On the principle of virtual power for arbitrary parts of a body

Recently, a principle of virtual power has been adopted to model the behavior of materials that involve multiple length scales. In these works, the principle is stated for arbitrary parts of a body and this arbitrariness is used, but not to its fullest extent, to draw conclusions concerning the structure of the theory that results. Here, a theorem and an example application are given to illustrate the restrictive nature of the requirement that it hold for arbitrary parts of a body and to draw attention to the full consequences that result from this requirement. Several key results that have been reported in the recent literature are incomplete, and this incompleteness has lead to superficial conclusions.