Is there a nonstandard principle of virtual power? From balance laws to variational principles

This work is neither technical nor historical but philological: it collates all its sources with an apparatus of comments. Such an approach is also needed for the literature upon the principle of virtual power in Continuum Mechanics. From 2002 onward, a corpus of works by one of the most authoritative members of the Truesdellian school founded theories of plasticity, second-grade materials, and structured fluids upon a “nonstandard” principle of virtual power, stated for every subbody and used to determine tractions and local force balances. Collation answers the title question: that formulation coincides in all five characterizing features with the canon published in 1973 by the leading French mechanician of the same generation, the subbody requirement included. Distribution theory imposes the subbody enunciation: distributions restrict to open subsets only, and the boundary carrying the contact actions of a subbody cannot be seen by every restriction of the whole-body functional; the subbody functionals must be independently postulated. A system of forces is the assignment of a functional to each subbody, a set function determining the stress uniquely. The memoirs of the canon were cataloged in the corpus’s monograph of 2000, 2 years before the introduction of the nonstandard label, the implicit standard being the whole-body statement of the Classical Field Theories , with the stresses accepted a priori. We conclude that there is no nonstandard principle of virtual power, the corpus having compared its version of the principle against a nonstandard notion of the standard.