Snap buckling of NiTi tubes

The aim of this article is to model and analyze the buckling behaviors of NiTi-based moderately thick shape memory alloy (SMA) tubes with short, intermediate and long lengths. A robust three-dimensional constitutive model is implemented so that it is capable of realistic simulations of anisotropic martensitic transformation, reorientation of martensite variants and asymmetry in tension and compression in the finite-strain regime. The governing equations of equilibrium are derived based on the total Lagrangian description and discretized in a finite element framework. They are then solved using an elastic-predictor inelastic-corrector return mapping algorithm along with iterative Newton–Raphson and Riks techniques to trace the non-linear equilibrium path. Experimental result of a uniaxial tension–compression test performed on an NiTi tube is first simulated in a Gauss point level. It is shown that the present constitutive model replicates well the main features such as martensitic phase transformation in a smooth and gradual manner, strain hysteresis width, pseudo-elasticity and asymmetry in tension and compression. Afterwards, computational assessment of mechanical response of NiTi tubes under axial edge load is carried out and comparisons with available experimental data are made. Effects of radial geometric imperfection and length as well as finite-strain modeling are investigated, and their implications on the buckling behaviors of NiTi moderately thick tubes are put into evidence and conclusions are drawn. It is shown that increasing the length tube reduces the structural resistance so that buckling–unbuckling behavior of short NiTi moderately thick tubes changes to kinking phenomenon in intermediate tubes and finally results in a smooth snap-type buckling in long tubes. Finally, it is concluded that the finite-strain model implementing a displacement/force-controlled method and kinking consideration is able to replicate well the main buckling features observed in the experiments.