Finally, a sensitivity analysis is performed varying the pitch of the helix. Then, the helix structural element is considered and results are again compared with finite element outcomes. 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. Several numerical applications are presented to assess the reliability of the proposed SMA helix model and the implemented numerical procedure, and to investigate the response of the helix. 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. 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. 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. The proposed model is based on a simplified but effective theory of the helix that assumes small strains and large displacements. In the present paper a mathematical model able to reproduce the mechanical response of a shape memory alloy (SMA) helical spring is presented.
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