A computational approach for the simulation of shape memory polymer-based structures via finite elements and mesh morphing

Shape-memory polymers (SMPs) are a widely-used class of smart materials capable of recovering a pre-defined permanent shape from a deformed temporary configuration when exposed to external stimuli. A crucial step in this behavior is shape-programming, which enables the fixation of the temporary shape. Simulating this step through numerical models can be both computationally expensive and prone to inaccuracies. This is primarily due to the difficulty in identifying the appropriate set of boundary conditions needed to deform the structure into the desired temporary shape, often requiring multiple trial-and-error iterations. This paper proposes a computational approach that overcomes such a difficulty and enables an accurate simulation of the shape-memory cycle. The core innovation lies in the use of mesh morphing techniques to directly impose the temporary shape, thereby eliminating the need to determine complex mechanical loading conditions during the programming step. This method is integrated within a finite element framework and applied to a representative 4D printed structure. Numerical results confirm the robustness and accuracy of the approach, which replicates the recovery behavior of the SMP while significantly reducing computational effort in finding and applying the right set of boundary conditions. This work provides a valuable tool for the design of SMP systems.