Temperature-responsive 4D printing with shape memory polymers: Advancing simulation with a viscoelastic constitutive model

The field of 4D printing using shape memory polymers (SMPs) faces challenges in accurately simulating the entire process. Existing models often fail to capture these dynamics, limiting design optimization. This study introduces an advanced simulation technique for 4D printing using fused deposition modeling (FDM), combined with experimental validation to ensure accuracy. A temperature-dependent viscoelastic constitutive model was developed to represent the thermomechanical behavior of thermoplastic SMPs. Implemented in ABAQUS through a UMAT subroutine, this model enables comprehensive finite element analysis of the entire 4D printing process, including the printing, cooling, and reheating stages. The simulation successfully predicts deformation behavior under fixed printing speed and temperature, across different geometries and printing paths. Experimental validation using PLA demonstrates strong consistency between simulated and actual deformation. This simulation technique offers predictive capabilities that facilitate optimization of the 4D printing process, saving time and cost through precise pre-manufacturing simulations. Additionally, this approach provides new theoretical insights into the programming and control of SMP-based 4D printing, supporting the design of adaptive structures for various applications.