Analytical study on torsion of shape-memory-polymer prismatic bars with rectangular cross-sections

Abstract

In this paper, the response of shape memory polymer (SMP) bars with rectangular cross-sections under torsional loadings is analytically studied. To this end, we first reduce the recently proposed small-strain 3D phenomenological constitutive model for SMPs to the shear case. Then, an analytical solution for torsional response of SMP rectangular bars in a full cycle of stress-free strain recovery is derived. We also implement the 3D constitutive equations in a finite element program and simulate a full cycle of stress-free strain recovery of a rectangular SMP bar. Analytical and numerical results are then compared showing that the analytical solution gives, besides the global load–deflection response, accurate stress distributions in the cross-section of the rectangular SMP bar. Some case studies are also presented to show the validity of the presented analytical method. Results are compared with the experimental data recently reported in the literature which showing an agreement between the predicted results and experiments. The analytical solution can also be used for analysis of helical springs in which both the curvature and pitch effects are negligible. This is the case for helical springs with large ratios of mean coil radius to the cross-sectional equivalent radius (spring index) and also small pitch angles. Using this solution simplifies the analysis of the helical springs to that of the torsion of a straight bar with rectangular cross-section.