Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations

In this study, a nonlinear superelastic bending of shape memory alloy (SMA) beam with consideration of the material and geometric nonlinearity effects which are coupled with each other, has been investigated. By using the Timoshenko beam theory and applying the principle of virtual work, the governing equations were extracted. In this regard, Von Karman strains were applied to take the large deflections into account. Via Boyd-Lagoudas 3D constitutive model, SMA was simulated, which was properly reduced to two dimensions. With the development of an iterative nonlinear finite element model, and for the purpose of obtaining characteristic of finite element beam, the Galerkin weighted-residual method was applied. In this study, by considering the different force and support conditions for the SMA beam, their effects on the distribution of martensitic volume fraction (MVF) and stress distribution were investigated. The obtained results indicate that the magnitude of MVF and consequently the level of hysteresis increases, which leads to the reduction of the modulus of elasticity and the strength of the material and therefore the deflection of SMA beam increases consequently. To validate the proposed formulation, the results were compared with other experimental and numerical results and a good agreement was achieved between outcomes.