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In this paper, a three-dimensional size-dependent constitutive model of SMP Timoshenko micro-beam is developed to describe the micromechanical properties.

According to the Hamilton's principle, the equilibrium equations and boundary conditions of the model are established and according to the modified couple stress theory, the model is available to capturing the size effect because of the material length scale parameter. Based on the model, the simply supported beam was taken for example to be solved and simulated.

Results show that the size effect of SMP micro-beam is more obvious when the dimensionless beam height is similar or the larger of the value of loading time. The rigidity and strength of the SMP beam decrease with the increasing of the dimensionless beam height or the loading time. The viscous property of SMP micro-beam plays a more important role with the larger dimensionless beam height. And the smaller the dimensionless beam height is, the more obvious the shape memory effect of the SMP micro-beam is.

This work implies prediction of size-dependent thermo-mechanical behaviors of the SMP micro-beam and will provide a theoretical basis for design SMP microstructures in the field of micro/nanomechanics.