A closed-form solution for superelastic shape memory alloy beams subjected to bending

A macroscopic phenomenological framework is used for developing a closed-form solution for analyzing the pure bending of shape memory alloy (SMA) beams. In order to study the effect of tension-compression asymmetry on the bending response, two different transformation functions are considered; a J 2-based solution with symmetric tension-compression response, and a J 2 - I 1-based solution capable of modeling the tension-compression asymmetry. The constitutive equations are reduced to an appropriate form for studying the pseudoelastic bending response of SMAs, and closed-form expressions are obtained for the stress and martensitic volume fraction distributions in the cross section. These expressions are used for calculating the bending moment-curvature analytically. Both circular and rectangular cross sections are considered and several case studies are presented for analyzing the accuracy of the presented method and also the effect of considering the tension-compression asymmetry on the bending response of SMAs. © 2012 SPIE.