  We propose an explanation for the self-organization towards criticality
observed in martensites during the cyclic process known as `training'. The
scale-free behavior originates from the interplay between the reversible phase
transformation and the concurrent activity of lattice defects. The basis of the
model is a continuous dynamical system on a rugged energy landscape, which in
the quasi-static limit reduces to a sandpile automaton. We reproduce all the
principal observations in thermally driven martensites, including power-law
statistics, hysteresis shakedown, asymmetric signal shapes, and correlated
disorder.
