Constitutive Modelling and Numerical Implementation of SMA Material with Internal Loops

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The article presents a constitutive model for Shape Memory Alloys (SMA) along with result of dynamic simulations of SMA model. The applications of devices incorporating SMA in civil engineering focus mostly on mitigation of the seismic hazard effects in new-build and historical buildings or improvement of fatigue resilience. The unique properties of SMA, such as shape memory effect and superelasticity give promising results for such applications. The presented model includes additional phenomenon of SMA – internal loops. The paper shows the method of formulation of physical relations of SMA based on special rheological structure, which includes modified Kepes’s model. This rheological element, introduced as dual-phase plasticity body, is given in the context of martensite phase transformation. One of the advantages of such an approach is a possibility of formulation of constitutive relationships as a set of explicit differential equations. The application of the model is demonstrated on example of dynamic simulations of three dimensional finite element subjected to dynamic excitation.

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

  • 2 Y. Chang Wenn-Shao; Araki Use of shape-memory alloys in construction : a critical review Proceedings of the Institution of Civil Engineers - Civil Engineering. 169 (2016) 87–95.

  • 3 W. Terlikowski Interdisciplinary diagnostics in the process of revitalization of historic buildings in terms of changing their function MATEC Web of Conferences. 117 (2017) 00165.

  • 4 K. Wasilewski A. Zbiciak Proposal of a new constitutive model for SMA with internal loops in: F.M. Mazzolani (Ed.) 3rd International Conference on Protection of Historical Constructions Lisbon 2017: pp. 129–130.

  • 5 C. Menna F. Auricchio D. Asprone Applications of Shape Memory Alloys in Structural Engineering Elsevier Ltd 2015.

  • 6 F. Auricchio D. Fugazza* R. Desroches Earthquake Performance of Steel Frames With Nitinol Braces Journal of Earthquake Engineering. 10 (2006) 45–66.

  • 7 H. Tamai Y. Kitagawa Pseudoelastic behavior of shape memory alloy wire and its application to seismic resistance member for building Computational Materials Science. 25 (2002) 218–227.

  • 8 K. Wilde P. Gardoni Y. Fujino Base isolation system with shape memory alloy device for elevated highway bridges Engineering Structures. 22 (2000).

  • 9 E. Choi T.H. Nam J.T. Oh B.S. Cho An isolation bearing for highway bridges using shape memory alloys Materials Science and Engineering A. 438–440 (2006) 1081–1084.

  • 10 S. Das S.K. Mishra Optimal performance of buildings isolated by Shape-Memory-Alloy-Rubber- Bearing (SMARB) under random earthquakes International Journal of Computational Methods in Engineering Science and Mechanics. 15 (2014) 265–276.

  • 11 M.G. Castellano M. Indirli A. Martelli 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.

  • 12 M. Indirli M.G. Castellano Shape Memory Alloy Devices for the Structural Improvement of Masonry Heritage Structures International Journal of Architectural Heritage. 2 (2008) 93–119.

  • 13 F.M. Mazzolani A. Mandara Modern trends in the use of special metals for the improvement of historical and monumental structures Engineering Structures. 24 (2002) 843–856.

  • 14 M. Indirli M.G. Castellano P. Clemente A. Martelli 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. 4330 (2001) 262–272.

  • 15 M.G. Castellano Seismic protection of monuments by shape memory alloy devices and shock transmitters (2005) 1229–1234.

  • 16 V. Torra C. Auguet A. Isalgue G. Carreras P. Terriault F.C. Lovey Built in dampers for stayed cables in bridges via SMA. The SMARTeR-ESF project: A mesoscopic and macroscopic experimental analysis with numerical simulations Engineering Structures. 49 (2013) 43–57.

  • 17 L. Dieng G. Helbert S.A. Chirani T. Lecompte P. Pilvin Use of shape memory alloys damper device to mitigate vibration amplitudes of bridge cables Engineering Structures. 56 (2013) 1547–1556.

  • 18 A. Zbiciak R. Michalczyk R. Oleszek Vibration reduction of cable-stayed bridge model retrofitted with SMA restrainers Vibroengineering PROCEDIA. 3 (2014) 180–185.

  • 19 P. Soroushian K. Ostowari A. Nossoni H. Chowdhury Repair and Strengthening of Concrete Structures Through Application of Corrective Posttensioning Forces with Shape Memory Alloys Transportation Research Record: Journal of the Transportation Research Board. 1770 (2001) 20–26.

  • 20 M.A. Savi A. Paiva Describing internal subloops due to incomplete phase transformations in shape memory alloys Archive of Applied Mechanics. 74 (2005) 637–647.

  • 21 A. Ziółkowski Pseudosprężystość stopów z pamięcią kształtu badania doświadczalne i opis teoretyczny Prace Instytutu Podstawowych Problemów Techniki PAN. 6 (2006) 200.

  • 22 B. Peultier T. Ben Zineb E. Patoor Macroscopic constitutive law of shape memory alloy thermomechanical behaviour. Application to structure computation by FEM Mechanics of Materials. 38 (2006) 510–524.

  • 23 A. Masud K. Xia A variational multiscale method for inelasticity: Application to superelasticity in shape memory alloys Computer Methods in Applied Mechanics and Engineering. 195 (2006) 4512–4531.

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

  • 25 N.S. Ottosen M. Ristinmaa The mechanics of constitutive modeling Elsevier 2005.

  • 26 F. Auricchio E. Sacco A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite International Journal of Non-Linear Mechanics. 32 (1997) 1101–1114.

  • 27 ABAQUS Analysis User’s Manual Ver. 6.12 Dassault Systèmes 2012.

  • 28 W. Grzesikiewicz A. Wakulicz A. Zbiciak Mathematical modelling of rate-independent pseudoelastic SMA material International Journal of Non-Linear Mechanics. 46 (2011) 870–876.

  • 29 W. Grzesikiewicz A. Zbiciak Mathematical modelling of rate-dependent SMA material subjected to dynamic loads in: Proceedings of 15th French-Polish Seminar of Mechanics Polytech’Lille Villeneuve d’Ascq France 2007: pp. 138–143.

  • 30 A. Zbiciak Dynamic analysis of pseudoelastic SMA beam International Journal of Mechanical Sciences. 52 (2010) 56–64.

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