  In this article, we introduce a framework to investigate the growth of
nano-crystallites in a polymer matrix numerically. This framework combines the
Flory theory of entropic elasticity with phase-field approaches commonly used
to model crystal growth. We investigate in particular the growth kinetics of a
crystallite in the presence of topological constraints such as entanglements or
cross-links, and show that depending on the coupling between the topological
constraints and the growth kinetics various structures can be observed:
branched structures looking like spherulites or stable nano-crystallites as
observed in strain-induced crystallization.
