Asymmetric bending response of shape memory alloy beam with functionally graded porosity

In this study, an innovative semi-analytical model is presented to simulate the bending behavior of a shape memory alloy porous beam throughout loading and unloading cycles. The basis of the proposed method is the improved Brinson model which can capture the asymmetry behaviors of shape memory alloys in tension and compression. The comparison of the semi-analytical solution with two-dimensional finite element analysis results for both symmetric and asymmetric models of a homogeneous shape memory alloy beam is presented for model validation. Afterward, bending analysis of shape memory alloy beams with uniform porosity and functionally grading porosity is studied. For this purpose, first, the bending analysis of a shape memory alloy beam with uniform porosity is investigated to show the effects of porosity coefficient on the free tip deflection and slope. Then, the bending analysis of a shape memory alloy beam with functionally grading porosity is simulated. Reported findings with respect to symmetric and asymmetric models indicate that raising the porosity coefficient brings about an increase in deflection and slope. Also, it highlights the significant difference between the results of the asymmetric and symmetric models. The proposed semi-analytical solution can be utilized as an efficient tool for studying the effects of changing any of the porosity coefficient, the geometry, and material of shape memory alloy beams.