Skip to main content
SpringerLink
Log in

Homogenization techniques for the analysis of porous SMA

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

In this paper the mechanical response of porous Shape Memory Alloy (SMA) is modeled. The porous SMA is considered as a composite medium made of a dense SMA matrix with voids treated as inclusions. The overall response of this very special composite is deduced performing a micromechanical and homogenization analysis. In particular, the incremental Mori–Tanaka averaging scheme is provided; then, the Transformation Field Analysis procedure in its uniform and nonuniform approaches, UTFA and NUTFA respectively, are presented. In particular, the extension of the NUTFA technique proposed by Sepe et al. (Int J Solids Struct 50:725–742, 2013) is presented to investigate the response of porous SMA characterized by closed and open porosity. A detailed comparison between the outcomes provided by the Mori–Tanaka, the UTFA and the proposed NUTFA procedures for porous SMA is presented, through numerical examples for two- and three-dimensional problems. In particular, several values of porosity and different loading conditions, inducing pseudoelastic effect in the SMA matrix, are investigated. The predictions assessed by the Mori–Tanaka, the UTFA and the NUTFA techniques are compared with the results obtained by nonlinear finite element analyses. A comparison with experimental data available in literature is also presented.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Wen CE, Xiong JY, Li YC, Hodgson PD (2010) Porous shape memory alloy scaffolds for biomedical applications: a review. Phys Scr T 139:1–8

    Google Scholar 

  2. Zhao Y, Taya M, Izui H (2006) Study on energy absorbing composite structure made of concentric NiTi spring and porous NiTi. Int J Solids Struct 43:2497–2512

    Article  MATH  Google Scholar 

  3. Martynova I, Skorohod V, Solonin S, Goncharuk S (1996) Shape memory and superelasticity behaviour of porous Ti-Ni material. Journal de Physique IV C4:421–426

    Google Scholar 

  4. Li B-Y, Rong L-J, Li Y-Y (1998) Porous NiTi alloy prepared from elemental powder sintering. J Mater Res 13:2847–2851

    Article  Google Scholar 

  5. Ashrafi MJ, Arghavani J, Naghdabadi R, Sohrabpour S (2015) A 3D constitutive model for pressure-dependent phase transformation of porous shape memory alloys. J Mech Behav Biomed 42:292–310

    Article  Google Scholar 

  6. Nemat-Nasser S, Su Y, Guo WG, Isaacs J (2005) Experimental characterization and micro- mechanical modeling of superelastic response of a porous NiTi shape-memory alloy. J Mech Phys Solids 53(10):2320–2346

    Article  Google Scholar 

  7. Qidwai MA, De Giorgi VG (2002) A computational mesoscale evaluation of material characteristics of porous shape memory alloys. Smart Mater Struct 11:435–443

    Article  Google Scholar 

  8. Qidwai MA, De Giorgi VG (2004) Numerical assessment of the dynamic behavior of hybrid shape memory alloy composite. Smart Mater Struct 13:134–145

    Article  Google Scholar 

  9. Panico M, Brinson LC (2008) Computational modeling of porous shape memory alloys. Int J Solids Struct 45:5613–5626

    Article  MATH  Google Scholar 

  10. Liu B, Dui G, Zhu Y (2012) On phase transformation behavior of porous Shape Memory Alloys. J Mech Behav Biomed Mater 5:9–15

    Article  Google Scholar 

  11. Sepe V, Marfia S, Auricchio F (2014) Response of porous SMA: a micromechanical study. Frattura ed Integrità Strutturale 29:85–96

    Google Scholar 

  12. Sepe V, Auricchio F, Marfia S, Sacco E (2015) Micromechanical analysis of porous SMA. Smart Mater Struct 24:20

    Article  Google Scholar 

  13. Fritzen F, Forest S, Kondo D, Böhlke T (2013) Computational homogenization of porous materials of Green type. Comput Mech 52:121–134

    Article  MathSciNet  MATH  Google Scholar 

  14. Qidwai MA, Entchev PB, Lagoudas DC, De Giorgi VG (2001) Modeling of the thermomechanical behavior of porous shape memory alloys. Int J Solids Struct 38:8653–8671

    Article  MATH  Google Scholar 

  15. Entchev PB, Lagoudas DC (2002) Modeling porous shape memory alloys using micromechanical averaging techniques. Mech Mater 34(1):1–24

    Article  Google Scholar 

  16. Entchev PB, Lagoudas DC (2004) Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part II: porous SMA response. Mech Mater 36(9):893–913

