Dynamic snap-through phenomena in pseudoelastic shape memory alloy arch-beams

This work deals with the dynamic snap-through phenomena in shape memory alloy (SMA) arch-beams taking into account the pseudoelastic effect of SMAs, a type of material nonlinearity, for the first time. For this aim, the Lagoudas formulation is used to model the pseudoelastic effect of SMAs. The SMA arch-beams are modeled employing the Timoshenko beam theory. By assuming the von Karman nonlinear strains, the governing equations of motion are derived while are coupled with the nonlinear phase transformation equations of SMAs. In this regard, the differential quadrature method (DQM) is employed to solve the nonlinear governing equations and the Newmark method is implemented to integrate these equations in the time domain. Meanwhile, the return mapping algorithm along with the Newton–Raphson technique is used to overcome the nonlinearities of the problem. In this work, the Budiansky criterion is employed to detect the dynamic buckling load of the SMA arch-beam. Under the dynamic buckling load, the arch-beams made of elastic materials exhibit multiple subsequent snap-throughs. A very interesting finding in this study is that, the material nonlinearity or pseudoelastic effect of SMAs prevents the subsequent dynamic snap-throughs in the SMA arch-beams, such that after the first snap phenomenon, the response of the system reaches a stable condition. The reason for this fact is the dissipation of energy due to the phase transformation in SMAs. In this regard, some novel results for pinned-pinned and fixed-fixed boundaries for different geometrical parameters have been presented.