4D printing, as an emerging technology, fabricates structures with smart materials which deform under stimuli. The bilayer structure is special in 4D printing that has lots of capabilities such as self-folding. The prediction of bilayer structure deformation in the design phase is very important to meet the application requirements better. However, there has been little research on simulating the self-deformation of 4D printed bilayer structures before fabricating and most of these studies only consider the bending of bilayer plates. In our work, a common model is proposed which can simulate the complicated self-deformation of 4D printed bilayer structures. Firstly, the deformation reason of 4D printed bilayer structures is analyzed and the mismatch of the two layers in a bilayer structure is modeled with a simplified energy density function. Secondly, a reduced bilayer plate model proposed by Bartels is introduced and improved by considering the different anisotropic expansions of each layer. Under this model, the deformation simulating of the bilayer plate is transformed into an energy minimization problem. Thirdly, the optimization problem is solved using the numerical iterative scheme established by Bartels and the deformation process of the simulated bilayer plate is also visualized. Lastly, some numerical simulations on bending, twisting, and ringing deformations of bilayer structures are conducted and compared with the corresponding experiments based on thermal-driven PLA bilayer structures and the results verify the validity of this common simulating model. This method also has the advantages of high efficiency and good convergence by simplifying the simulation into a 2D problem and avoiding contact analysis. This work provides a new view for predicting the deformation of 4D printed bilayer structures which we think is highly significant.

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