Dike intrusions are often associated with surface deformation and propagating swarms of earthquakes. These are understood to be manifestations of the same underlying physical process, although rarely modeled as such. We construct a physics-based model of the 2014 Bárðarbunga dike, by far the best observed large dike (>0.5 km3 ) to date. We constrain the background stress state by the total dike deformation, the time-dependent dike pressure from continuous GPS and the extent of the seismic swarm, and the spatial dependence of frictional properties via the space-time evolution of seismicity. We find that the geodetic and earthquake data can be reconciled with a self-consistent set of parameters. The complex spatial and temporal evolution of the Bárðarbunga seismicity can be explained by dike-induced elastic stress changes on preexisting faults, constrained by observed focal mechanisms. In particular, the model captures the segmentation of seismicity, where only the newest dike segment is seismically active. Our results indicate that many features of the seismicity result from the interplay between time-dependent magma pressure within the dike and stress memory effects. The spatial variability in seismicity requires heterogeneity in frictional properties and/or local initial stresses. Modeling suggests that the dike pressure drops during rapid advances and increases during pauses, which primarily causes the segmentation of the seismicity. Joint analysis of multiple data types could potentially lead to improved, physics-based eruption forecasts.