A model for shape memory alloy beams accounting for tensile compressive asymmetry

A new analytical model is derived for cantilever beams made from superelastic shape memory alloy and subjected to tip load. The deformation of the beam is described based on Timoshenko beam theory using constitutive relations that account for asymmetric shape memory alloy response in tension and compression. Analytical moment and shear force equations are developed and the position of the neutral axis and the different solid phase regions in the beam are tracked throughout a full loading–unloading cycle. Validation of the proposed model is carried out against data from the literature and from the finite element analysis considering tensile–compressive asymmetry in shape memory alloy behavior.