Inertia-induced power-law scaling in martensites

Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards apparent criticality remains obscure. Here we argue that the power law structure of intermittent fluctuations can be at least partially interpreted as an effect of inertia. We build on the insight that inertial dynamics, evidenced by acoustic emission, can become an important factor if the underlying mechanical system is only marginally stable. We first illustrate the possibility of inertia-induced \textit{heavy-tailed} avalanche size distributions using a prototypical example of a discrete chain with bi-stable springs. We then explore the effects of inertia in fully realistic two- and three-dimensional continuum models of elastic phase transitions. In particular, we demonstrate that a three-dimensional model can produce not only qualitative but also quantitative agreement with experiment.