Title: Collisions in shape memory alloys,
Abstract: We present here a model for instantaneous collisions in a solid made of shape
memory alloys (SMA) by means of a predictive theory which is based on the
introduction not only of macroscopic velocities and temperature, but also of
microscopic velocities responsible of the austenite-martensites phase changes.
Assuming time discontinuities for velocities, volume fractions and temperature,
and applying the principles of thermodynamics for non-smooth evolutions
together with constitutive laws typical of SMA, we end up with a system of
nonlinearly coupled elliptic equations for which we prove an existence and
uniqueness result in the 2 and 3 D cases. Finally, we also present numerical
results for a SMA 2D solid subject to an external percussion by an hammer
stroke.