Abstract: Based on the existing piecewise linear model of shape memory alloy (SMA), combined with the relationship between temperature and critical stress of phase transition, a simple piecewise linear model of SMA with clearer physical meaning, which can reveal mechanical behavior of SMA under thermal-mechanical load, are proposed from the perspective of strain. Based on the Bernoulli-Euler beam theory, the mechanical model of the relationship between bending moment and curvature in the nonlinear bending process of SMA beams is established by using the SMA piecewise linear model. Combined with the SMA beam mechanical model, the purely curved beam and simply supported beam with uniform load are numerically solved respectively by a simple solving process. The stress distribution, bending moment and deflection, and memory factor changes are analyzed. The results show that the established SMA piecewise linear model can effectively describe the mechanical behavior of SMA under thermo-mechanical load. The simple and effective mechanical model of SMA structure can be established using the piecewise linear model, which is more convenient for engineering application and theoretical analysis.

Key words: shape memory alloy, piecewise linear model, thermal-mechanical load, Bernoulli-Euler beam, mechanical model