On the longitudinal impact of two phase transforming bars. Elastic versus a rate-type approach. Part II: The rate-type case

AbstractWe study the propagation of phase transformation fronts induced by the longitudinal impact of two shape memory alloy bars modeled by a general form of a rate-type approach to non-monotone elasticity. We illustrate that such a rate-type law should be seen like a kinetic law for phase transformation. This investigation continues in a comparative way the analysis of the dynamic theory of elastic bar considered in Part I in relation with a viscosity criterion. We focus here on mathematical, thermodynamical and experimental aspects related with the wave structure which accompanies both the forward and reverse transformation. We analyze the propagation of disturbances in a pure phase near and far from their sources, that is the instantaneous waves and the delayed waves as well as the traveling wave solutions and the accompanying dissipation. In the numerical experiments one focuses on the influence of the impact velocity on the way the phase boundary propagates and on the results which can indicate indirectly the existence of a phase transformation like the time of separation, the velocity–time profile at the rear end of the target and the stress history at the impact face