Wave propagation in shape memory alloy rods under impulsive loads

Abstract

A dynamic analysis is given of the wave propagation in a polycrystalline shape memory alloy semi-infinite rod subject to an impulsive load described by a rectangular loading function. This is a continuation of the previous study for which the impact load is described by a step loading function, and for which the rod undergoes martensitic phase transformation only. In the presence of unloading, the rod also undergoes reverse transformation from martensite to austenite. A maximum internal dissipation criterion is proposed to select a unique dynamic solution, in which an elastic unloading wave front precedes the reverse transformation wave front. This elastic unloading wave will meet with the forward transformation wave at a later time, leading to a sequence of wave encounters and progressively more complicated profiles of the state variables. The asymptotic behaviour of the solution and the energy dissipation are discussed.