Wave Propagation in a Shape Memory Alloy Bar under an Impulsive Loading

We analyze wave propagation in a semi-infinite shape memory alloy (SMA) bar under a rectangular impulsive loading. Different trilinear up-down-up nominal stress-strain curves for loading and unloading processes are adopted to complete the dynamical system. The chord criterion (equivalent to maximally dissipative kinetics) is employed to single out the unique solution for the impact problem. The interactions among discontinuities (loading/unloading elastic shock waves and phase boundaries) can yield some complicated wave structure. In particular, it is found that the encounter of the unloading elastic shock wave and the loading phase boundary can yield three different wave patterns depending on the level of impact stress, which are different from those for a hardening response studied in the literature. Solutions in the whole temporal and spatial domain are obtained, which reveal interesting wave structures induced by two different levels of impact. Phase transformation regions and tension/compression regions are also determined. The results also suggest that the SMAs can be used for impact-protection purpose effectively.