A finite element analysis for shape memory polymer beams considering geometric non-linearity

In this research, using a thermomechanical constitutive model for shape memory polymers and employing the von Kármán theory, a finite element analysis of a shape memory polymer beam is presented. The importance of introducing the von Kármán theory for shape memory polymers is that the beam can have relatively high slopes during loading. Also, for optimization and designing processes we need to solve multiple problems and due to the high processing time the use of 3D model is not suitable. To validate the presented formulations, the reported results are compared with the 3D solution which was previously reported by the same authors. Accordingly, the effect of the hard segment volume on response of a thin beam has been investigated, and the results of the von Kármán beam have been reported and compared with the 3D and Euler-Bernoulli solutions. As an example, the error of the beam response in one of the solved examples is 27% for Euler-Bernoulli beam and 1% for the von Kármán solution compared to the three-dimensional solution. In general, the lower the beam thickness or the beam is longer, the Euler-Bernoulli beam error will be higher. The proposed finite element model can provide a reliable alternative response comparing to 3D modeling that requires a lot of processing time, and can be used for geometry and material parametric study.