparison of different biaxial tests for the inverse identification of sheet steel material parameters. Strain 50:389–403CrossRefGoogle Scholar
  26. Wang X, Li H, Chandrashekhara K, Rummel SA, Lekakh S, Van Aken DC, O’Malley RJ (2017) Inverse finite element modeling of the barreling effect on experimental stress-strain curve for high temperature steel compression test. J Mater Process Technol 243:465–473CrossRefGoogle Scholar
  27. Wikman B, Bergman G, Oldenburg M, Häggblad H (2006) Estimation of constitutive parameters for powder pressing by inverse modelling. Struct Multidiscip Optim 31:400–409CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Modelling and Digital ScienceCouncil for Scientific and Industrial ResearchPretoriaSouth Africa
  2. 2.Computer Science and Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa
  3. 3.Centre for Asset Integrity Management, Department of Mechanical and Aeronautical EngineeringUniversity of PretoriaPretoriaSouth Africa

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