Computational Mechanics

, Volume 55, Issue 2, pp 421–437 | Cite as

An \(\hbox {FE}^{2}\) model for the analysis of shape memory alloy fiber-composites

Original Paper
First Online:
Received:
Accepted:

Abstract

This contribution deals with a computational model for a shape memory alloy fiber composite. Three main topics have been considered within the presented model. First, a 1D fiber model is derived which accounts for all relevant nonlinear material phenomena of shape memory alloys. These are pseudoelasticity in the high temperature range and pseudoplasticity in the low temperature range. The latter is closely connected to the shape memory effect. The constrained and two-way shape memory effect are captured as well. Second, the shape memory fiber model is implemented into the finite element method. Two different structural elements are derived which lead to two different discretization schemes. A non-conform meshing concept and a conform meshing concept are presented. Randomly oriented and distributed fibers are considered. Both schemes are compared within the paper. Third, an \(\hbox {FE}^{2}\) ansatz is presented. The computational homogenization process makes the detailed description of the complicated fiber-structure on macro-level dispensable. The micro-structure is considered in a representative volume element. It captures the main characteristics of the multi-functional composite. Finally, numerical examples present the capability of the formulation.

Keywords

Shape memory fiber Composite  Rebar concept \(\hbox {FE}^{2}\) approach 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    McCormick J, DesRoches R, Fugazza D, Auricchio F (2006) Seismic vibration control using superelastic shape memory alloys. J Eng Mater-T ASME 128:294CrossRefGoogle Scholar
  2. 2.
    Castellano M, Colato G, Infanti S (2004) Use of viscous dampers and shock transmission units in the seismic protection of buildings. In: Proceedings of 13th world conference on earthquake engineering, pp. 1–15. Paper No. 2172Google Scholar
  3. 3.
    Indirli M, Castellano M, Clemente P, Martelli A (2001) Demo-application of shape memory alloy devices: the rehabilitation of the S. Giorgio Church bell tower. In: Liu SC (ed) Smart structures and materials 2001: Smart systems for bridges, structures, and highways, society of photo-optical instrumentation engineers (SPIE) conference series, vol 4330, Society of photo-optical instrumentation engineers (SPIE) conference series, vol 4330, pp. 262–272Google Scholar
  4. 4.
    Indirli M, Spadoni B, Carni R, Clemente C, Martelli A, Castellano M (2008) Shape memory alloy devices for the structural improvement of masonry heritage structures. Int J Archit Herit 2:93CrossRefGoogle Scholar
  5. 5.
    Song G, Ma N, Li HN (2006) Applications of shape memory alloys in civil structures. Eng Struct 28:1266CrossRefGoogle Scholar
  6. 6.
    Moser K, Bergamini A, Christen R, Czaderski C (2005) Feasibility of concrete prestressed by shape memory alloy short fibers. Mater Struct 38:593CrossRefGoogle Scholar
  7. 7.
    Janke L, Czaderski C, Motavalli M, Ruth J (2005) Formgedächtnislegierungen in Ingenieurstrukturen des Stahlbetonbaues: Materialphänomene, Anwendungskonzepte und Visionen. Mater Struct 38(279):578CrossRefGoogle Scholar
  8. 8.
    Klinkel S, Kohlhaas B (2011) Modellierung und Anwendung von Formgedächtnislegierungen im Bauwesen. Bauingenieur-germany Jahresausgabe 2011/2012:101Google Scholar
  9. 9.
    Achenbach M, Müller I (1982) A model for shape memory. J Phys Paris 43(C4):163CrossRefGoogle Scholar
  10. 10.
    Seelecke S, Müller I (2004) Shape memory alloy actuators in smart structures: modeling and simulation. Appl Mech Rev 57:23CrossRefGoogle Scholar
  11. 11.
