This paper presents a general semi-analytic solution for the thermomechanical behavior of shape memory polymer (SMP) in large deformation, based on a thermo-viscoelastic constitutive model. The formulation presented in this paper is suitable for describing shape memory behaviors such as fixed-strain, stress-recovery and stress-free, strain-recovery, as well as for multiple shape memory effect in uniaxial and combined extension-torsion problems. To verify the results, a comparison has been carried out among the proposed formulation results and those of experiments and 3D finite element analysis outcomes. Compared to the finite element analysis, semi-analytical solutions are interesting due to their very low computational cost. It was observed that the solution time for the proposed method is much lower than the computational time needed for the FE analyses (around 1%). Therefore, the presented solution can be employed as an efficient tool for examining the effects of changing any of the material or geometrical parameters on smart structures consisting of SMP components under torsion-extension for their design and optimization, which involves a large number of simulations. Additionally, the proposed solution is suitable for calibrating material parameters in both uni-axial and 3D benchmark problem of torsion-extension.

In this research, the bending of a two-way shape memory polymer beam is examined implementing a one-dimensional phenomenological macroscopic constitutive model into Euler–Bernoulli and von-Karman beam theories. Since bending loading is a fundamental problem in engineering applications, a combination of bending problem and two-way shape memory effect capable of switching between two temporary shapes can be used in different applications, for example, thermally activated sensors and actuators. Shape memory polymers as a branch of soft materials can undergo large deformation. Hence, Euler–Bernoulli beam theory does not apply to the bending of a shape memory polymer beam where moderate rotations may occur. To overcome this limitation, von-Karman beam theory accounting for the mid-plane stretching as well as moderate rotations can be employed. To investigate the difference between the two beam theories, the deflection and rotating angles of a shape memory polymer cantilever beam are analyzed under small and moderate deflections and rotations. A semi-analytical approach is used to inspect Euler–Bernoulli beam theory, while finite-element method is employed to study von-Karman beam theory. In the following, a smart structure is analyzed using a prepared user-defined subroutine, VUMAT, in finite-element package, ABAQUS/EXPLICIT. Utilizing generated user-defined subroutine, smart structures composed of shape memory polymer material can be analyzed under complex loading circumstances through the two-way shape memory effect.

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