A modified one-dimensional constitutive model of pseudoelastic SMAs and its application in simulating the force–deformation relationship of SMA helical springs

The Graesser–Cozzarelli constitutive model of shape memory alloys (SMAs) has been widely applied in seismic engineering due to its concise functions with well-defined material parameters. However, this model has some limitations, e.g. it fails to model the hardening behavior of SMAs under relatively large strain amplitudes and the effects of ambient temperature. In this paper, a modified Graesser–Cozzarelli constitutive model of pseudoelastic SMAs is proposed, through consideration of the changes of the elastic moduli of SMAs induced by different martensite fractions, the effects of ambient temperature on the pseudoelastic characteristics, the hardening behavior and the phenomenon of degradation of the pseudoelasticity of SMAs under large strain amplitudes. Furthermore, the modified model was validated by the results of experiments on SMA wires under different strain amplitudes and ambient temperatures. The modified model was then utilized to simulate the force–deformation relationship of SMA helical springs for the first time. In the procedure used to simulate the springs, the torsional and bending moments on the cross-section of the coiled wire of the springs were considered simultaneously, and the effect of the pitch angle was also included. Moreover, the spring simulation procedure was verified by tensile tests of SMA helical springs with complex loading patterns and existing simulated results of the effects of ambient temperature. The research results indicate that the spring simulation procedure based on the modified model can simulate the force–deformation relationship of the springs under different complex loading conditions and ambient temperature reasonably well. Furthermore, the effects of the spring index and the initial height of the springs on the characteristics of the force–deformation relationship were investigated in detail. (paper)