SFEM-4DP: A strain-based finite element model for 4D printing

Abstract

Four-dimensional (4D) printing extends three-dimensional (3D) printing by adding a time-based dimension, allowing printed structures to change and adapt over time. This smart behavior is built into smart materials during printing and activated by external stimuli. Unlike 3D-printed static structures, 4D-printed structures evolve, offering dynamic functionality for various applications. This study opens up new avenues for efficient modeling of 4D-printed structures by introducing a Strain-based Finite Element Model for 4D Printing (SFEM-4DP) that predicts time-dependent deformation behavior. By incorporating viscoelastic effects and nonlinear Green strain formulation, the proposed model captures large deformations while simplifying the modeling process and reducing the need for extensive parameter identification. A simulation tool is developed to implement the model and facilitate practical 4D printing predictions. Several numerical simulation cases are used to demonstrate the model’s flexibility and efficiency. The experimental verification include hydrogel doughnuts and bilayer composites of thermoplastic polyurethane (TPU) and hydrogel, demonstrating the model’s capability of dynamic deformation prediction. Finally, two application cases of soft robotics-a transformable wheel and a soft gripper-are demonstrated based on the bilayer composites. • A strain-based model is proposed to simplify modeling in 4D printing. • Nonlinear Green strain is used to capture large deformations. • A simulation tool is developed for 4D printing prediction. • Results validate the model’s capability in predicting dynamic deformation. • Further applications in soft robotics are provided.