  Many types of mammalian cells exert active contractile forces and
mechanically deform their elastic substrate, to accomplish biological functions
such as cell migration. These substrate deformations provide a mechanism by
which cells can sense other cells, leading to long range mechanical intercell
interactions and possible self organization. Here, we treat cells as noisy
motile particles that exert contractile dipolar stresses on elastic substrates
as they move. By combining this minimal model for the motility of individual
cells with a linear elastic model that accounts for substrate mediated cell
cell interactions, we examine emergent collective states that result from the
interplay of cell motility and long range elastic dipolar interactions. In
particular, we show that particles self assemble into flexible, motile chains
which can cluster to form diverse larger scale compact structures with polar
order. By computing key structural and dynamical metrics, we distinguish
between the collective states at weak and strong elastic interactions, as well
as at low and high motility. We also show how these states are affected by
confinement, an important characteristic of the complex mechanical
microenvironment inhabited by cells. Our model predictions are generally
applicable to active matter with dipolar interactions ranging from biological
cells to synthetic colloids endowed with electric or magnetic dipole moments.
