R. Mirzaeifar, R. DesRoches, A. Yavari, Georgia Institute of Technology, Atlanta, GA
In this study, the torsion of superelastic shape memory alloy bars with circular cross sections is investigated. A phenomenological macroscopic SMA constitutive model is used for modeling pure torsion. Due to the highly nonlinear response of SMAs, a closed form solution cannot be obtained for this problem. We solve the problem by first partitioning the bar into a finite number of hollow cylinders. Then, in each region the constitutive relation is linearized and appropriate assumptions are made in order to find a closed-form solution for the equilibrium equations in terms of the twist angle in the region. By enforcing the continuity equations in the intersection of these annular regions and the boundary conditions in the cross sections, the global solution for the torsion of the bar is obtained. Some numerical examples are presented to demonstrate the performance and efficiency of the proposed method and the results are compared with three-dimensional finite element simulations.
Summary: In this study, a new solution is presented for the torsion of superelastic shape memory alloy bars with circular cross sections.
