Abnormal Buckling of Thin-Walled Bodies with Shape Memory Effects Under Thermally Induced Phase Transitions

Buckling and postbuckling of thin-walled structures made from the Nickel-Titanium shape memory alloy and undergoing non-isothermal direct martensite transitions under varying temperatures are simulated. The once coupled Movchan's model of thermo-elastic shape memory alloy behavior is represented in the incremental formulation for the use within numerical algorithms of nonlinear solid mechanics. The equilibrium state's bifurcation is studied on the background of Lyapunov's stability concept. The physically and geometrically nonlinear solid model allows one to study the martensite phase distribution over the cross-section as well as along the structure during its' buckling and postbuckling deforming. It is shown that the direct martensite transition induced by temperature changes and heterogeneous stress fields in compressed prismatic beams with initial imperfections causes the buckling phenomenon. The obtained results are consistent with the analytical predictions of A.Movchan and L.Silchenko assuming the supplementary phase transform occurring everywhere in accordance with the extended Shenley concept. Thus, the fundamental assumption about decisive contribution of martensite phase transitions in the buckling of thin-walled structures of shape memory alloys is vindicated.