The method of virtual power is generally used to produce balance equations for
nontraditional continua such as continua with various types of microstructure. Here I
show that the expression of the internal power can be deduced from that of the
external power using a general invariance requirement due to Noll and a generalized
version of Cauchy’s tetrahedron theorem. In other words, the measures of
deformation and stress, as well as the balance equations, are determined by the
expression chosen for the external power and by the invariance assumptions. A pair
of examples taken from the literature shows that both ingredients are essential for
defining a specific class of continua.
Dedicated to the memory of Paul
Germain
Keywords
foundations of continuum mechanics, virtual power, continua
with microstructure, materials with microstructure
