Theoretical model for the post-buckling of straight ribbons under static rotation and translation at bonding sites

Shape reconfigurations are gaining increasing attention in applications such as ingestible medical devices, microrobots, and tunable optoelectronics. The shape recovery and temporary fixation capabilities of shape memory polymer (SMP) substrates enable precise control over the placement of bonding sites, where 2D precursors are selectively attached to the substrate. This enables the controlled transformation of 2D precursors into 3D reconfigurable shapes. This work presents a finite-deformation buckling model for predicting the stable, post-buckling configurations of straight ribbons under the static rotations and translations imposed by the SMP substrate at the bonding sites. The model predictions are validated against finite element analysis and experimental results, confirming their accuracy and effectiveness. This provides a theoretical foundation for the precise control of shape transformation processes and potential applications in soft robotics and flexible electronics.