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Abstract
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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.
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Keywords
foundations of continuum mechanics,
virtual power, continua with microstructure, materials with
microstructure
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Milestones
Received: 20 December 2007
Accepted: 7 March 2008
Published: 12 April 2009
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