Suspensions of self-propelled bodies generate a unique mechanical stress
owing to their motility that impacts their large-scale collective behavior. For
microswimmers suspended in a fluid with negligible particle inertia, we have
shown that the virial `swim stress' is a useful quantity to understand the
rheology and nonequilibrium behaviors of active soft matter systems. For larger
self-propelled organisms like fish, it is unclear how particle inertia impacts
their stress generation and collective movement. Here, we analyze the effects
of finite particle inertia on the mechanical pressure (or stress) generated by
a suspension of self-propelled bodies. We find that swimmers of all scales
generate a unique `swim stress' and `Reynolds stress' that impacts their
collective motion. We discover that particle inertia plays a similar role as
confinement in overdamped active Brownian systems, where the reduced run length
of the swimmers decreases the swim stress and affects the phase behavior.
Although the swim and Reynolds stresses vary individually with the magnitude of
particle inertia, the sum of the two contributions is independent of particle
inertia. This points to an important concept when computing stresses in
computer simulations of nonequilibrium systems---the Reynolds and the virial
stresses must both be calculated to obtain the overall stress generated by a
system
