Computational Mechanics

, Volume 54, Issue 5, pp 1315–1329 | Cite as

A new SMA shell element based on the corotational formulation

  • P. Bisegna
  • F. Caselli
  • S. Marfia
  • E. SaccoEmail author
Original Paper


Aim of this paper is to develop a new shape memory alloy (SMA) facet-shell finite element accounting for material and geometric nonlinearities. A corotational formulation is exploited, able to filter out large rigid-body motions from the element transformation. Accordingly, a geometrically linear core-element is employed, along with a SMA constitutive model formulated in the small strain framework. In particular, in accordance with the formulation of the classical thin shell theory, a plane-stress SMA model accounting for the pseudo-elastic as well as the shape memory effect is adopted. The time integration of the evolutive equation is performed developing a step-by-step backward-Euler numerical procedure. A highly efficient implementation of the corotational machinery is used, endowed with a fully consistent tangent stiffness. Applications are carried out for assessing the performances of the developed computational procedure and to investigate on some interesting engineering examples. The numerical results show the effectiveness of the proposed shell element, whose simplicity makes it attractive for the design of new advanced SMA-based devices undergoing significant configuration changes during their operation.


Shape memory alloy Shells  Large displacements and rotations Corotational formulation 



The financial supports of PRIN 2009, project “Multi-scale modelling of materials and structures” CUP n. H31J1100021001, and PRIN 2010-11, project “Advanced mechanical modeling of new materials and technologies for the solution of 2020 European challenges” CUP n. F11J12000210001 are gratefully acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Civil Engineering and Computer ScienceUniversity of Rome “Tor Vergata”RomeItaly
  2. 2.Department of Civil and Mechanical EngineeringUniversity of Cassino and Southern LazioCassinoItaly

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