  We perform a general study of the relic density and LHC constraints on
simplified models where the dark matter coannihilates with a strongly
interacting particle X. In these models, the dark matter depletion is driven by
the self-annihilation of X to pairs of quarks and gluons through the strong
interaction. The phenomenology of these scenarios therefore only depends on the
dark matter mass and the mass splitting between dark matter and X as well as
the quantum numbers of X. In this paper, we consider simplified models where X
can be either a scalar, a fermion or a vector, as well as a color triplet,
sextet or octet. We compute the dark matter relic density constraints taking
into account Sommerfeld corrections and bound state formation. Furthermore, we
examine the restrictions from thermal equilibrium, the lifetime of X and the
current and future LHC bounds on X pair production. All constraints are
comprehensively presented in the mass splitting versus dark matter mass plane.
While the relic density constraints can lead to upper bounds on the dark matter
mass ranging from 2 TeV to more than 10 TeV across our models, the prospective
LHC bounds range from 800 to 1500 GeV. A full coverage of the strongly
coannihilating dark matter parameter space would therefore require hadron
colliders with significantly higher center of mass energies.
