Skip to main content
SpringerLink
Log in

A comparative study of hyperelastic and hypoelastic material models with constant elastic moduli for large deformation problems

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Many finite element programs including commercial codes for large deformation analysis employ incremental formulations of rate-type constitutive equations which are based on hyperelastic or hypoelastic material models with constant elastic moduli. In this paper, a comparative study is carried out for hyperelastic and hypoelastic material models with constant elastic moduli of a face-centered cubic single crystal of copper. A strain energy function from the inter-atomic potential for single-crystal copper is also considered for the hyperelastic material model to obtain physically based elastic deformations. Numerical results show that constant elastic moduli of hypoelastic material models can cause considerable errors in stress and strain increments when the changes in volume and cross-sectional area of a material are not negligible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bathe K.J., Ramm E., Wilson E.: Finite element formulations for large deformation dynamic analysis. Int. J. Numer. Methods Eng. 9, 353–386 (1975)

    Article  MATH  Google Scholar 

  2. Bažant Z.: A correlation study of formulations of incremental deformation and stability of continuum bodies. J. Appl. Mech. 38, 919–928 (1971)

    Article  MATH  Google Scholar 

  3. Bažant Z., Gattu M., Vorel J.: Work conjugacy error in commercial finite-element codes: its magnitude and how to compensate for it. Proc. R. Soc. A 468, 3047–3058 (2012)

    Article  MathSciNet  Google Scholar 

  4. Bažant Z., Vorel J.: Energy-conservation error due to use of Green–Naghdi objective stress rate in commercial finite-element codes and its compensation. J. Appl. Mech. 81, 021008 (2014)

    Google Scholar 

  5. Ericksen J.L.: On the Cauchy–Born rule. Math. Mech. Solids 13, 199–220 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hanson A.W.: Elastic behavior and elastic constants of zinc single crystals. Phys. Rev. 45, 324 (1934)

    Article  Google Scholar 

  7. Hibbitt H.D., Marcal P.V., Rice J.R.: A finite element formulation for problems of large strain and large displacement. Int. J. Solids Struct. 6, 1069 (1970)

    Article  MATH  Google Scholar 

  8. Ji W., Waas A.M., Bažant Z.: Errors caused by non-work-conjugate stress and strain measures and necessary corrections in finite element programs. J. Appl. Mech. 77, 044504 (2010)

    Article  Google Scholar 

  9. McMeeking R.M., Rice J.R.: Finite element formulations for problems of large elastic–plastic deformation. Int. J. Solids Struct. 11, 601–616 (1975)

    Article  MATH  Google Scholar 

  10. Mishin Y., Mehl M.J., Papaconstantopoulos D.A., Voter A.F., Kress J.D.: Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Phys. Rev. B 63, 224106 (2001)

    Article  Google Scholar 

  11. Nagtegaal J.C., Rebelo N.: On the development of a general finite element program for analysis of forming processes. Int. J. Numer. Methods Eng. 25, 113–131 (1988)

    Article  MATH  Google Scholar 

  12. Nagtegaal, J.C., Veldpaus, F.E. et al. : On the implementation of finite strain plasticity equations in a numerical model. In: Pittman, J.F.T. (ed.) Numerical Analysis of Forming Processes, pp. 351–371. Willey, New York (1984)

  13. Oldroyd J.G.: On the formulation of rheological equations of state. Proc. R. Soc. Lond. A 200, 523–541 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  14. Page Y.L., Saxe P.: Symmetry-general least-square extraction of elastic data for strained materials from ab initio calculation of stress. Phys. Rev. B 65, 104104 (2002)

    Article  Google Scholar 

  15. Simmons G., Wang H.: Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook. MIT Press, Cambridge (1971)

    Google Scholar 

  16. Simo J.C.: On the computational significance of the intermediate configuration and hyperelastic relations in finite deformation elastoplasticity. Mech. Mater. 4, 439–451 (1985)

    Article  Google Scholar 

  17. Simo J.C., Hughes T.J.R.: Computational Inelasticity. Springer, New York (1998)

    MATH  Google Scholar 

  18. Simo J.C., Pister K.S.: Remarks on rate constitutive equations for finite deformation problems: computational implications. Comput. Methods Appl. Mech. Eng. 46, 201–215 (1984)

    Article  MATH  Google Scholar 

  19. Weber G.G., Lush A.M., Zavaliangos A., Anand L.: An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic–plastic constitutive equations. Int. J. Plast. 6, 701–744 (1990)

    Article  MATH  Google Scholar 

  20. Zabaras N., Arif A.F.M.: A family of integration algorithms for constitutive equations in finite deformation elasto-viscoplasticity. Int. J. Numer. Methods Eng. 33, 59–84 (1992)

    Article  MATH  Google Scholar 

  21. Zotov N., Ludwig A.: First-principle calculations of the elastic constants of Fe–Pt alloys. Intermetallics 16, 113–118 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, Seoul, 139-743, South Korea

    Hyun-Gyu Kim

Authors
  1. Hyun-Gyu Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hyun-Gyu Kim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, HG. A comparative study of hyperelastic and hypoelastic material models with constant elastic moduli for large deformation problems. Acta Mech 227, 1351–1362 (2016). https://doi.org/10.1007/s00707-015-1554-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-015-1554-5

Keywords

Search

Navigation