Contact/impact modeling and analysis of 4D printed shape memory polymer beams

This study examines contact and impact behaviors of shape memory polymer (SMP) beams fabricated by four-dimensional (4D) printing technology. A 3D phenomenological constitutive model is developed to predict visco-elastic-plastic characteristics of SMPs and their shape memory effect in large deformation range for the first time. A novel finite element method (FEM) based on non-linear Green strains is established to analyze the SMP beam under contact/impact loadings. Newmark and Newton-Raphson methods along with an iterative-incremental approach based on a visco-elastic-predictor visco-plastic-corrector return mapping algorithm are implemented to solve FEM governing equations in spatial and time domains. Fused deposition modeling is employed to 4D print samples from polyurethane-based filaments. Thermo-mechanical experimental tests are performed to acquire the parameters needed for the SMP constitutive model. The effects of indentation location, substrate thickness, and edge effect are examined numerically for cylindrical indentation of elastic-plastic SMPs at glassy phase. The validation and application of the Hertzian load-displacement relation for indentation of elastic materials are also clarified. Then, experimental and numerical tests are conducted to examine impact responses of 4D printed SMP beams. Influences of impact position and impactor initial velocity and energy on the responses of the structure in forced and free vibration regimes are studied in detail. The results revealed that the projectile with low velocity or high velocity accompanied with low energy impacted the beam is able to produce plastic deformation. It is shown that the large residual plastic deformation can be fully recovered by simply heating. Due to the absence of similar results in the specialized literature, this paper provides pertinent results that are instrumental in the design of SMP beam-like structures under impact loadings.