In this study we present the results from realistic N-body modelling of massive star clusters in the Magellanic Clouds. We have computed eight simulations with N∼ 105 particles; six of these were evolved for at least a Hubble time. The aim of this modelling is to examine in detail the possibility of large-scale core expansion in massive star clusters, and search for a viable dynamical origin for the radius–age trend observed for such objects in the Magellanic Clouds. We identify two physical processes which can lead to significant and prolonged cluster core expansion – mass-loss due to rapid stellar evolution in a primordially mass-segregated cluster, and heating due to a retained population of stellar mass black holes, formed in the supernova explosions of the most massive cluster stars. These two processes operate over different time-scales and during different periods of a cluster's life. The former occurs only at early times and cannot drive core expansion for longer than a few hundred Myr, while the latter typically does not begin until several hundred Myr have passed, but can result in core expansion lasting for many Gyr. We investigate the behaviour of each of these expansion mechanisms under different circumstances – in clusters with varying degrees of primordial mass segregation, and in clusters with varying black hole retention fractions. In combination, the two processes can lead to a wide variety of evolutionary paths on the radius–age plane, which fully cover the observed cluster distribution and hence define a dynamical origin for the radius–age trend in the Magellanic Clouds. We discuss in some detail the implications of core expansion for various aspects of globular cluster research, as well as the possibility of observationally inferring the presence of a significant population of stellar mass black holes in a cluster.