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A shape memory alloy helix model accounting for extension and torsion
یک مدل مارپیچ آلیاژ حافظه شکل برای محاسبه گسترش و پیچش -2021 In the present paper a mathematical model able to reproduce the mechanical response of a shape memory alloy
(SMA) helical spring is presented. The proposed model is based on a simplified but effective theory of the helix
that assumes small strains and large displacements. The kinematics of the helix and the related generalized strain
measures are introduced, with stress resultants conjugated to them and the corresponding equilibrium equations
of the curved beam. A specific constitutive law for this structural model is then presented for the SMA material,
which accounts for the phase transformation due to the coupling of the shear and axial strains and to the effect of
the temperature variation as well. Then, a numerical procedure, based on the backward Euler time integration
algorithm and the prediction-correction technique for solving the nonlinear time step, is developed. Several
numerical applications are presented to assess the reliability of the proposed SMA helix model and the imple-
mented numerical procedure, and to investigate the response of the helix. Initially, the behavior of a circular
SMA cross-section is studied, comparing the results obtained by the proposed modeling approach with the ones
carried out by finite element analyses. Then, the helix structural element is considered and results are again
compared with finite element outcomes. Finally, a sensitivity analysis is performed varying the pitch of the helix. keywords: آلیاژ حافظه شکل | بهار | مدل Helix | روش عددی | Shape memory alloy | Spring | Helix model | Numerical procedure |
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