A three-dimensional constitutive equation for shape memory polymer composites considering energy dissipation under single loading–unloading condition

Shape memory polymer composites (SMPCs), composed of shape memory polymers (SMPs) and fabrics, can recover their deformed shapes to initial configurations by changing temperature. The shape recovery energy of the SMPs and the elastic energy of the fabrics are regarded as key points to predict the restored configuration of the SMPCs. In this research, a three-dimensional constitutive equation for SMPCs is newly developed, considering the energy dissipation of fabrics under a single loading–unloading condition. The constitutive equation is derived from Mooney–Rivlin, viscoelastic, and stored strain energy models for SMPs, as well as polynomial functions for fabrics. The Mooney–Rivlin and viscoelastic models describe the time- and temperature-dependent hyperelastic properties, and the stored strain energy model can explain the shape recovery. The polynomial functions are newly proposed to take into account the dissipated energy of fabrics, such as residual deformation and hysteresis effect. Because the elastic energy of fabrics considerably influences the shape recovery of SMPCs, the proposed constitutive equation can accurately predict the recovered configuration. Analyses of SMPCs are conducted using the finite element method and validated by comparing them with the results obtained from experiments. The constitutive equation is used to analyze the shape recovery behaviors of an SMPC skin. The skin can be largely stretched, and the deformed shape can be restored to its initial shape by applying electricity. The SMPC skin is applied to a morphing flap, and its shape-changing behaviors are demonstrated experimentally.