An analytical model for a shape memory alloy beam accounting for tension-compression stress asymmetry effect

The study deals with a development of a novel analytical model based on extended ZM’s model together with Timoshenko beam theory for a superelastic shape memory alloy (SMA) cantilever beam taking into account the tension-compression asymmetry stress effect during loading/unloading process. The beam structure evolution is first identified by the trial method based on the geometric relation and force equilibrium. Subsequently, an analytical moment-curvature-neutral axis deviation and shear force-shear strain relations are derived for the identified beam structure. The moment-curvature response from theoretical model based on asymmetric effect, and theory and 3D FEM based on symmetric effect are shown to reveal the difference between them. Subsequently, the neutral axis deviation-tip load response and distribution of mertensite volume fraction along the beam length obtained from theory and 3D FEM based on asymmetric effect is demonstrated.