Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

This paper addresses the problem of deformation modeling and simulation of 4D printed polymeric bilayer structures considering the thickness ratio. Through an equivalent transformation, the folding deformation model is transformed into two simpler deformation models, stretching and bending, which greatly reduces the complexity of the modeling problem. The stretching deformation model is developed by Hooke’s law, and based on the final strain of the stretching deformation, which is determined by the thickness ratio, a new hyperelastic energy density function considering the thickness ratio is defined to calculate the energy of the bilayer structure during the bending deformation. According to the new energy density function, the bending deformation model considering the thickness ratio is developed by minimizing the energy of the bilayer structure during the bending deformation. Numerical simulations show encouraging results obtained by the proposed model.