Development of a large strain formulation for multiple shape-memory-effect of polymers under bending

•Proposing an accurate semi-analytical solution for shape memory polymers response.•Developing a fast and efficient tool to design smart structures under finite bending.•Prediction of dual shape memory polymers behavior in different shape memory effect paths.•Being successful in triple shape memory effect path as well as force and shape recovery.•The model is capable of capturing both the temperature and time dependent effects. The purpose of this paper is to present a semi-analytical solution for shape memory polymers (SMPs) in large deformation upon temperature changes as an external stimulus, which is developed based on the thermo-visco-hyperelasticity theory. The presented formulation is employed in a dual-shape shape memory effect (SME) cycle in both free-stress strain recovery and fixed-strain stress recovery, as well as a triple-shape SME cycle in finite bending problem. Finite element simulations of the same problems are also carried out to confirm the accuracy of the semi-analytical solution where outcomes verify the semi-analytical results successfully. The great agreement between the presented method results and those of FEM demonstrates the capability of this approach to study SMP structures under finite bending. The proposed solution requires much less time compared to FEM simulations. Therefore, in design and optimization of the smart structures under bending that involve numerous analyses, the proposed semi-analytical solution can make a significant difference and be considered as an efficient tool for studying the effects of different material and geometrical parameters. [Display omitted]