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One  of  the  main  fields  of  shape  memory  alloy  application  in  civil  engineering  is oriented on mitigation of earthquake effects on structures. Vibration isolators that incorporate elements made of SMA take advantage of its characteristic phenomenon of nonlinear hysteretic response,  also  known  as  superelasticity.  In  this  work,  authors  presents  an  approach  to phenomenological modelling of SMA by using rheological schemes. One of the advantages of this  approach  is  a  possibility  of  formulation  of  constitutive  relationships  as  a  set  of  explicit differential  equations.  As  an  illustration  of  validity  of  the  formulation,  authors  present  the response of single degree of freedom oscillator that incorporates SMA elements modelled by different existing SMA models. The response obtained based on the model that uses rheological schemes  is  compared  with  Lagoudas  thermodynamic  constitutive  SMA  model  and  simplified material  model.  All  of  the  compered  models  are  found  to  match  well  and  show  important reduction in displacement transmissibility.

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== Full document ==

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== References ==

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[1] Mohd Jani, J. Leary, M. Subic, A. and Gibson, M.A., A review of shape memory alloy  research,  applications  and  opportunities,  Materials  and  Design  (2014)  56:  pp.  1078–1113  

​

[2] Lagoudas, D.C. Bo, Z. and Qidwai, M.A., A unified thermodynamic constitutive model for  SMA  and  finite  element  analysis  of  active  metal  matrix  composites,  Mechanics  of Composite Materials and Structures (1996) 3: pp. 153–179.  

​

[3] Qidwai, M.A. and Lagoudas, D.C., Numerical implementation of a shape memory alloy thermomechanical  constitutive  model  using  return  mapping  algorithms,  International Journal for Numerical Methods in Engineering (2000) 47: pp. 1123–1168.  

​

[4] Lagoudas,  D.C.  Mayes,  J.J.  and  Khan,  M.M.,  Simplified  shape  memory  alloy  (SMA) material  model  for  vibration  isolation,  in:  Rao,  V.S.  (Ed.),  International  Society  for Optics and Photonics, 2001: pp. 452–461.  

​

[5] Ölander, A., An electrochemical investigation of solid cadmium-gold alloys, Journal of the American Chemical Society (1932) 54: pp. 3819–3833.  

​

[6] Chang, L.C. and Read,  T.A., Plastic Deformation and Diffusionless Phase Changes in Metals — the Gold-Cadmium Beta Phase, JOM (1951) 3: pp. 47–52.  

​

[7] Buehler, W.J. Gilfrich, J. V. and Wiley, R.C., Effect of Low-Temperature Phase Changes on  the  Mechanical  Properties  of  Alloys  near  Composition  TiNi,  Journal  of  Applied  Physics (1963) 34: pp. 1475–1477.  

​

[8] Asanović, V. and Delijić, K., The mechanical behavior and shape memory recovery of  Cu-Zn-Al alloys, Metalurgija (2007) 13: pp. 59–64.  

​

[9] Cladera, A. Weber, B. Leinenbach, C. Czaderski, C. Shahverdi, M. and Motavalli, M.,  Iron-based shape memory alloys for civil engineering structures: An overview,  Construction and Building Materials (2014).  

​

[10] Concilio,  A.  and  Lecce,  L.,  Historical  Background  and  Future  Perspectives,  in:  Shape Memory Alloy Engineering, Elsevier Ltd, 2015: pp. 3–30.  

​

[11] Pecora, R. and Dimino, I., SMA for Aeronautics, Elsevier Ltd, 2014.  

​

[12] Auricchio,  F.  Boatti,  E.  and  Conti,  M.,  SMA  Biomedical  Applications,  Elsevier  Ltd, 2014.  

​

[13] Auricchio, F. Boatti, E. and Conti, M., SMA Cardiovascular Applications and Computer- Based Design, Elsevier Ltd, 2014.  

​

[14] Song, G. Ma, N. and Li, H.N., Applications of shape memory alloys in civil structures, Engineering Structures (2006) 28: pp. 1266–1274.  

​

[15] Menna,  C.  Auricchio,  F.  and  Asprone,  D.,  Applications  of  Shape  Memory  Alloys  in  Structural Engineering, Elsevier Ltd, 2015.  

​

[16] Castellano,  M.G.  Indirli,  M.  and  Martelli,  A.,  Progress  of  application,  research  and  development, and design guidelines for shape memory alloy devices for cultural heritage structures in Italy, in: Smart Structures and Materials 2001: Smart Systems for Bridges, Structures, and Highways, 2001: pp. 250–261.  

​

[17] Arato, G.B. Carpani, B. Forni, M. Indirli, M. Martelli, A. Castellano, M.G. and Medeot,  R.,  Application  of  innovative  antiseismic  techniques  to  the  seismic  retrofit  of  Italian  cultural  heritage  damaged  by  recent  earthquakes,  in:  Monument-98,  Workshop  on  Seismic Performance of Monuments, 1998.  

​

[18] Indirli, M. Castellano, M.G. Clemente, P. and Martelli, A., Demo-application of shape  memory alloy devices: The rehabilitation of the S. Giorgio Church Bell-Tower, Proceedings of SPIE - The International Society for Optical Engineering (2001) 4330: pp. 262–272.  

​

[19] Cardone,  D.  Angiuli,  R.  and  Gesualdi,  G.,  Application  of  Shape  Memory  Alloys  in  Historical Constructions, International Journal of Architectural Heritage (2019) 13: pp. 390–401.  

​

[20] Ferretti,  E.  and  Pascale,  G.,  Some  of  the  latest  active  strengthening  techniques  for  Masonry Buildings: A critical analysis, Materials (2019) 12:.  

​

[21] Cisse,  C.  Zaki,  W.  and  Ben  Zineb,  T.,  A  review  of  constitutive  models  and modeling techniques for shape memory alloys, International Journal of Plasticity (2016) 76: pp. 244–284.  

​

[22] Grzesikiewicz,  W.  and  Zbiciak,  A.,  Constitutive  modelling  of  pseudoelastic  material  using Kepes-type rheological element, Computer Systems Aided Science and Engineering Work in Transport, Mechanics and Electrical Engineering (2008) 122: pp. 159–164.  

​

[23] Zbiciak,  A.,  Dynamic  analysis  of  pseudoelastic  SMA  beam,  International  Journal  of Mechanical Sciences (2010) 52: pp. 56–64.  

​

[24] Grzesikiewicz,  W.  Wakulicz,  A.  and  Zbiciak,  A.,  Mathematical  modelling  of  rate-independent pseudoelastic SMA material, International Journal of Non-Linear Mechanics (2011) 46: pp. 870–876.  

​

[25] Zbiciak, A. and Wasilewski, K., Constitutive Modelling and Numerical Implementation  of SMA Material with Internal Loops, Archives of Civil Engineering (2018) 64: pp. 211–232.  

​

[26] Zbiciak, A. and Wasilewski, K., Modelling of single degree of freedom SMA oscillators by using rheological schemes, in: MATEC Web of Conferences, 2018.

​