Three-dimensional constitutive model for shape memory polymers using multiplicative decomposition of the deformation gradient and shape memory strains

• A 3D constitutive equation for SMPs based on a two-phase is developed.
• Shape memory strain is introduced to simulate the shape memory effect.
• The total deformation gradient is multiplicatively decomposed into each element.
• Shape memory strain is determined by assuming proportionality to the total deformation.
• The simulation results are in good agreement with experiments.

Using a two-phase (rubbery and glassy) phenomenological model and shape memory strains, a three-dimensional constitutive model for shape memory polymers (SMPs) was developed that can simulate multi-axial and large deformation behavior (up to 200% of strain) of SMPs. To derive a constitutive equation, the total deformation gradient was multiplicatively decomposed into hyperelastic, viscoelastic, viscoplastic, and shape memory strains using Helmholtz free energy and the Clausius–Duhem inequality. The shape memory strain was determined from the total deformation by assuming proportionality to the total deformation. The developed constitutive model was validated by simulating the shape memory behavior of SMPs using a finite element method and comparing the simulation results with experiments. Finally, the capabilities of the constitutive equation were demonstrated by simulating constrained shape recovery behavior of SMPs.