    Brinson L (1993) One-dimensional behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J Intel Mater Syst Struct 4:229CrossRefGoogle Scholar
  12. 12.
    Leclercq S, Lexcellent C (1996) A general macroscopic description of the thermomechanical behavior of shape memory alloys. J Mech Phys Solids 44(6):953CrossRefGoogle Scholar
  13. 13.
    Raniecki B, Lexcellent C (1998) Thermodynamics of isotropic pseudoelasticity in shape memory alloys. Eur J Mech A Solid 17:185CrossRefMATHGoogle Scholar
  14. 14.
    Bo Z, Lagoudas D (1999) Thermomechanical modeling of polycrystalline {SMAs} under cyclic loading, Part I: theoretical derivations. Int J Eng Sci 37(9):1089CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Lagoudas D, Bo Z (1999) Thermomechanical modeling of polycrystalline {SMAs} under cyclic loading, Part II: material characterization and experimental results for a stable transformation cycle. Int J Eng Sci 37(9):1141CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Bo Z, Lagoudas D (1999) Thermomechanical modeling of polycrystalline {SMAs} under cyclic loading, Part III: evolution of plastic strains and two-way shape memory effect. Int J Eng Sci 37(9):1175CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Bo Z, Lagoudas D (1999) Thermomechanical modeling of polycrystalline {SMAs} under cyclic loading, Part IV: modeling of minor hysteresis loops. Int J Eng Sci 37(9):1205CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Helm D (2001) Formgedächtnislegierungen: experimentelle Untersuchung, phänomenologische Modellierung und numerische Simulation der thermomechanischen Materialeigenschaften. Ph.D. thesis, Universität Gesamthochschule KasselGoogle Scholar
  19. 19.
    Helm D, Haupt P (2003) Shape memory behaviour: modelling within continuum thermomechanics. Int J Solids Struct 40:827CrossRefMATHGoogle Scholar
  20. 20.
    Helm D (2007) Numerical simulation of martensititc phase transitions in shape memory alloys using an improved integration algorithm. Int J Numer Methods Eng 69:1997CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Helm D (2007) Thermomechanics of martensititc phase transformations in shape memory alloys – I. Constitutive theories for small and large deformations. J Mech Mater Struct 2:87CrossRefGoogle Scholar
  22. 22.
    Christ D, Reese S (2008) Thermomechanically coupled modelling of shape memory alloys in the framework of large strains. GAMM-Mitteilungen 31(2):176CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Christ D, Reese S (2009) A finite element model for shape memory alloys considering thermomechanical couplings at large strains. Int J Solids Struct 46:3694CrossRefMATHGoogle Scholar
  24. 24.
    Christ D (2009) Thermomechanical modelling of shape memory alloy structures in medical applications. Ph.D. thesis, Technische Universität BraunschweigGoogle Scholar
  25. 25.
    Lagoudas D (2008) Shape memory alloys: modeling and engineering applications. Springer, BostonGoogle Scholar
  26. 26.
    Evangelista V, Marfia S, Sacco E (2009) Phenomenological 3D and 1D consistent models for shape-memory alloy materials. Comput Mech 44(3):405CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Khandan R, Mahzoon M, Fazelzadeh S, Ali H (2009) A consistent approach for deriving a 1D constitutive equation for shape memory alloys. Smart Mater Struct 18(9):1CrossRefGoogle Scholar
  28. 28.
    Aboudi J, Freed Y (2006) Two-way thermomechanically coupled micromechanical analysis of shape memory alloy composites. J Mech 1:937Google Scholar
  29. 29.
    Armstrong W, Kino H (1995) Martensitic transformations in a NiTi fiber reinforced 6061 aluminium matrix composite. J Intel Mater Syst Struct 6:809CrossRefGoogle Scholar
  30. 30.
    Boyd J, Lagoudas D (1996) A thermodynamical constitutive model for shape memory materials—Part I: The monolithic shape memory alloy. Int J Plast 12(7):843CrossRefMATHGoogle Scholar
