  We derive the stress tensor of a rigid dumbbell by using the virtual work
method. In the virtual work method, we virtually apply a small deformation to
the system, and relate the change of the energy to the work done by the stress
tensor. A rigid dumbbell consists of two particles connected by a rigid bond of
which length is constant (the rigid constraint). The energy of the rigid
dumbbell consists only on the kinetic energy. Also, only the deformations which
do not violate the rigid constraint are allowed. Thus we need the dynamic
equations which is consistent with the rigid constraint to apply the virtual
deformation. We rewrite the dynamic equations for the underdamped SLLOD-type
dynamic equations into the forms which are consistent with the rigid
constraint. Then we apply the virtual deformation to a rigid dumbbell based on
the obtained dynamic equations. We derive the stress tensor for the rigid
dumbbell model from the change of the kinetic energy. Finally, we take the
overdamped limit and derive the stress tensor and the dynamic equation for the
overdamped rigid dumbbell. We show that the Green-Kubo type linear response
formula can be reproduced by combining the stress tensor and the dynamic
equation at the overdamped limit.