    Article  Google Scholar 

  17. Zhao Y, Taya M (2007) Analytical modeling for stress–strain curve of a porous NiTi. J Appl Mech 74(2):291–297

    Article  MATH  Google Scholar 

  18. Zhu Y, Dui G (2011) A model considering hydrostatic stress of porous NiTi shape memory alloys. Acta Mech Solida Sin 24(4):289–298

    Article  Google Scholar 

  19. Dvorak G (1992) Transformation field analysis of inelastic composite materials. Proc R Soc Lond A 437:311–327

    Article  MathSciNet  MATH  Google Scholar 

  20. Marfia S, Sacco E (2007) Analysis of SMA composite laminates using a multiscale modeling technique. Int J Numer Methods Eng 70:1182–1208

    Article  MathSciNet  MATH  Google Scholar 

  21. Dvorak GJ, Bahei-El-Din A (1997) Inelastic composite materials: transformation field analysis and experiments. In: Suquet P (ed) Continuum micromechanics. CISM course and lecture 377. Springer, Berlin, pp 1–59

  22. Chaboche J, Kruch LS, Maire J, Pottier T (2001) Towards a micromechanics based inelastic and damage modeling of composites. Int J Plast 17:411–439

    Article  MATH  Google Scholar 

  23. Michel J, Suquet P (2003) Nonuniform transformation field analysis. Int J Solids Struct 40:6937–6955

    Article  MathSciNet  MATH  Google Scholar 

  24. Michel J, Suquet P (2004) Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. Comput Methods Appl Mech Eng 193:5477–5502

    Article  MathSciNet  MATH  Google Scholar 

  25. Fritzen F, Böhlke T (2010) Three-dimensional finite element implementation of the nonuniform transformation field analysis. Int J Numer Meth Eng 84:803–829

    Article  MathSciNet  MATH  Google Scholar 

  26. Marfia S, Sacco E (2012) Multiscale damage contact-friction model for periodic masonry walls. Comput Methods Appl Mech Eng 205–208:189–203

    Article  MathSciNet  MATH  Google Scholar 

  27. Sepe V, Marfia S, Sacco E (2013) A nonuniform TFA homogenization technique based on piecewise interpolation functions of the inelastic field. Int J Solids Struct 50(5):725–742

    Article  Google Scholar 

  28. Fritzen F, Marfia S, Sepe V (2015) Reduced order modeling in nonlinear homogenization: a comparative study. Comput Struct 157:114–131

    Article  Google Scholar 

  29. Souza AC, Mamiya EN, Zouain N (1998) Three-dimensional model for solids undergoing stress-induced phase transformations. Eur J Mech A Solids 17:789–806

    Article  MATH  Google Scholar 

  30. Auricchio F, Petrini L (2004) A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems. Int J Numer Methods Eng 61:807–836

    Article  MathSciNet  MATH  Google Scholar 

  31. Evangelista V, Marfia S, Sacco E (2009) Phenomenological 3D and 1D consistent models for shape memory alloy materials. Comput Mech 44:405–421

    Article  MathSciNet  MATH  Google Scholar 

  32. Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21:571–574

    Article  Google Scholar 

  33. Benveniste Y (1987) A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech Mater 6:147–157

    Article  Google Scholar 

  34. Mura T (1987) Micromechanics of defects in solids. Kluwer Academic Publisher, Dordrecht

    Book  MATH  Google Scholar 

  35. Nemat-Nasser S, Hori M (1993) Micromechanics: overall properties of heterogeneous materials. North-Holland, London

    MATH  Google Scholar 

  36. Zienkiewicz OC, Taylor RL (1991) The finite element method, 4th edn. McGraw-Hill, London

    MATH  Google Scholar 

  37. Zhao Y, Taya M, Kang YS, Kawasaki A (2005) Compression behavior of porous NiTi shape memory alloy. Acta Mater 53(2):337–343

    Article  Google Scholar 

  38. Weng GJ (1990) The theoretical connection between Mori–Tanaka’s theory and the Hashin–Shtrikman–Walpole bounds. lnt J Eng Sci 28(11):1111–1120

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The financial supports of PRIN 2010-11, project “Advanced mechanical modeling of new materials and technologies for the solution of 2020 European challenges” CUP n. F11J12000210001 and of the University of Cassino and of the Southern Lazio are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, Cassino, Italy

    V. Sepe, S. Marfia & E. Sacco

  2. Department of Civil Engineering and Architecture, University of Pavia, Pavia, Italy

    F. Auricchio

Authors
  1. V. Sepe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Auricchio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Marfia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. Sacco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Sacco.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sepe, V., Auricchio, F., Marfia, S. et al. Homogenization techniques for the analysis of porous SMA. Comput Mech 57, 755–772 (2016). https://doi.org/10.1007/s00466-016-1259-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-016-1259-1

Keywords

Search

Navigation