  31. 31.
    Carvelli V, Taliercio A (1999) A micromechanical model for the analysis of unidirectional elastoplastic composites subjected to 3D stresses. Mech Res Commun 26(5):547CrossRefMATHGoogle Scholar
  32. 32.
    Cherkaoui M, Sun Q, Song G (2000) MIcromechanics modeling of composite with ductile matrix and shape memory alloy reinforcement. Int J Solids Struct 37:1577CrossRefMATHGoogle Scholar
  33. 33.
    Notta-Cuvier D, Lauro F, Bennani B, Balieu R (2013) An efficient modelling of inelastic composites with misaligned short fibres. Int J Solids Struct 50:2857CrossRefGoogle Scholar
  34. 34.
    Freed Y, Aboudi J (2008) Micromechanical investigation of plasticity-damage coupling of concrete reinforced by shape memory alloy fibers. Smart Mater Struct 17:1CrossRefGoogle Scholar
  35. 35.
    Gilat R, Aboudi J (2004) Dynamic response of active composite plates: shape memory fibers in polymeric/metallic matrices. Int J Solids Struct 41:5717CrossRefMATHGoogle Scholar
  36. 36.
    Kawai M, Ogawa H, Baburaj V, Koga T (1999) Micromechanical analysis for hysteretic behavior of unidirectional TiNi SMA fiber composites. J Intel Mater Syst Struct 10:14Google Scholar
  37. 37.
    Klinkel S, Sansour C, Wagner W (2005) An anisotropic fibre-matrix material model at finite elastic–plastic strains. Comput Mech 35:409CrossRefMATHGoogle Scholar
  38. 38.
    Marfia S (2005) Micro-macro analysis of shape memory alloy composites. Int J Solids Struct 42:3677CrossRefMATHGoogle Scholar
  39. 39.
    Song G, Cherkaoui M, Sun Q (1999) Role of microstructure in the thermomechanical behavior of SMA composites. J Eng Mater-T ASME 121(1):86CrossRefGoogle Scholar
  40. 40.
    Gebbeken N (1996) Zur Untersuchung des linearen Tragverhaltens von Verbundkonstruktionen mittels numerischer Methoden. Technical Report 96/1, Universität der Bundeswehr MünchenGoogle Scholar
  41. 41.
    Huber F (2006) Nichtlineare dreidimensionale Modellierung von Beton- und Stahlbetontragwerken. Ph.D. thesis, Universität StuttgartGoogle Scholar
  42. 42.
    Miehe C, Schröder J, Schotte J (1999) Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput Method Appl Mech 171(3–4):387CrossRefMATHGoogle Scholar
  43. 43.
    Geers M, Coenen E, Kouznetsova V (2007) Multi-scale computational homogenization of structured thin sheets. Model Simul Mater Sci 15(4):S393CrossRefGoogle Scholar
  44. 44.
    Oskay C, Fish J (2007) Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comput Method Appl Mech 196(7):1216CrossRefMATHMathSciNetGoogle Scholar
  45. 45.
    Gruttmann F, Wagner W (2013) A coupled two-scale shell model with applications to layered structures. Int J Numer Method Eng 94(13):1233CrossRefMathSciNetGoogle Scholar
  46. 46.
    Simo J, Hughes T (2000) Computational inelasticity, interdisciplinary applied mathematics mechanics and materials, vol 7. Springer, New YorkGoogle Scholar
  47. 47.
    Neunzert H, Blickensdörfer-Ehlers A (1998) Analysis, 3rd edn. Springer, BerlinMATHGoogle Scholar
  48. 48.
    Juhász L (2004) Herleitung eines konstitutiven Modells für Formgedächtnislegierungen. Ph.D. thesis, Universität KarlsruheGoogle Scholar
  49. 49.
    Zohdi T, Wriggers P (2005) Introduction To computational micromechanics. Lecture Notes in applied and computational mechanics. Springer Verlag, Berlin HeidelbergCrossRefGoogle Scholar
  50. 50.
    Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11(5):357CrossRefMATHGoogle Scholar
  51. 51.
    Gross D, Seelig T (2001) Bruchmechanik: Mit einer Einführung in die Mikromechanik. Springer, Berlin. URL http://www.books.google.de/books?id=ySI3E0YoEMQC

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Lehrstuhl für Baustatik und BaudynamikRWTH Aachen UniversityAachenGermany

Personalised recommendations