On the method of virtual power in continuum mechanics

The method of virtual power is generally used to produce balance equations for non-traditional continua such as, for example, 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