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The mechanical properties of functional-graded shape memory alloy (FG-SMA) is of highly significance for its applications and structural design. This paper establishes a constitutive model of the FG-SMA beam, considering the influence of the temperature variation and the tension-compression asymmetry coefficient. The fiber element method and the virtual work principle were employed to establish the governing equation of the bending of FG-SMA beam, which is solved using the Newton–Raphson algorithm. Furthermore, the effect of the tension-compression asymmetry coefficient, temperature, gradient index, bending moment, and axial load on the mechanical properties of the FG-SMA beams was analyzed. The results showed that the tension-compression asymmetry coefficient, gradient index, bending moment, and axial load significantly have relatively obvious influence on the cross-sectional mechanical response of the FG-SMA beams, while the effect of the temperature was not noticeable.

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Shape memory alloys (SMA) are widely used in micro-electro-mechanical systems due to shape memory effect and hyperelasticity. The surface effects on mechanical properties cannot be ignored because of their small structure size. Based on Euler Bernoulli beam theory and Gurtin-Murdoch surface elasticity theory, the influence of tension-compression asymmetry factors on SMA beams is considered, and a phase transformation mechanical model of SMA nanobeams considering surface effects is established. The effects of surface effects on load, curvature and neutral axis displacement are investigated The study demonstrates that regardless of whether considering the surface effect, the neutral axis displacement initially increases and subsequently decreases with the growth of the dimensionless bending moment. The neutral axis displacement of nanobeams can be significantly affected by taking surface effects into account. When considering the surface effect, the difference in neutral axis displacement of the nanobeam increases as the nanobeam’s size diminishes. Neglecting surface effects will underestimate the bending stiffness of the microbeam.