Developing a semi-analytical model for thermomechanical response of SMA laminated beams, considering SMA asymmetric behavior

In this study, thermomechanical behavior of a beam reinforced with Shape Memory Alloy (SMA) elements is investigated (an elastic core with upper and bottom SMA layers). The improved Brinson constitutive model is used in order to account for the asymmetric behavior of SMA in tension and compression. Assuming a plane stress model for the beam reinforced with SMA layers, a semi-analytical formulation is proposed. This formulation has two parts: the first part consists of a linear distribution of strain along the cross section and the second part is an iterative numerical procedure to satisfy classical equilibrium equations. For the numerical procedure, bisection method is used. Moreover, the semi-analytical results are compared with a 2D Finite Element (FE) solution. The proposed model is applicable for Euler–Bernoulli beams with any material and geometric features. For example, for a composite beam including both superelastic and shape memory SMA layers the proposed model can be employed. Regarding the results, there is more than 95% agreement between the present numerical solutions and those of 2D FE method. Also, for the numeric examples discussed in this paper, it is shown that considering the asymmetry between the tension and compression behavior of SMA, leads to at least 25% change in the force–displacement plot with respect to the cases when considering symmetric behavior and also, there is 8% (of the width of the structure) shift in the location of the neutral axis from the centerline. In addition, hysteresis inner loops are investigated, using the asymmetric proposed model and compared against 2D FE solution, where results show a good agreement between two solutions.