Bending theory for laminated composite cantilever beams with multiple embedded shape memory alloy layers

Nguyen Van Viet, Wael Zaki, Rehan Umer

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


In this article, a new analytical model is proposed for laminated composite cantilever beams consisting of multiple alternating superelastic shape memory alloy and elastic layers. The model is based on the Zaki–Moumni model for shape memory alloys combined with Timoshenko’s beam theory. The Zaki–Moumni model accounts for solid phase transformation as well as detwinning and reorientation of martensite under multiaxial thermomechanical loading conditions. Mathematical formulas are first derived to characterize the evolution of the solid phase structure within the beam with a prescribed load at the tip during loading and unloading. Analytical moment–curvature and shear force–shear strain relations are then obtained following the strength of materials approach. The present work is the first to fully develop the nonlinear expressions of the axial stress in terms of the distance from the neutral plane and to allow the description of the phase distribution in both the longitudinal and the transverse directions in the beam as the load evolves. The proposed model is validated against finite element analysis and high-accuracy numerical solutions. The influence of temperature and the number of shape memory alloy layers on the superelastic behavior of the laminate is also investigated.

Original languageBritish English
Pages (from-to)1549-1568
Number of pages20
JournalJournal of Intelligent Material Systems and Structures
Issue number10
StatePublished - 1 Jun 2019


  • analytical model
  • bending
  • laminate
  • loading–unloading cycle
  • Shape memory alloys
  • superelasticity
  • Timoshenko’s beam theory


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