Vol. 4, No. 2, 2009

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On the method of virtual power in continuum mechanics

Gianpietro Del Piero

Vol. 4 (2009), No. 2, 281–292
Abstract

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
Milestones
Received: 20 December 2007
Accepted: 7 March 2008
Published: 12 April 2009
Authors
Gianpietro Del Piero
Dipartimento di Ingegneria
Università di Ferrara
Via Saragat 1
44100 Ferrara
Italy