Abstract 

We study the kinetics of phase transformations in solids using the peridynamic formulation of
continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve
spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces.

We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We
show that unlike the classical continuum theory, the peridynamic formulation does not require any
extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the
interface and the thermodynamic driving force acting across it) or the nucleation criterion (the
criterion that determines whether a new phase arises from a single phase). Instead this information is
obtained from inside the theory simply by specifying the inter-particle interaction. We derive a
nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic
relation by analyzing the solutions of impact and release problems, and also directly by viewing phase
boundaries as traveling waves.

We also study the interaction of a phase boundary with an elastic non-transforming inclusion in
two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further,
we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase
boundaries at the edges of the inclusion while the original phase boundary slows down or stops.
Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some
untransformed martensite around the inclusion.

This paper has appeard in the Journal of the Mechanics and Physics of
Solids, 54 (2006) 1811–1842, and is available at doi:10.1016/j.jmps.2006.04.001