Development and implementation of a beam theory model for shape memory polymers

In this paper we focus on the development of a beam theory for a small strain continuum model of thermoviscoelastic shape memory polymers (SMP). Rather than a history integral model that is common for viscoelastic materials, a thermodynamically based state evolution model developed by Ghosh and Srinivasa (2011a) is used as the basis for the beam model based on the Euler–Bernoulli beam theory. An example of a three-point bend test is simulated using the beam theory model. The numerical solution is implemented by using an operator split technique that utilizes an elastic predictor and dissipative corrector. The key idea is that the elastic predictor is based on the solution to a beam theory boundary value problem while the dissipative corrector is entirely local (and hence can be parallelized) and is applied by considering the beam as a two or three dimensional body. This enables a very rapid solution of the problem yet maintaining fidelity of the distribution of inelastic strains across the cross-section. A displacement based convergence criterion is used in each time step. This algorithm is validated by using a three-point bending experiment for three different material cases: elastic, plastic and thermoplastic response. Time step convergence and mesh density convergence studies are carried out for the thermoviscoelastic FEM model. Finally, we implement and study this model for a SMP beam undergoing three-point bending strain recovery and stress recovery thermomechanical loading.