Compressive behavior of 4D-printed shape memory polymer auxetic structures: Numerical and experimental analysis

This study examines the compressive behavior of 4D-printed auxetic lattice structures, emphasizing deformation mechanisms, buckling, post-buckling responses, and energy absorption. These aspects are investigated through combined experimental and numerical approaches, providing insights for design optimization and engineering applications. A simple yet efficient 3D macroscopic constitutive model for shape memory polymers (SMPs), accounting for both glassy and rubbery phases, is developed. Subsequently, a robust finite element analysis (FEA) framework is employed to derive the nonlinear governing equilibrium equations, which are solved using the Newton–Raphson iterative method. Following validation of the proposed numerical model (the FE formulation and the constitutive model), six SMP-based auxetic lattice structures with distinct unit cell (UC) geometries are fabricated using 4D-printing. These specimens undergo quasi-static compression tests at room temperature, and then plastic deformation is recovered through heating. The findings reveal that UC geometric parameters exert a strong nonlinear influence on compressive behavior. For instance, increasing the connection angle (θ) from 11° to 18° leads to a 37% reduction in the critical buckling force. A maximum energy absorption (0.88 J) is achieved by the structure that has unstable post-buckling behavior. Finally, the proposed numerical model shows strong agreement with experimental results.